We present Vibrational Field Dynamics (VFD), a novel theoretical framework that introduces a fundamental resonance structure to spacetime and field interactions. The theory extends the stan-dard model and general relativity through a unified mathematical formalism characterized by resonance functions Rh(ω), which naturally emerge from the theory’s core principles. VFD addresses several outstanding problems in theoretical physics, including quantum gravity unification, dark sector dynamics, and the information paradox in black hole physics. The framework introduces modifications to quantum field theory and gravitational interactions through a resonance based coupling mechanism, leading to specific, experimentally testablepredictions. We derive modified field equations that reduce to known physics in appropriate limits while providing new insights into high energy phenomena, cosmological evolution, and quantum-gravitational effects. Key predictions include modifications to gravitational wavesignatures, quantum interference patterns, and dark sector interactions, all parameterized by experimentally accessible coupling constants. The theory’s mathematical structure maintains consistency with existing observational constraints while offering novel explanations for current anomalies in cosmological and high-energy physics data.

This paper presents a novel perspective on the nature of space and time, arguing for the coexistence of both absolute and relative aspects at the classical level and the existence of only absolute aspects at the quantum level. We propose using various arguments that the static space-in-itself exists as absolute space and the universal objective present moment with an infinitesimal duration continuously exists as absolute time in the universe since its creation until the present, along with the measured space being relative space and the measured time being relative time. We also prove the continuous nature of absolute and relative space, absolute and relative time, and relative spacetime and, thus, challenge all theories that use discrete relative space or discrete relative time or discrete relative spacetime, such as loop quantum gravity and causal set theory, among others. This framework dissolves several fundamental problems: the quantum gravity question by proving its impossibility due to the absence of reference frames at quantum scales, the unified field theory question by proving its impossibility by showing gravity’s classical-only nature, whereas electromagnetic force being present at quantum and classical level both, and the wave-particle duality through establishing universal quantum fields/waves as the sole quantum reality with each of these fields being one singular reality with varying level of intensity at different spatial regions in the universe and with continuous non-deterministic interactions explaining quantum phenomena without randomness while preserving causality and particles being just the 1emergent reality at the classical level. We also disprove string theory and any potential higher spatial dimensional theory using fundamental logic. Thus, this comprehensive framework completes Einstein’s unfinished revolution in understanding space, time, and physical reality at both quantum and classical levels.

A continuation of the Born Reciprocal Relativity Theory (BRRT) program in phase space shows that a natural temperature-dependence of mass occurs after recurring to the Fulling-Davies-Unruh effect. The temperature dependence of the mass $ m ( T ) $ resemblances the energy-scale dependence of mass and other physical parameters in the renormalization (group) program of QFT. It is found in a special case that the effective photon mass is no longer zero, which may have far reaching consequences in the resolution of the dark matter problem. The Fulling-Davies-Unruh effect in a $ D = 1 + 1$-dim spacetime is analyzed entirely from the perspective of BRRT, and we explain how it may be interpreted in terms of a linear superposition of an infinite number of states resulting from the action of the group $ U (1,1) $ on the Lorentz non-invariant vacuum $ | {tilde 0 } angle$ of the relativistic oscillator studied by Bars cite{Bars}.

This paper presents a novel interpretation of black holes within theframework of the Spacetime Superfluid Hypothesis (SSH). We proposethat black holes can be understood as vortex-like structures in a su-perfluid spacetime, offering new perspectives on singularities, Hawkingradiation, and the information paradox. Our model provides a phys-ical basis for black hole phenomena without invoking spacetime sin-gularities, potentially offering new insights into longstanding puzzlesin black hole physics. We derive the fundamental equations governingblack hole vortices in superfluid spacetime, present predictions for ob-servational tests, and discuss the implications for our understandingof gravity and quantum mechanics in extreme condition

My work represents a macroscopic generalization of the Kaluza-Klein theories for quantum systems, concerning the existence of an additional fifth dimension in our space. This allowed Kaluza to unify the descriptions of gravity and electromagnetism within a single mathematical structure. Later, Oskar Klein added a crucial element to Kaluza's theory by proposing that the fifth dimension is compactified into a very small circle with a radius on the order of the Planck length. Due to its minuteness, this dimension remains invisible at ordinary scales. Additionally, I drew upon ideas proposed by Feynman, who suggested using the concept of energy density in space to describe electromagnetic interactions at the quantum level within the framework of Quantum Electrodynamics (QED). This theory helps explain how, at short distances, charge screening and renormalization occur due to interactions with virtual particles in the vacuum.In my work, I attempt to describe the observable effects at the macroscopic level, such as the electric interaction of charges and the gravitational interaction of massive bodies, through an intuitively understandable process of spatial disturbance. This disturbance is first expressed in the disruption of the uniform distribution of spatial density and then in the curvature of the spherically symmetric structure of the disturbance. In formulating my theory at a macroscopic level, which implies a statistical averaging of the processes described by Kaluza, Klein, and Feynman at the quantum level, I was primarily inspired by the ideas proposed by these scientists. I aimed to formalize their mathematical concepts into simple and intuitively understandable postulates, which lead to observable effects in macro-objects. One such effect is the attenuation of the electric field at short distances between charges, similar to the processes occurring at the quantum level. Based on innovative theoretical insights, this work provides yet another alternative confirmation of the Theory of Relativity regarding the equivalence of energy and mass of elementary particles.

In this paper I propose that the 'Hubble expansion' phenomenon is universal and isotropic and countered by space absorption as an activity of central massess. With mass sucking in space on the one hand and space expanding isotropically with the Hubble rate on the other hand, we get a continuous drift of space towards the central mass. We can define a critical distance from the central mass as the distance where the two effects are balanced. The cosmic density parameter is given a different, more local, interpretation because it now devides space into regions where absorption of space is dominant and regions where space creation is dominant. I add to this that at elementary particle level, the space absorption process is quantized and periodic, with the de Broglie internal frequency as the quantized space volume absorption frequency. This then leads to a mass independend quantized volume of space of approximately the size of the largest nuclei. De Broglie's subquantum gas is identified with space that is thus quantized. Nuclei occupy at most one single quantum bubble of space. Inside these quantized space bubbles, we have the physics of the weak and strong nuclear forces. In between quantizes space bubbles we have the physics of wave mechanics and gravity. The same process of quantized space cell absorption by elementary particles lies at the basis of both gravity on the macro level and wave mechanics on the meso level. It also produces inertia in a way that is, conceptually at least, somewhat similar to the Higgs mechanism by which elementary particles of the weak and strong interactions acquire mass. The concept of stochastic drift of quantized bubbles of space is a refined version of earlier 'velocity of space' approaches towards gravity.

Recently we have argued [1] that the noncommutativity of the spacetime coordinates is the answer to the question : Why is area, mass, entropy quantized ? Furthermore, it casts light into a deep interplay among black hole entropy, discrete calculus, number theory, theory of partitions, random matrix theory, fuzzy spheres, ..... We extend our previous construction of Schwarzschild black holes and derive the corrections to the Kerr-Newman temperature and black hole entropy, to all orders, from the discrete mass transitions taken place among different mass states. The mass spectrum for Kerr, Kerr-Newman, and Reissner-Nordstrom black holes is explicitly obtained which reduces to the Schwarzschild case when the angular momentum and charge is set to zero. One of the most salient features in the expansion of the $modified$ temperature $ {cal T } = T + c_1{ T over N } + c_2 { T over N^2 } + ldots $ is that it spells a correspondence between the loop expansion in QFT in powers of $ hbar$, after setting $ hbar leftrightarrow ( 1/ N)$. $ N $ is the principal quantum number labeling the spectrum of mass states and which is given by $ N = l_3 ( l_3 + 2 ) - l_2 ( l_2 + 1) + l_1^2$, with $ l_3 ge l_2 ge | l_1|$ being the quantum numbers associated with the hyper-spherical harmonics of the three-sphere $ S^3$. These results can be extended to higher dimensions. To finalize, we should add that the deviation from a full thermal spectrum and the corrections to the Hawking temperature might be relevant to the solution of the Black Hole Information paradox.

This paper presents a novel Quantum Gravity Theory (QGT) that reinterprets the gravitational field as being derived from the Higgs field within a flat spacetime framework. Unlike General Relativity (GR), which attributes gravity to spacetime curvature, QGT integrates quantum corrections, nonlinear dynamics, and a variable speed of light to describe gravitational phenomena [1]. The theory successfully predicts key cosmic phenomena such as the expansion of the universe [6], gravitational time dilation, and lightdeflection, while addressing discrepancies in observational data, such as the nature of gravitational waves [4]. By calibrating the coupling constant λ using empirical data from cosmological expansion instead of perihelion precession or light deflection, QGT shows potential as a bridge between quantum mechanics and cosmology, offering a new perspective on gravity that does not rely on dark energy or spacetime curvature.

We review a 3d quantum gravity model, which incorporates massive spinning fields into the Euclidean path integral in a Chern-Simons formulation. Fundamental matter as defined in our previous preon model is recapped. Both quantum gravity and the particle model are shown to be derivable from the supersymmetric 3d Chern-Simons action. Forces--Matter unification is achieved.

In this paper, the author first reviews the essential contradictions of general relativity(GR) and quantum mechanics(QM) from the perspective of background manifolds,while pointing out a fundamental principle that both must be satisfied. Schrodinger's cat experiment, Yang's double slit interference experiment, and the ERP paradox are discussed based on this principle. The author proposes to unify GR and QM in a mathematical context by introducing the concept of virtual potential field and virtual mass. A model of black hole is given under the inspiration of this discussion, and a possible explanation for black hole information paradox is offered under this scheme, which may also provide some hints for the mystery of the antimatter. The author analyzes the possible applications of virtual particles to quantum field theory, including the treatment of divergent terms in the quantization of real scalar field and the physical implications of the Pauli-Villars renormalization method, while giving an estimate of the Lamb movement. Finally, the author suggests a plausible approach for the quantization of the gravitational field.

This paper argues for the continuous nature of time, space and spacetime, based on all observers' internal experience of the present moment as having zero duration and all observers internally experiencing always being in the present moment without any divisibility and discontinuity of this present moment and the logical consistency based on the space being the substratum for the existence of time. The implications of this continuity challenge the physical theories proposing discrete structures of space or time or spacetime, such as loop quantum gravity, causal set theory, etc.

It is shown how a Noncommutative spacetime leads to an area, mass and entropy quantization condition which allows to derive the Schwarzschild black hole entropy A/4G, the logarithmic corrections, and further corrections, from the discrete mass transitions taken place among different mass states in D = 4. The higher dimensional generalization of the results in D = 4 follow. The discretization of the entropy-mass relation S = S ( M ) leads to an entropy quantization of the form S = S ( M_n) = n, and such that one may always assign n ``bits" to the discrete entropy, and in doing so, make contact with quantum information. The physical applications of mass quantization, like the counting of states contributing to the black hole entropy, black hole evaporation, and the direct connection to the black holes-string correspondence via the asymptotic behavior of the number of partitions of integers, follows. To conclude, it is shown how the recent large N Matrix model (fuzzy sphere) leads to very similar results for the black hole entropy as the physical model described in this work and which is based on the discrete mass transitions originating from the noncommutativity of the spacetime coordinates.

This paper elaborates upon and further develops https://vixra.org/abs/2402.0149, which proposed a novel realist framework for making sense of standard quantum theory. The framework is said to be "realist" in that it provides a complete observerless picture of quantum state ontology and dynamics, in conjunction with a mechanistic account of measurement processes, that answers basic questions of what, where, when, and how.The framework embodies a general quantum ontology consisting of two entities, called W-state and P-state, that respectively account for the wave- and particle-like aspects of quantum systems. W-state is a generalization of the wavefunction, but has ontic stature and is defined on the joint time-frequency domain. It constitutes a non-classical local reality, consisting of superpositions of quantum waves writ small. P-state is a non-local hidden variable that constrains the probability distributions governing deferred measurement outcomes, such as in the Einstein-Podolsky-Rosen (EPR) thought experiment. This paper presents a full solution of the core measurement problem, which pertains to the global coordination within quantum systems required to bring about wavefunction collapse in causal fashion consistent with special relativity.The framework has a tri-partite structure, consisting of Q-1 (unitary evolution of W-state), Q-2 (measurement-like events that continually occur in the absence of observer intervention), and Q-3 (measurement events in experimental settings). Traditional quantum theory draws a sharp dichotomy between Q-1 and Q-3. The new framework incorporates physical wavefunction collapse, which is held to be a real physical process and ubiquitous feature of nature in the quantum realm, as Q-2, which fills the gap between Q-1 and Q-3.Quantum systems have a built-in dynamic proper time, which is relativistically invariant and plays a central role in the measurement problem solution. The framework is thus background-independent, a key requirement for making quantum theory compatible with general relativity. Quantum gravity is introduced as Q-4 atop the tri-partite foundation.

Since 1905 physics lost his soul, the intimate contact with the reality and rationality. The corepillars of modern physics, the general relativity, the special relativity and the quantum mechanicscontains some basics but fundamentals errors with profound consequences.Neoclassical physics is a completion of classical Newtonian physics with a new classification ofmatter according to the capacity to generate a gravitational interaction: structured matter andunstructured matter. Its formalism is based on the mathematical apparatus of classical physicswith the integration of some elements of quantum mechanics and relativity.This article will show that with a modification of the Newton law, by a modification of gravitational potential, we will find a relation equivalent to that of the field equation in general relativity. Through outthis and with a minimal modification of Maxwell laws and Lorentz transformations, neoclassicalphysics rediscovers all the theoretical and empirical results of modernity but with a completely different interpretation and use, all within the realistic, rational, local and deterministic framework ofclassicism.We demonstrate the Newtonian limit, the advancement of Mercury’s perihelion, the deviation ofthe light ray in gravitational fields with the phenomenon of gravitational lensing, the slowing downof measured time, the red-shift of light, the light ring for black holes, as well as the quantum natureof neoclassical gravitation with the expression of it’s quantum form and Einsteinian limit.

This theory is an attempt to unify general relativity and quantum mechanics by integrating:Einstein Field Equation for Gravitational Wave in General Relativity; Schrödinger Field Equation for Quantum Wave in Quantum Mechanics; Maxwell Field Equation for Photon Wave in Electromagnetism;Hawking Field Equation for Radiation Wave in Black Holes; and Heisenberg Uncertainty Principle for Minimal Action (or Entropy). This unification leads to the potential prediction of Graviton (mass, charge, and spin).

This paper presents a comprehensive framework that integrates quantum gravitational corrections derived from string theory, loop quantum gravity (LQG), and non-commutative geometry into the Einstein-Hilbert action. By combining these three approaches, we derive modified field equations that encapsulate quantum effects in spacetime curvature. The unified corrections are formulated as higher-order curvature terms and modifications arising from the discrete structure of spacetime and non-commutative coordinates. Our results demonstrate that these corrections can resolve classical singularities, leading to a finite Ricci scalar even at small radii, thus providing a non-singular description of black hole interiors. Additionally, the framework predicts alterations in the effective potential near black holes, which could manifest as observable deviations in gravitational wave signals and other astrophysical phenomena. This work not only bridges the gap between general relativity and quantum mechanics but also opens new avenues for both theoretical exploration and observational verification of quantum gravitational effects.

We revisit the nonlinear Klein-Gordon-like equation that was proposed by us which capture how quantum mechanical probability densities curve spacetime, and find an exact solution that may appear to be ``trivial" but with important physical implications related to the physics of frozen stars and with Mach's principle. The nonlinear Klein-Gordon-like equation is essentially the static spherically symmetric relativistic analog of the Newton-Schr"{o}dinger equation. We finalize by studying the higher dimensional generalizations of the nonlinear Klein-Gordon-like equation and examine the relativistic Bohm-Poisson equation as yet another equation capturing the interplay between quantum mechanical probability densities and gravity.

For a long time scientists try to find methods to combine Gravity and standard model together. By calculate Einstein tensor $G_{ab}$, this article reach a solution with a form can help Gravity take part in particles' interaction like gauge transform. Different with gauge transform, this transform is not unitary. This transform can be linked in parallel or in series.

In this paper was proved (i) the equivalence of Dirac equation for mass $mathsf{m}$ with two entangled Proca fields of mass $mathsf{2m}$ and (ii) is proposed an equation and (iii) an 12-dimensional Lie algebra for the entangled spin fields.

The first string theory was a purely 26-dimensional bosonic theory. He did not implement fermions. But there is a notable empirical fact that seems to indicate that these twenty-six dimensions could refer to the number of elementary particles of the standard model on the energy scale of the Higgs vacuum. Or maybe that there really are 26 dimensions, 22of them compacted into circles. Perhaps there is some ingredient that can convert the original 26-dimensional purely bosonic string theory intoa string theory with bosons and fermions. A mass that could be either the scale of the unification energy or even the mass of gravitino, and even that of the magnetic monopole. We do not know. In this work we obtainthe value of a mass in the way indicated in the title of this article. The Gaussian system of units is used to obtain the dimensions of the electric charge as a function of mass, length and time.

Following the path of our previous articles on the masses of charged leptons and quarks, in this paper we derive in a theoretical way the Weinberg angle and in a heuristic-empirical way the angles of the mixing matrices of quarks and neutrinos.Except for the CP violation angle of the neutrino mixing matrix which has a large indeterminacy.

The time-neutral metric is introduced and the time-neutral exterior Schwarzschild metric is con- verted to polynomial form in r and total mass M. The polynomials are found to be cubic with no constant term, which allows the two non-zero roots of each to be extracted from the reduced quadratic form.

Physical action is a spacetime bivector. Based on this single assumption, this paper argues that spacetime itself is responsible for much of physics. The properties of its elements and their derivatives, especially the transformations of special relativity, allow us to successively derive and confirm major empirically found laws and equations. We exemplary derive equations for electromagnetism including: Biot-Savart Law, Electrostatic Force, Lorentz Force, Maxwell's Equations including charges, and also constants like the fine-structure constant, electric permittivity, and even additional terms that are related to spin. In strict analogy, we gain very similar equations for gravitation which, e.g., include Poisson's equation for gravity. A further derivation of these equations of gravitation leads to field equations which are comparable to the field equations of general relativity. Electromagnetism and gravitation unite into one set of equations. The fact that bivectors can be written as wave equations also unify classical physics with wave mechanics.

This empirical heuristic work on the masses of quarks is a continuation of our previous work on the masses of electrically charged leptons.Onceagain the first four non-trivial zeros of the Riemann zeta function appear very clearly. Parameters from the standard model are also used.

We validly ignore even prime number 2. Based on all arbitrarily large number of even prime gaps 2, 4, 6, 8, 10...; the complete set and its derived subsets of Odd Primes fully comply with Prime number theorem for Arithmetic Progressions. With this condition being satisfied by all Odd Primes, we argue that Modified Polignac's and Twin prime conjectures are proven to be true when these conjectures are treated as Incompletely Predictable Problems. In so doing [and with Riemann hypothesis being a special case], this action also support the generalized Riemann hypothesis formulated for Dirichlet L-function. By broadly applying Hodge conjecture, Grothendieck period conjecture and Pi-Circle conjecture to Dirichlet eta function (which acts as proxy function for Riemann zeta function), Riemann hypothesis is separately proven to be true when this hypothesis is treated as Incompletely Predictable Problem. We highlight crucial connections between these Incompletely Predictable Problems in Number theory and Quantum field theory.

In this work the connection of the non-trivial zeros of the Riemann zeta function and a unification theory appears again. From this hypothetical theory yet to be developed, we obtain equations that connect these nontrivaial zeros with the masses of the electron, tau and muon leptons. In this case the imaginary parts of the second, third and fourth non-trivial zeros are used.

In a series of 4 papers an approach to a unified physics is presented. In part 1 the foundationis given. In part 2 and 3 particle and gravitational physics are derived. In this 4th part openquestions of actual physics will be answered based on new interpretations becoming possibleby the approach.

In a series of 4 papers an approach to a unified physics is presented. In part 1 the founda-tion of such an approach is given. In part 2 it was shown how particle physics follows. Inthis 3rd part gravitational physics will be derived. In part 4 open fundamental questionsof actual physics are answered and the concept of a new cosmology is introduced.

Modern physics is no longer comprehensible to most people. This book explores the question of whether it is possible to develop a simpler and more intuitive physics. For this purpose, many ignored and overlooked physics relations are presented, which cannot be found in any textbook. These relations allow to develop a more holistic physics, which also builds a bridge to information theory and philosophy. Specifically, the book investigates, among other things, whether space consists of a structure of smallest elements, whether our universe is fractal, i.e. self-similar, whether we live in a black hole, what hidden commonalities there are in the fundamental forces, whether fundamental particles and hydrogen can be meaningfully described without quantum physics, whether black holes and fundamental particles are related, whether the formalism of special relativity really makes sense, whether particle spin can be explained classically, how gravity and quantum physics might be brought together and what the Sommerfeld constant is all about. To shed light on these questions, also parts of the works of Horst Thieme, Nassim Haramein, Dr. Randell Mills and Erik Verlinde are presented.

In a series of 4 papers an approach to a unified physics is presented. In part 1 the foundation of such an approach is given. Here in part 2 it will be shown how particle physics follows. In part 3 gravitational physics will be derived. In part 4 open fundamental questions of actual physics are answered and the concept of a new cosmology is introduced.

Maxwell wrote that he wanted to "leaven" his Treatise on Electromagnetism with Quaternions. Maxwell died before doing this. Silberstein and Conway accomplished this partially.This presentation claims the Lorentz condition field is the gravitational potential. Resulting in a Gravitic-Electromagnetic unification.

As in spite to intense search at present apparently there is no approach leading to a theory including the standard model of particle physics and general relativity, it is discussed whether such a theory is possible at all. In the following is shown that a ToE is possible if the either/or condition of current unification theories for background-dependent or -independent is replaced by a both/and. In this part 1, the foundation of such a theory is presented. In the following parts 2 and 3 particle and gravitational physics are derived from this foundation and in part 4 fundamental open fundamental questions of actual physics are answered by a new interpretation of physical quantities and an outline of a new cosmology is given.

Recently we have shown how the Schwarzschild Black Hole Entropy in all dimensions emerges from truly point mass sources at r = 0 due to a non-vanishing scalar curvature R involving the Dirac delta distribution in the computation of the Euclidean Einstein-Hilbert action. As usual, it is required to take the inverse Hawking temperature beta as the length of the circle S^1_beta obtained from a compactification of the Euclidean time in thermal field theory which results after a Wick rotation, i t = tau, to imaginary time. In this work we extend our novel procedure to evaluate both the Reissner-Nordstrom and Kerr-Newman black hole entropy from truly charge spinning point mass sources.

It is explicitly shown how the Schwarzschild Black Hole Entropy (in all dimensions) emerges from truly point mass sources at r = 0 due to a non-vanishing scalar curvature involving the Dirac delta distribution. It is the density and anisotropic pressure components associated with the point mass delta function source at the origin r = 0 which furnish the Schwarzschild black hole entropy in all dimensions $ D ge 4$ after evaluating the Euclidean Einstein-Hilbert action. As usual, it is required to take the inverse Hawking temperature $beta_H$ as the length of the circle $S^1_beta$ obtained from a compactification of the Euclidean time in thermal field theory which results after a Wick rotation, $ i t = tau $, to imaginary time. The appealing and salient result is that there is $no$ need to introduce the Gibbons-Hawking-York boundary term in order to arrive at the black hole entropy because in our case one has that $ {cal R } ot= 0$. Furthermore, there is no need to introduce a complex integration contour to $avoid$ the singularity as shown by Gibbons and Hawking. On the contrary, the source of the black hole entropy stems entirely from the scalar curvature $singularity$ at the origin $ r = 0$. We conclude by explaining how to generalize our construction to the Kerr-Newman metric by exploiting the Newman-Janis algorithm. The physical implications of this finding warrants further investigation since it suggests a profound connection between the notion of gravitational entropy and spacetime singularities.

A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.

In this paper, I tried to provide an overview of how various quantum gravity approachesprompt us to reconsider our understanding of space and time. The primary focus hasbeen on two prominent contenders: string theory and loop quantum gravity. However,it’s important to bear in mind that these theories remain unverified and lack a universallyaccepted consensus.As we navigate through these ideas, it becomes evident that our conventional notionsof space and time might necessitate a fundamental shift. The very fabric of spacetimecould reveal intricacies that challenge our prior assumptions. Moreover, our explorationwill encompass diverse viewpoints on the nature of time within the realm of quantumgravity.

A brief introduction of the Extended Relativity Theory in Clifford Spaces (C-space) paves the way to the explicit construction of the generalized relativistic transformations of the Clifford multivector-valued coordinates in C-spaces. The most general transformations furnish a full mixing of the grades of the multivector-valued coordinates. The transformations of the multivector-valued momenta follow leading to an invariant generalized mass M in C-spaces which differs from m. No longer the proper mass appearing in the relativistic dispersion relation E^2 - p^2 = m^2 remains invariant under the generalized relativistic transformations. It is argued how this finding might shed some light into the cosmological constant problem, dark energy, and dark matter. We finalize with some concluding remarks about extending these transformations to phase spaces and about Born reciprocal relativity. An appendix is included with the most general (anti) commutators of the Clifford algebra multivector generators.

The purpose of this article is to outline a framework of concepts and principles to combine quantum mechanics and general relativity so that time and measurement (reduction) are present as integral parts of the basic foundations. First, the problem of time in quantum gravity and the measurement problem in quantum mechanics are briefly reviewed and the popular proposals to tackle these two problems are briefly discussed. Next, on the already known foundations of quantum mechanics, a framework of principles of dynamics is built: 1) Self-Time Evolution - Newtons first law is reinterpreted to define time, 2) Local Measurement by Local Reduction - Quantum diffusion theory is adapted, and 3) Global Evolution by Global Reduction. Ideas on how to apply the framework to study quantum general relativistic physics are discussed. Further, more general and modified forms of some of these principles are also discussed. The theoretical elements in the framework to be made concrete by further theoretical and experimental investigations are listed. Revision information is included.

Developing Planck scale physics requires addressing problem of time, quantum reduction, determinism and continuum limit. In this article on the already known foundations of quantum mechanics, a set of proposals of dynamics is built on fully constrained discrete models: 1) Self- Evolution - Flow of time in the phase space in a single point system, 2) Local Measurement by Local Reduction through quantum diffusion theory, quantum diffusion equation is rederived with different assumptions, 3) Evolution of a multipoint discrete manifold of Systems through a foliation chosen dynamically, and 4) Continuum limit, and determinism are enforced by adding terms and averaging to the action. The proposals are applied to the various physical scenarios such as: 1) Minisuperspace reduced cosmology of isotropic and homogenous universe with scalar field, 2) Expanding universe with perturbation, and 3) Newtonian Universe. Ways to experimentally test the theory is discussed.

In this paper we discuss quantum gravity framework 3.0, where we discuss relative time formulations. Applications of relative time formulations are discussed. The conventional Hamiltonian of bulk matter is derived from quantum gravity Hamiltonian. The derivation of Hamiltonians in the contexts of fields is briefly discussed.

In this paper I give a major update of quantum gravity framework project. The heuristic conceptual framework proposed in previous versions is expanded to include structure formation and consciousness in the universe. A Path Integral version of decoherence in curved space-time is introduced as major update. Then we discuss the philosophical insights into structure formation in the universe and consciousness. We introduce various mathematical concepts to describe structure formation in the universe and consciousness.

We compare, following Pati, global symmetries our topological supersymmetric preon model with the heterotic E_8 x E_8 string theory. We include Pati's supergravity based preon model in this work and compare the preon interactions of his model to ours. Based on preon-string symmetry comparison and preon phenomenological results we conclude that the fundamental particles are likely preons rather than standard model particles.

This hypothesis will present a possible extension of Einstein's field equations cite{1}cite{2}cite{3}cite{4} which reduces to his field equation by contractions. Basic concepts such as the description of the inertial system or the definition of a physical observer are discussed. The field equation predicts the existence of exactly four-dimensional space-time, as only four-dimensional space-time has an equal number of unknowns for each term of the equation. The equation itself can be written in two mixed and fully covariant forms:begin{gather}R_{mu sigma u}^ho-frac{1}{2}R_{sigmakappa}g^{kappa ho}g_{mu u}=kappa T_{mu kappa}g^{kappa ho} g_{sigma u}R_{phimu sigma u}-frac{1}{2}R_{sigmaphi} g_{mu u}=kappa T_{mu phi} g_{sigma u }end{gather}This model relates the field of matter to the curvature of space-time in a direct way, if matter is not present at a given point in space, it is simply flat space-time, which makes it a requirement that the momentum energy tensor does not zero in the presence of space-time curvature. In this work, I do not give the exact solutions of the equations, only their derivation and their form in a particular case. Field equation can be reduced to statement about equality between energy momentum tensor and Ricci tensor:begin{gather}R_{mu u} =-2 kappa T_{mu u }end{gather}I will also present a possible way to quantize field equations using complex space-time. This gives the quantum field equation which I can write asbegin{gather}left(R_{phimu sigma u}ight) ^dagger R_{phimu sigma u} = kappa left(R_{phimu sigma u}ight) ^dagger left(kappa T_{mu phi} g_{sigma u }+frac{1}{2}R_{sigmaphi} g_{mu u} ight) end{gather}This equation uses a special complex space-time and generates real invariants by using complex conjugates and transpositions. This removes it from singularity field theory as only normalizable fields that do not possess any kind of infinity are a consequence of this normalization.

We investigate the traversable wormholes in (2 + 1) dimensions in the context of Gravity’s Rainbow which may be one of the approaches to quantum gravity. The cases in the presence of cosmological constant and Casimir energy are studied.

This paper investigates the potential connection between Fermat's Last Theorem and quantum gravity, aiming to bridge the gap between seemingly unrelated fields of mathematics and physics. Fermat's Last Theorem, formulated by Pierre de Fermat in the 17th century, states that no non-trivial solutions exist for the equation $x^n + y^n = z^n$, where n > 2 and x, y, z are integers. Its proof was established by Andrew Wiles in 1995. On the other hand, quantum gravity seeks to unify general relativity and quantum mechanics, describing gravity as a curvature of spacetime and the fundamental particles and forces that constitute the universe, respectively.

Nature can be understood as a set of rational numbers, Q. This is to be distinguished from how we see the world, a 3-dimensional space with time. Observations and Physics is the subset Q⁺. As described in the general relativity, 10 independent equations are required. The micro world also requires these ten parameters in quanta. This allows the description and simulation of nature as a polynomial of ten parameters P(2) Imagining a space with revolutions of 2π provides the basis for polynomials at P(2π). E.g.m_neutron / m_e=(2π)⁴ +(2π)³+(2π)²-(2π)¹-(2π)⁰-(2π)^-1+2(2π)^-2+2(2π)^-4-2(2π)^-6 +6(2π)^-8 = 1838.6836611 measured: 1838.68366173(89) m_eThe charge operator for all particles is:C = -π+2π^-1- π^-3+2π^-5-π^-7+π^-9- π^-12 Together with the neutron mass, the result for the proton is:m_proton=m_neutron + C m_e= 1836.15267363 m_eFor an observer and two objects, from the torque and angular momentum alone, a common constant of h, G, and c can be derived, giving a ratio of meters and seconds:h G c⁵s⁸ /m¹⁰ √ (π⁴ -π² -1/π-1/π³) = 1.00000 Fine structure constant: 1/α= π ⁴+ π ³+ π <sup>2</sup >-1- π^-1 + π^-2-π^-3 + π^-7 - π^-9- 2π^-10-2π^-11-2π^-12 = 137.035999107The ratios of energies are raw natural data. The length and time are derived values. The calculations go beyond quantum theory and general relativity. E.g.2 π c m day = (Earth's diameter) <sup>2</sup This formula provides the equatorial radius of the earth with an accuracy of 489 m. From the details of the radius and rotation of the sun, the radii and, orbits can be calculated using polynomials P(2 π) and orbital times in the planetary system with P(8). E.g.R_Mond/(R_Erde + R_Mond) = 2^3/(2 π) rel. Fehler = 1,0001$Merkur:r_Apoapsis = 696342 km sqrt((2 π)^5 / 2 - (2 π)^4 /2 + (2 π)^3) = 46006512 km rel. Fehler = 1,0001 r<sub>Periapsis /= 696342 km sqrt(2 π)^5 - 0*(2 π)^4 + (2 π) ^3) = 69775692 km rel. Fehler = 1,0005 r_Venus / r_Merkur = 6123,80 / 2448,57 = 2,5009

We explore the construction of a generalized Dirac equation via the introduction of the notion of Clifford-valued actions, and which was inspired by the work of [1],[2] on the De Donder-Weyl theory formulation of field theory. Crucial in this construction is the evaluation of the $exponentials$ of $multivectors$ associated with Clifford (hypercomplex) analysis. Exact $matrix$ solutions (instead of spinors) of the generalized Dirac equation in $ D = 2,3$ spacetime dimensions were found. This formalism can be extended to curved spacetime backgrounds like it happens with the Schroedinger-Dirac equation. We conclude by proposing a wave-functional equation governing the quantum dynamics of branes living in $ C$-spaces (Clifford spaces), and which is based on the De Donder-Weyl Hamiltonian formulation of field theory.

Since 1905, physics has lost its soul, the intimate contact with reality and reason.The modern era has brought a revolution, a profound change in the representationswe have of the world. But the old classical Newtonian physics is resisting, it hasnot yet said its last word. Throughout this article, we will show that it provides anelegant, clear and precise answer to current questions in physics. Despite appearances,it remains consistent with all the empirical, experimental data that it can explain whilemaintaining a requirement for realism and rationality.

The idea of using the gauge theory paradigm of the SM to couple Quark-Lepton Model of matter and fields to Space-Time, as an emergent structure, is suggested. The color QCD quark fields, as SU(2)-connections of EM type, allows to define an adapted Space-Time metric compatible with the SU(3)-symmetry. It uses the double role of EM U(1)-connection, with the electric charge of the electron as a 4th color T, aside the RGB quark colors. The Quantum Flavor-Dynamics (Weak Force) corresponds to the break of symmetry due to finite subgroups of symmetry of SU(2), of Platonic type, and plays the role of a theory of transitions of states defined by principal quantum number in 3D, that we call "generation", similar to the case of electron transitions in an atom (2D finite subgroups). Gravity is a nuclear spin-spin dependent interaction, resulting from the fractional electric charge of quarks, as U(1)-components of the quark fields. This allows to derive Newtonian gravity as an emergent force, always attractive, by averaging over quark spin directions, providing a solution to the Hierarchy Problem. The compatibility between the fiber structure (SM Gauge Theory) and base connections (Space-Time and EM) is conjectured to allow in principle to relate the SM and General Relativity. This approach provides a unified approach to the four fundamental interactions. Several other remarks are included, e.g. regarding the relation between the emergent Space-Time approach and String Theory, GUTs, TOEs and Quantum Gravity.

We investigate the equation of motion for the throat of wormhole in three dimen-sions , both classically and quantum mechanically. Minisuperspace model is applied tothe latter case. Our main purpose is to treat the motion of the throat in the same wayas the wave function of the universe by Hartle-Hawking. The resulting wave functionmay have the Yukawa potential like solution. In this article some part is preliminary.u20021

All N = 4 conformal supergravities in four space-time dimensions are constructed. These are theonly N = 4 supergravity theories whose actions are invariant under off-shell supersymmetry. Theyare encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalarfields that parametrize an SU(1, 1)/U(1) coset space. When this function equals a constantthe Lagrangian is invariant under continuous SU(1, 1) transformations. Based on the knownnon-linear transformation rules of the Weyl multiplet fields, the action of N = 4 conformalsupergravity is constructed up to terms quadratic in the fermion fields. The bosonic sectorcorrects a recent result in the literature. The construction of these higher-derivative invariantsalso opens the door to various applications for non-conformal theories.

After a brief introduction of Born's reciprocal relativity theory is presented, we review the construction of the deformed Quaplectic group that is given by the semi-direct product of U (1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative fiber coordinates and momenta $ [ X_a, X_b ] ot= 0$; $[ P_a, P_b ] ot=0$. This construction leads to more general algebras given by a two-parameter family of deformations of the Quaplectic algebra, and to further algebraicextensions involving antisymmetric tensor coordinates and momenta of higher ranks $ [ X_{a_1 a_2 cdots a_n}, X_{b_1 b_2 cdots b_n} ] ot= 0$; $[ P_{a_1 a_2 cdots a_n}, P_{b_1 b_2 cdots b_n} ] ot=0$. We continue by examining algebraic extensions of the Yang algebra in extended noncommutative phase spaces and compare them with the above extensions of the deformed Quaplectic algebra. A solution is found for the exact analytical mapping of the non-commuting $ x^mu, p^mu$ operator variables (associated to an $8D$ curved phase space) to the canonical $ Y^A, Pi^A$ operator variables of a flat $12D$ phase space. We explore the geometrical implications of this mapping which provides, in the $classical$ limit, with the embedding functions $ Y^A (x,p), Pi^A (x,p) $ of an $8D$ curved phase space into a flat $12D$ phase space background. The latter embedding functions determine the functional forms of the base spacetime metric $ g_{mu u} (x,p) $, the fiber metric of the vertical space $h^{ab}(x,p)$, and the nonlinear connection $N_{a mu} (x,p) $ associated with the $8D$ cotangent space of the $4D$ spacetime. Consequently, one has found a direct link between noncommutative curved phase spaces in lower dimensions to commutative flat phase spaces in higher dimensions.

The scientific article reviews some properties of the low-energy effective actions for consistentsupergravity models. We summarize the current state of knowledge regarding quantum gravitytheories with minimal supersymmetry. We provide an elegant extension of the theory and give adeffinitions of the anomaly-free models in advanced supergravity constructions. The deep relationbetween anomalies and inconsistency is emphasized in this research. The conditions for anomalycancellation in these supergravity theories typically constitute determined types of equations.For completeness of theoretical framework, we are including anomaly-free models, which areconsistent supergravity theories.

The two discrete generators of the full Lorentz group $O(1,3)$ in $4D$ spacetime are typically chosen to be parity inversion symmetry $P$ and time reversal symmetry $T$, which are responsible for the four topologically separate components of $O(1,3)$. Under general considerations of quantum field theory (QFT) with internal degrees of freedom, mirror symmetry is a natural extension of $P$, while $CP$ symmetry resembles $T$ in spacetime. In particular, mirror symmetry is critical as it doubles the full Dirac fermion representation in QFT and essentially introduces a new sector of mirror particles. Its close connection to T-duality and Calabi-Yau mirror symmetry in string theory is clarified. Extension beyond the Standard model can then be constructed using both left- and right-handed heterotic strings guided by mirror symmetry. Many important implications such as supersymmetry, chiral anomalies, topological transitions, Higgs, neutrinos, and dark energy, are discussed.

In this work, the deep relationship between the monster group and the standard model is once again manifested. This was already manifested in the calculation of the entropy of black holes by proving the E. Witten's conjecture. Some parameters obtained are the mass of the Higgs boson, the value of the Higgs vacuum, the Fine-structure constant for zero momentum, and the entropy between the Planck mass and the mass of the electron. Despite being purely empirical equations, their logical consistency is based on the exclusive use of dimensionless parameters of the standard model. This makes us think about its relevance and not coincidence. The dimension of the monster group, 196883 and its prime divisors,47,59 and 71; are the basis of these equationsWe also think that the monster group plays an essential role in a theory of quantum gravity and even a theory of everything. It is even possiblethat the 26 exceptional groups are also involved.

We present the deep connections among (Anti) de Sitter geometry, complex conformal gravity-Maxwell theory, and grand unification, from a gauge theory of gravity based on the complex Clifford algebra Cl(4,C). Some desirable results are found, like a plausible cancellation mechanism of the cosmological constant involving an algebraic constraint between e^a_mu, b^a_mu (the real and imaginary parts of the complex vierbein).

This article try to unified the four basic forces by Maxwell equations, the only experimental theory. Self-consistent Maxwell equations with the e-current coming from matter current is proposed, and is solved to electrons and the structures of particles and atomic nucleus. The static properties and decay are reasoned, all meet experimental data. The equation of general relativity sheerly with electromagnetic field is discussed as the base of this theory. In the end the conformation elementarily between this theory and QED and weak theory is discussed.

In 2007, E. Witten suggested that AdS/CFT correspondence yields a duality between pure quantum gravity in (2+1)-dimensional anti de Sitter space and extremal holomorphic CFTs. Pure gravity in 2+1 dimensions has no local degrees of freedom, but when the cosmological constant is negative, there is nontrivial content in the theory, due to the existence of BTZ black hole solutions. Extremal CFTs, introduced by G. Höhn, are distinguished by a lack of Virasoro primary elds in low energy, and the moonshine module is one example. Part of Witten's proposal is that Virasoro primary elds are dual to black-hole-creating operators, and as a consistency check, he found that in the large-mass limit, the Bekenstein-Hawking semiclassical entropy estimate for a given black hole mass agrees with the logarithm of the corresponding Virasoro primary multiplicity in the moonshine module. In the low-mass regime, there is a small quantum correction to the entropy, e.g., the lowest energy primary elds yield In(196883) ~ 12.19, while the BekensteinHawking estimate gives 4π ∼ 12.57.

In this paper, I aim to describe a system of interconnected energy models. These models produce inferences that may enhance our understanding of classical and quantum mechanics. From the formulated models, an empirical test is derived to validate the proposed light projection hypothesis. It is understood that a chasm exists between our classical understanding of relativity and the subatomic descriptions of quantum mechanics. Many theories provide solutions to this discrepancy: from superstrings to loop quantum gravity and other numerous paradigms, each with their significant contributions to furthering our knowledge of theoretical physics. The system of models I present provides a foundation for reframing the underlying assumptions of special relativity and an alternate description of quantum activity. By simplifying our understanding of time, we are able to shift to homogeneous coordinates as a viable basis. From homogeneous coordinates, we can create a spatial framework of reality. The spatial framework allows us to hypothesize the function of black holes and discern the projections of higher dimensions of light. The projections of light hint toward a cosmic camera obscura that a pinhole camera matrix can model. We can then view the entire structure through a different lens and relate the layers of light projections to a Deep Restricted Boltzmann Network (DRBN) representation of quantum information.

We begin with a review of the basics of the Yang algebra of noncommutative phase spaces and Born Reciprocal Relativity. A solution is provided for the exact analytical mapping of the non-commuting $ x^mu, p^mu$ operator variables (associated to an $8D$ curved phase space) to the canonical $ Y^A, Pi^A$ operator variables of a flat $12D$ phase space. We explore the geometrical implications of this mapping which provides, in the $classical$ limit, with the embedding functions $ Y^A (x,p), Pi^A (x,p) $ of an $8D$ curved phase space into a flat $12D$ phase space background. The latter embedding functions determine the functional forms of the base spacetime metric $ g_{mu u} (x,p) $, the fiber metric of the vertical space $h^{ab}(x,p)$, and the nonlinear connection $N_{a mu} (x,p) $ associated with the $8D$ cotangent space of the $4D$ spacetime. A review of the mathematical tools behind curved phase spaces, Lagrange-Finsler, and Hamilton-Cartan geometries follows. This is necessary in order to answer the key question of whether or not the solutions found for $ g_{mu u} , h^{ab}, N_{a mu}$ as a result of the embedding, also solve the generalized gravitational vacuum field equations in the $8D$ cotangent space. We finalize with an Appendix with the key calculations involved in solving the exact analytical mapping of the $ x^mu, p^mu$ operator variables to the canonical $ Y^A, Pi^A$ operator ones.

[In] viXra:2201.0082[,] I put forward a method to resolve the contradiction between the existence of Planck units (length, time, mass) and Special Relativity (length contraction, time dilation, relativistic mass). In this note, [], I present the final solution, but postpone the derivation and implications to a detailed future treatment.

Starting with a brief review of our prior construction of $n$-ary algebras in noncommutative Clifford spaces, we proceed to construct in full detail the Clifford-Yang algebra which is an extension of the Yang algebra in noncommutative phase spaces. The Clifford-Yang algebra allows to write down the commutators of the $noncommutative$ polyvector-valued coordinates and momenta and which are compatible with the Jacobi identities, the Weyl-Heisenberg algebra, and paves the way for a formulation of Quantum Mechanics in Noncommutative Clifford spaces. We continue with a detail study of the isotropic $3D$ quantum oscillator in $noncommutative$ spaces and find the energy eigenvalues and eigenfunctions. These findings differ considerably from the ordinary quantum oscillator in commutative spaces. We find that QM in noncommutative spaces leads to very different solutions, eigenvalues, and uncertainty relations than ordinary QM in commutative spaces. The generalization of QM to noncommutative Clifford (phase) spaces is attained via the Clifford-Yang algebra. The operators are now given by the generalized angular momentum operators involving polyvector coordinates and momenta. The eigenfunctions (wave functions) are now more complicated functions of the polyvector coordinates. We conclude with some important remarks.

The philosophy of presented multiversum doctrina dominum article is related to the coloring of the theoretical framework with respect to holographic complexity on extremal branes in exclusive higher- dimensional representations. We examine holographic complexity in the doubly holographic model introduced in the current literature to study quantum extremal islands. We focus on the holographic complexity volume proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the extremal brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the extremal brane. We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories in terms of Q-curvature actions. Motivated by the exceptional results, we propose a generalization of the higher-dimensional derivative actions of exotic extremal branes.

Given a granular space-time where the grains can move freely in x, y, z, and also t. But there is a very small, symmetry-breaking increased probability of a grain moving forward versus moving backward in time. At this juncture then, there is no discernible arrow of time. In order that masses not be pulled apart by moving grains, we assume that grains clump together when the grains hold mass. The more mass there is, the more grains are in the clump. We show that as the clump grows larger, the more the probability increases of the clump moving forward in time as opposed to moving backward. So when the clump size grows to measurable dimensions, the arrow of time points consistently forward.

Granular space-time posits that everything can be expressed as a function of space-time and matter. And this includes the quantum wave function Ψ . To give a geometric interpretation of Ψ , we First need to examine time. The fact that the wave function is complex results in the time dimension also being complex with the imaginary component being rolled-up. The symmetry of time is deduced.

In this paper, we take into account Lorentz’s relativistic mass and then derive formulas for the Planck length and the Planck time that are not dependent on any other constants. Thus we can find the Planck length, the Planck time, and also the speed of gravity, from gravitational observations without any knowledge of any physical constants. This is in strong contrast to what has been, and currently is, thought to be the case. Since we take into account relativistic mass, our formulas are also fully accurate for a strong gravitational field. We will claim general relativity theory cannot be fully precise in respect to strong gravitational fields. For example, general relativity theory leads to an imaginary time dilation factor when at the Planck length distance from a Planck mass, but when taking into account Lorentz’s relativistic mass, the time dilation works properly all the way down to, and including, the Planck length distance.

Starting with a brief review of our prior construction of $n$-ary algebras, based on the relation among the {\bf n}-ary commutators of noncommuting spacetime coordinates $ [ X^1, X^2, ......, X^n ] $ with the polyvector valued coordinates $X^{123 ...n} $ in noncommutative Clifford spaces, $ [ X^1, X^2, ......, X^n ] = n ! ~X^{123 ...n} $, we proceed to construct generalized brane actions in noncommutative matrix coordinates backgrounds in Clifford-spaces ($C$-spaces). An instrumental role is played by the Clifford-valued field $\Phi (\sigma^A) = \Phi^M (\sigma^A) \Gamma_M $ which allows to construct a matrix realization of the $n$-ary algebra of the form $ {\bf X}^M \equiv \Phi^{ -1} ( \sigma^A) \Gamma^M \Phi (\sigma^A) $, and that is given in terms of the world manifold's $\sigma^A$ polyvector-valued coordinates of the generalized brane, and which by construction, $satisfy$ the $n$-ary algebra. One then learns that is the presence of matter which $endows$ the spacetime points with a noncommutative algebraic structure. We finalize with an extension of coherent states in $ C$-spaces and provide a preliminary study of strings in target $C$-space backgrounds.

This article puts forward a hypothesis.In this article, the derivative of the cosmological constant is positive, and there is a possibility that the constant evolves from negative in the early universe to positive in the later period. We assume that both macroscopic and microscopic systems are closed systems and the entropy of the system increases to 0. The entropy of the macroscopic open system increases and the entropy of the microscopic system decreases. We know that Adspace can constitute Ads/CFT theory, but there are serious difficulties with ds-space (experimentally, the universe is ds-spacetime). Assuming that the microsystem has a spontaneous entropy reduction process, Ads-space can evolve into ds-space.

There is no formal difference between particles and black holes. This formal similarity lies in the intersection of gravity and quantum theory; quantum gravity. Motivated by this similarity, 'wave-black hole duality' is proposed, which requires having a proper energy-momentum tensor of spacetime itself. Such a tensor is then found as a consequence of 'principle of minimum gravitational potential'; a principle that corrects the Schwarzschild metric and predicts extra periods in orbits of the planets. In search of the equation that governs changes of observables of spacetime, a novel Hamiltonian dynamics of a Pseudo-Riemannian manifold based on a vector Hamiltonian is adumbrated. The new Hamiltonian dynamics is then seen to be characterized by a new 'tensor bracket' which enables one to finally find the analogue of Heisenberg equation for a 'tensor observable' of spacetime.

In this article, we make a simulation, when the boundary conditions are preset, the ratio of the temperature of the two systems is a complex number, which is consistent with $f(R, \phi)$ theory, then a new solution (prediction) appears, ordinary scalars will undergo topological phase transitions under $f(R, \phi)$.

The Donut Chain Theory of Space and Matter started during the late 1970’s as one person’s attempt to understand the journey taken by nature to create space and matter in the universe. The development focused on gaining a personal conceptual understanding of how such a journey might occur. Originally, the process was never intended to be definitive; nor, was it intended to produce numerical results of any significance. It was simply meant to provide a personally plausible understanding of space and matter.

Frequency distribution and variation law of the GW150914 waveform, one of a large number of ancient and distant binary merging gravitational waves claimed by LIGO, are deeply studied, and the recurrence relation of frequency of GW150914 waveform with macro quantization significance is accurately fitted. Firstly, the characteristic equation for effectively correcting the amplitude time of the waveform is proposed, the normative conditions of the numerical analysis method of the minimum solution of the characteristic Diophantine equations are determined, the new correction value of the amplitude time of the GW150914 waveform is given, and then the quantized recursive equation characterizing the frequency distribution of the signal is obtained. Secondly, the complex but clear data processing procedure for drawing the com quantum theory waveform is introduced, and the standard waveform of GW150914 waveform is drawn. It is pointed out that the drawing of LIGO numerical relativistic waveform is opaque, and the conclusion is vague and lacks due scientific analysis. Thirdly, the missing characteristic frequency in GW150914 waveform is confirmed, and then the reason why Hanford waveform and Livingston waveform have no corresponding band of characteristic frequency is analyzed. It is proved that LIGO's GW150914 spiral binary black holes failed to merge successfully, which shows that no matter how powerful the research team is it is difficult to create astronomical events without any flaws. Finally, an experimental proposal to effectively test the confidence of a laser interferometer gravitational wave detector is proposed to detect the gravitational wave of simulated spiral binary system. PS: LIGO made up enough lies that the gravitational wave of the merger of spiral binaries was detected because they naively believed that as long as they teased the readers and announced that the binaries in all gravitational wave events were merged, there would be no corresponding gravitational wave in the future, and it would never be possible for anyone to discover the truth of the so-called gravitational wave of spiral binaries. However, there is no perfect lie in the world. Theoretical physicists only need to master the correct theoretical knowledge of gravity and understand the precise motion law of binary stars, and they can find many fatal loopholes in LIGO's lies. What is introduced here is just one of the loopholes in LIGO's lie of detecting the gravitational wave of the merger of spiral black holes: if the story of spiral double black holes is true, it must radiate a peak corresponding to a specific frequency. LIGO is obviously very ignorant about the basic knowledge of these gravitational theories, so it is unable to carry out the necessary calculations. This unfortunate ignorance has become one of the huge loopholes in the lie of LIGO's spiral binary gravitational wave. In fact, readers can also expose the lie of LIGO gravitational wave from other aspects, and finally find out what kind of laboratory signal LIGO's so-called gravitational wave signal is simulated with. Evidence to expose LIGO lies will be more wonderful one by one. However, LIGO and its cooperative institutions are likely to use the precise inferences of our paper to fabricate spikes of a specific frequency and further release false gravitational waves. Therefore, we have to keep other wonderful evidence secret for the time being, prepare for Jedi counterattack, and finally conclude for LIGO: there are many lies in the scientific community, and LIGO's lies, although very cunning, are the most ignorant, It can only deceive those non real theoretical physics scholars, especially the news media.

The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have since at least the 1980’s tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However already in 1987 it was pointed out that this led to a circular problem, namely that one must know G to find the Planck units, and that it is therefore is of little or no use to express G through the Planck units. This is a view repeated in the literature in recent years, and is the view held by the physics community. However a few years ago we will claim the circular problem was solved. In addition when one express the mass from the Compton wavelength formula then this leads to that the three universal constants G, h and c can be replaced with only lp and c to predict observable gravitational phenomena. This paper will review the history as well recent progress in the composite view of the gravitational constant.

Starting with a different action and following a different procedure than the construction of strings with dynamical tensions described by Guendelman [1], a variational procedure of our action leads to a coupled nonlinear system of D + 4 partial differential equations for the D string coordinates X and the quartet of scalar fields including the dilaton and the tension T field. Trivial solutions to this system of complicated equations lead to a constant tension and to the standard string equations of motion. One of the most relevant features of our findings is that the Weyl invariance of the traditional Polyakov string is traded for the invariance under area-preserving diffeomorphisms. The final section is devoted to the physics of maximal proper forces (acceleration), minimal length within the context of Born's Reciprocal Relativity theory [6] and to the Rindler world sheet description of accelerated open and closed strings from a very different approach and perspective than the one undertaken by [7].

We construct a non-relativistic limit of eleven and ten-dimensional supergravity theories from the point of view of the fundamental symmetries, the higher-dimensional effective action, and the equations of motion. This fundamental limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called Dilatation-invariant Superstring Newton-Cartan geometry and Membrane Newton-Cartan expansion. In order to obtain a finite fundamental limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The present research consider a non-relativistic fundamental limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a Covariant Membrane Newton-Cartan Supergeometry. We further show that the Membrane Newton-Cartan theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

It is known that the existence of Planck length and time contradicts the Lorentz-FitzGerald length contraction and time dilation of special relativity. After showing that the solution of this paradox leaves the spacetime transformations undetermined, it is shown that determining the transformations necessitates a new fundamental equation that governs the local amount of spacetime contraction/dilation.

This paper introduces the construction of spontaneous symmetry breaking When the Goldstone boson effective Laplaceman calculates the effective Laplaceman of the Goldstone boson with symmetry breaking $\mathrm{SO}(4) / \mathrm{SO}(3)$. By the result we put the graviton regarded as the Goldstone boson of symmetry breaking $\mathrm{SO}(4) / \mathrm{SO}(3)$.

It is shown how the crucial {\bf active diffs} symmetry of General Relativity allows to shift the radial location $ r = 2 G M $ of the horizon associated with the Schwarzschild metric to the $ r = 0^+$ location of a $diffeomorphic$ metric. In doing so, one ends up with a spacetime void surrounding the singularity at $ r = 0$. In order to explore the ``interior" region of this void we introduce complex radial coordinates whose imaginary components have a direct link to the inverse Hawking temperature, and which furnish a path that provides access to interior region. In addition, we show that the black hole entropy $ { A \over 4 } $ (in Planck units) is equal to the $area$ of a rectangular strip in the $complex$ radial-coordinate plane associated to this above path. The gist of the physical interpretation behind this construction is that there is an emergence of thermal dimensions which unfolds as one plunges into the interior void region via the use of complex coordinates. And whose imaginary components capture the span of the thermal dimensions. The filling of the void leads to an $emergent$ internal/thermal dimension via the imaginary part $ \beta_r$ of the complex radial variable $ {\bf r } = r + i \beta_r$.

It is known that existence of Planck length and time is in contradiction with fundamental results of special relativity, i.e. length contraction and time dilation. In a previous attempt. I approached the problem from a blindly-formal perspective, but Nature can be more subtle than what formal reasoning can achieve. Although that attempt of mine always had a little value for myself, I (and for that matter nobody) has still come up with a completely satisfactory solution, leaving my previous attempt the only work that at least gets some transformations. In this note I sketch the outlines of another approach that is completely satisfactory, but much more difficult to work out. Although I am not able to get any final result, I write this work to merely share the raw idea; maybe someone can build on this.

We have explained, and shown by feature stringy examples, why a D-brane in superstring theory, when treated as a fundamental dynamical object, can be described by a map from an Azumaya/matrix manifold with a fundamental module with a connection to the target spacetime. In this sequel, we construct a non-Abelian Dirac-Born-Infeld action functional for such pairs when the target spacetime is equipped with a background (dilaton, metric, B)-field from closed strings. We next develop a technical tool needed to study variations of this action and apply it to derive the first variation of with respect. The equations of motion that govern the dynamics of D-branes then follow. We introduce a new action standard for D-branes that is to D-branes as the Polyakov action is to fundamental strings. This ‘standard action’ is abstractly a non-Abelian gauged sigma model based on maps from an Azumaya/matrix manifold with a fundamental module with a connection enhanced by the dilaton term, the gauge-theory term, and the Chern-Simons/Wess-Zumino term that couples to Ramond-Ramond field. In a special situation, this new theory merges the theory of harmonic maps and a gauge theory, with a nilpotent type fuzzy extension. A complete action for a D-brane world-volume must include also the Chern-Simons/Wess-Zumino term that governs how the D-brane world-volume couples with the Ramond-Ramond fields . The current notes lay down a foundation toward the dynamics of D-branes along the line of this research project.

Assuming quanta of spacetime to be spin-2 particles, after developing a statistical theory that has no reference to Boltzmann constant, it is argued that below a certain critical pressure of vacuum, quanta of spacetime form a condensate. The possibility of explanation of Sonoluminescence as a quantum-gravitational effect is also envisaged.

In this paper, a cause for the lack of unification between quantum field theory and general relativity is identified. It is shown that the description of spacetime in current theoretical models assumes energy to be unchanging at small units of time on the quantum scale. As a means of counteraction, a condition is established for quantum gravity theories and the concept of ’two-point momentless’ is presented.

<p> This paper develops the theoretical ratio of the gravitational force to electromagnetic force between two electrons. I refer to this ratio as the <i>ggee</i> ratio. The <i>ggee</i>_theory ratio equals the product of a factor multiplied by <i>alpha</i>².</p> <p> The factor portion of the calculation comes from an unusual source. An underlying model posits a metaphysical structure of space and of the electron. A rational number solution to the geometry of the model leads directly to the factor. This solution emerges completely independently from the <i>ggee</i> ratio it produces. The rational factor seems to be an exact solution.</p> <p> The precision of <i>ggee</i> normally depends on the precision of G. The precision of ggee developed depends on the precision of <i>alpha</i>². Using Codata values for 2018, <i>ggee</i>_codata = 2.400610(54)E-43 and <i>ggee</i>_theory = 2.40071068266(72)E-43. The theoretical value is 1.85 sigma greater than the Codata derived value.</p> <p> The gravitational constant, G, has a history of disparate value ranges. A deviation of 1.85 sigma may fall into an acceptable range more so than would normally be the case.</p>

A previous supersymmetric preon scenario for visible matter particles is extended to the dark sector. In addition, the scenario is reformulated as a Double Field Theory (DFT) with four extra dimensions, to avoid a singular Big Bang in cosmology. T-duality and doubled local Lorentz symmetry of the model are genuine stringy properties. It is proposed that DFT preons may be an approximate pointlike projection of string theory.

This paper introduces a new quantum gravity field equation that is derived from collision space-time. It show how changes in energy (collision-space) is linked to changes in matter (collision-time). This field equation can be written in several different forms. Gravity, at the deepest level, is linked to change in gravitational energy over the Planck time. In our view, this is linked to the collision between two indivisible particles, and this collision has a duration of the Planck time. We also show how an equation of the universe, that was recently derived from relativistic Newtonian theory, can also be derived in a new way from the quantum gravity field equation presented in this paper. This equation gives a new explanation for a cosmological redshift that does not seem to be related to expanding space or the big bang hypothesis. Also, the approximately 13.9 billion years of the Hubble time do not seem to be at all related to the age of the universe, but to the collision time of the mass in the universe.

Signal waves of the monotone increasing frequency detected by LIGO are universally considered to be gravitational waves of spiral binary stars, and the general theory of relativity is thus universally considered to have been confirmed by the experiments. Here we present a universal method for signal wave spectrum analysis, introducing the true conclusions of numerical calculation and image analysis of GW150914 signal wave. Firstly, numerical calculation results of GW150914 signal wave frequency change rate obey the com quantization law which needs to be accurately described by integers, and there is an irreconcilable difference between the results and the generalized relativistic frequency equation of the gravitational wave. Secondly, the assignment of the frequency and frequency change rate of GW10914 signal wave to the generalized relativistic frequency equation of gravitational wave constructs a non-linear equation group about the mass of wave source, and the computer image solution shows that the equation group has no GW10914 signal wave solution. Thirdly, it is not unique to calculate the chirp mass of the wave source from the different frequencies and change rates of the numerical relativistic waveform of the GW150914 signal wave, and the numerical relativistic waveform of the GW150914 signal wave deviates too far from the original waveform actually. Other LIGO signal waveforms do not have obvious characteristics of gravitational frequency variation of spiral binary stars and lack precise data, so they cannot be used for numerical analysis and image solution. Therefore, LIGO signals represented by gw50914 signal do not support the relativistic gravitational wave frequency equation. However, whether gravitational wave signals from spiral binaries that may be detected in the future follow the same co quantization law? Only the numerical analysis results of detailed observation data can give an accurate answer.

Kerr-Sen black holes have stretchon parameters and hidden conformal symmetries. The superradiation stability and steady-state resonance are worth further study. This is the research motivation of this paper.In that article, a new variable y is added here to expand the results of the above article. When$\sqrt{2a^2}/{r^2_+}< \omega< m\varOmega_H+q\varPhi_H$,so the Kerr-sen black hole is superradiantly stable at that time,similar to the superradiation result of the Kerr-Newman black hole.

As we have recently shown, the Planck length can be found independently of G and h, despite its common physical notion. This enabled us to make a series of cosmological predictions based on only two constants: the Planck length and the speed of light. The present paper explores further the link between the Planck scale and large-scale Universe structures. We look at both the Friedmann cosmology and the recently proposed Haug cosmology from this new perspective.

There appears to be a lack of general consensus among the BIPM and the quantum gravity community regarding the definition of kilogram, in light of the 2019 convention, concerning the role of the gravitational constant $G$ as a defining constant. Unless a decision is reached, not only the task of the BIPM to ``ensure worldwide unification of measurements'' remains unfulfilled, but also the proposals of experimental tests of quantum gravity remain devoid of any scientific value.

In this manuscript we do the Quantum Field Theory (QFT) of Einstein's Gravity (EG) based on the developments previously made by Suraj N. Gupta and Richard P. Feynman, using a new and more general mathematical theory based on Ultrahyperfunctions \cite{ss} \\ \nd Ultrahyperfunctions (UHF) are the generalization and extension to the complex plane of Schwartz 'tempered distributions. This manuscript is an {\bf application} to Einstein's Gravity (EG) of the mathematical theory developed by Bollini et al \cite{br1, br2, br3, br4} and continued for more than 25 years by one of the authors of this paper. A simplified version of these results was given in \cite{pr2} and, based on them, (restricted to Lorentz Invariant distributions) QFT of EG \cite{pr1} was obtained. We will quantize EG using the {\bf most general quantization approach}, the Schwinger-Feynman variational principle \cite{vis}, which is more appropriate and rigorous than the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. \\ \nd We use the Einstein Lagrangian as obtained by Gupta \cite{g1,g2,g3}, but we added a new constraint to the theory. Thus the problem of lack of unitarity for the $S$ matrix that appears in the procedures of Gupta and Feynman.\\ \nd Furthermore, we considerably simplify the handling of constraints, eliminating the need to appeal to ghosts for guarantying unitarity of the theory. \\ \nd Our theory is obviously non-renormalizable. However, this inconvenience is solved by resorting to the theory developed by Bollini et al. \cite{br1,br2,br3,br4,pr2}\\ \nd This theory is based on the thesis of Alexander Grothendieck \cite{gro} and on the theory of Ultrahyperfunctions of Jose Sebastiao e Silva \cite{ss} \\ Based on these papers, a complete theory has been constructed for 25 years that is able to quantize non-renormalizable Field Theories (FT). \\ Because we are using a Gupta-Feynman based EG Lagrangian and to the new mathematical theory we have avoided the use of ghosts, as we have already mentioned, to obtain a unitary QFT of EG \\

The study of the ${\bf 4}$-tachyon off-shell string scattering amplitude $ A_4 (s, t, u) $, based on Witten's open string field theory, reveals the existence of a continuum of poles in the $s$-channel and corresponding to a continuum of complex spins $ J $. The latter spins $ J$ belong to the Regge trajectories in the $ t, u$ channels which are defined by $ - J (t) = - 1 - { 1\over 2 } t = \beta (t)= { 1\over 2 } + i \lambda $; $ - J (u) = - 1 - { 1\over 2 } u = \gamma (u) = { 1\over 2 } - i \lambda $, with $ \lambda = real$. These values of $ \beta ( t ), \gamma (u) $ given by ${ 1\over 2 } \pm i \lambda $, respectively, coincide precisely with the location of the critical line of nontrivial Riemann zeta zeros $ \zeta (z_n = { 1\over 2 } \pm i \lambda_n) = 0$. We proceed to prove that if there were nontrivial zeta zeros (violating the Riemann Hypothesis) outside the critical line $ Real~ z = 1/2 $ (but inside the critical strip) these putative zeros $ don't$ correspond to any $poles$ of the ${\bf 4}$-tachyon off-shell string scattering amplitude $ A_4 ( s, t , u ) $. One of the most salient features of these results is the $collinearity$ of the ${\bf 4}$ off-shell tachyons. We may speculate that this spatial $collinearity$ is actually reflected in the $collinearity$ of the poles of the string amplitude, lying in the critical line : $ \beta = \gamma^* = { 1\over 2 } + i \lambda$, where the nontrivial zeta zeros are located. We finalize with some concluding remarks on continuous spins, non-commutative geometry and other relevant topics.

In this work we develop the quantum theory of gravity in the gravitational compressed space. The equivalence of spatial compression to the Lorentz contraction of special relativity, supported by the relative gravitational red-shift using the black hole clock leads to the brane potential and gives the minimum length at which the extra dimensions become dominant, comparable to that of the Schwarzschild radius. For Planck mass the minimum length is almost Planck's length. When doing the quantization of the theory, we find that those responsible for the evolution of time for luminous matter, graviton and for dark matter, the axion, have the property that in compressed gravitational space, naked and dressed propagators are equal and coincide with the corresponding naked propagators.

The article shows how Quantum Mechanics and General Relativity could be unified within Einstein-Cartan spacetime which can be both compressed and torqued. The compression is responsible as well-known for astronomic gravity whereas the torsion for microscopic quantum effects as the Compton wavelength appearing into the Kerr metric strongly suggests. This could lead to a better understanding of both theories and promising applications such as macroscopic quantum and gravitational science and engineering based for instance on tremendous angular momenta.

The Schwarzschild solution of the Einstein field equation leads to a solution that has been interpreted as wormholes. Many have been skeptical about this interpretation. However, many researchers have also been positive about it. We show that wormholes are not mathematically allowed in the spherical metric of a newly- released unified quantum gravity theory known as collision space-time [1–3]. We therefore have reasons to believe that wormholes in general relativity theory are nothing more than a mathematical artifact due to an incomplete theory, but we are naturally open for discussions about this point. That wormholes likely do not exist falls nicely into line with a series of other intuitive predictions from collision space-time where general relativity theory falls short, such as matching the full specter of the Planck scale for micro black “holes”.

The covariant quantization and light cone quantization formalisms are followed to construct the coherent states of both open and closed bosonic strings. We make a systematic and straightforward use of the original definition of coherent states of harmonic oscillators to establish the coherent and their corresponding cat states. We analyze the statistics of these states by explicitly calculating the Mandel parameter and obtained interesting results about the nature of distribution of the states. A tachyonic state with imaginary mass and positive norm is obtained

The supercoherent states of the RNS string are constructed using the covariant quantization and analogously the light cone quantization formalisms. Keeping intact the original definition of coherent states of harmonic oscillators, we extend the bosonic annihalation operator into the superspace by inclusion of fermionic contribution to oscillator modes thus construct the supercoherent states with supersymetric harmonic oscillator. We analyse the statistics of these states by explicitly calculating the Mandel parameter and obtained interesting results about the nature of distribution of the states.

We consider here the simple derivation of the Einstein equations by Fock. Then, we approach the way from the spin 1 fields to the spin 2 fields for massive and massless particles and we derive the gravity equations from this base. In conclusion, we discuss the principle of equivalence in classical Einstein theory and in the Schwinger spin 2 gravity

The quantized model of Newtonian gravity indicates that the quantum effects of gravity become apparent when particles of sufficiently small mass are in the orbit of a gravitating body of mass. In particular, the stable orbital path of particles in such conditions are shown to be polygons. The stable circular path of classical mechanics emerges when the side counts of these polygons increase to infinity, as the quantum effects of gravity vanish due to the excessive mass of the orbiting particles. In this article, it is hypothesized that the particle mass in Saturn's North Pole jet stream is such that the quantum effects of gravity have become apparent. The hexagonal shape of Saturn's jet stream is therefore used to constrain the mass of its cloud particles to 7.4E-20 (kg). This in turn constrains the dimensions of ammonia ice crystals in the clouds to less than 100 nanometers. This theory also indicates that polygons of different side counts are also feasible at different latitudes, should the local particle mass permit the quantum effects of gravity to become visible. This aspect of the theory is also consistent with the presence of faint but still visible edges of some polygons at lower latitudes.

We consider the motion of string in free fall in gravity. The solutions are not identical with the string accelerated kinetically by acceleration a. So, we distinguish between non-inertial field and the gravity field and we discuss the principle of equivalence. In conclusion we suggest to drop the charged objects from the very high tower Burj Khalifa in order to say crucial words on the principle of equivalence.

The smooth Newtonian model of gravity is quantized using the results obtained from the combined theory of Special Relativity (SR) and Quantum Mechanics (QM). The resulting quantum model of gravity, unlike the classical Newtonian model, predicts that there exists an upper limit to the distance between a given pair of masses, called the action distance, beyond which they become gravitationally unbound. Equivalently, at any given radial distance from a large gravitating body of mass, there exists a minimum mass below which the particle would not gravitationally bind to the gravitating body. The attractable mass limit of a gravitating body is determined by equating action distance with the surface radius of the body. Moreover, the quantum model of gravity indicates that the escape velocity from a large gravitating body is a function of the mass of the escaping particle as well. This quantum effect of gravity become significant if the mass of the escaping particles, such as the gas molecules from the exosphere of a planet, are comparable to the attractable mass limit of the planet. The significant discrepancy observed in the escape rates of CH_4 and N_2 species from Pluto's exosphere is used to constrain the reference mass of the combined SR-QM theory to m= 3.2E-45 (kg). The latter is thought to be the physical cut-off limit for massless particles. An Earth-bound experiment is also proposed to test the predictions of the combined SR-QM theory and determine the reference mass with a higher accuracy.

We have recently suggested a new quantum gravity theory that can be unified with quantum mechanics. We have coined this theory collision space-time. This new theory seems to be fully consistent with a 3-dimensional space-time, that is, three space dimensions and three time-dimensions, so some would call it six-dimensional. However, we have shown that collision-time and collision-length (space) are just two different sides of the same ”coin” (space-time), so it is more intuitive to think of them as 3-dimensional space-time. In previous papers, we have not laid out a geometric coordinate system for our theory that also considers gravity, but we will do that here. We are pointing out that Einstein’s negative attitude towards relativistic mass can perhaps cause a weakness in the foundation of general relativity theory. When a relativistic mass is incorporated in the theory, this mass also seems to indicate one needs to move to three-dimensional space-time. Then, for example, our new theory matches fully up with all the properties of the Planck scale in relation to the mathematical properties of micro black holes, not only mathematically but also logically, something we demonstrate clearly is not the case of general relativity theory. Our new metric has many benefits as an alternative to the Schwarzschild metric and general relativity theory. It seems to be more consistent with the Planck units than the Schwarzschild metric. Most importantly, it seems to be fully consistent with a new quantum gravity theory that seems to unify gravity with quantum mechanics.

In the present article we aim to broaden the consideration of background geometry of manifolds/bundles arising in heterotic compactifications with an aim towards extending the validity and understanding of heterotic/F-theory duality. In particular, we will focus on elliptically fibered Calabi-Yau geometries arising in heterotic theories in the context of the so-called Fourier Mukai transforms of vector bundles on elliptically fibered manifolds. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theory description of low-energy chiral multiplets. We propose a generalization of heterotic/F-theory duality and in order to complete the translation, the dictionary of the heterotic/F-theory duality has to be refined in some aspects. The precise map of spectral surface and complex structure moduli is obtained, and with the map, we find that divisors specifying the line bundles correspond precisely to codimension singularities in F-theory.

We calculate the extremal higher dimensional effective actions of fundamental brane-antibrane systems elegantly presented in the theoretical framework of advanced membrane theory constructions. Detailed study of brane-antibrane systems reveals when brane separation is smaller than the superstring length scale, spectrum of this system has different tachyonic modes and interaction regimes in the moduli superspace. The higher dimensional effective actions should then include these modes because they are the most important ones which rule the extremal dynamics of the fundamental brane systems. In this regard, it has been shown that an effec- tive action of Born-Infeld type proposed in the current literature can capture many properties of the decay of non-BPS Dp-branes in superstring and membrane theory. The effective actions of brane-antibrane systems in Types IIA and IIB superstring theories should be given by some extension of the DBI action and the WZ terms which include the tachyon field configurations. The DBI part may be given by the projection of the effective action of two non-BPS Dp-branes in Type IIB theory. We are interested in this paper in the appearance of tachyon, gauge field and the RR field in these extremal higher dimensional actions. Using the consistency of the present constructions, we have also found the first higher derivative corrections to the exceptional part of the extremal effective actions with brane-antibrane systems.

We continue to explore the consequences of Thermal Relativity Theory to the physics of black holes. The thermal analog of Lorentz transformations in the $tangent$ space of the thermodynamic manifold are studied in connection to the Hawking evaporation of Schwarzschild black holes and one finds that there is $no$ bound to the thermal analog of proper accelerations despite the maximal bound on the thermal analog of velocity given by the Planck temperature. The proper entropic infinitesimal interval corresponding to the Kerr-Newman black hole involves a $ 3 \times 3 $ non-Hessian metric with diagonal and off-diagonal terms of the form $ ( d{\bf s} )^2 = g_{ ab } ( M, Q, J ) d Z^a dZ^b$, where $ Z^a = M, Q, J $ are the mass, charge and angular momentum, respectively. Black holes in asymptotically Anti de Sitter (de Sitter) spacetimes are more subtle to study since the mass turns out to be related to the $enthalpy$ rather that the internal energy. We finalize with some remarks about the thermal-relativistic analog of proper force, the need to extend our analysis of Gibbs-Boltzmann entropy to the case of Reny and Tsallis entropies, and to complexify spacetime.

Gravity is not a fundamental force. Alzofon’s Thermodynamic GravityTheory is derived from Qubit Model, an upgrade of the Quark Model within theStandard Model. Alzofon’s experiment is discussed: pros and cons. At the level of the Standard Model, Gravity is a result of the structure of the electric charges of quarks in nucleons, subject to Platonic symmetry and lack of parity invariance, related to CP-violation, due to the dihedral group as the QuantumMirror Symmetry group.The AGNUE experiment performed at Hathaway Research International is briefly explained. It is designed to test Alzofon’s Theory. A glimpse of Gravity Control and what inertial mass is are presented. FurtherR&D will be funded under the upcoming Kickstarter Gravity.

Gravity is not a fundamental force; in a nut-shell it is the result of a non-commutative interaction of the electric'' (i.e. Coulomb type) fractional charges of the proton and neutron U(1) neutral when compensated by the electronic cloud. This is no longer true at the SU(2) Electroweak level, once spherical symmetry is broken to a finite Platonic group of symmetry within it. The fine splitting of energy levels due to the SU(2) structure of the electric charge can be controlled using a MASER to invert the population and orient the nuclei the right way to reduce and turn-off Gravity.

The generic relativistic version of a particle-eld theory, with non-isotropic sources, includes a Gravity force perturbation of Coulombian Force, with the usual Magnetic Force resulting from Lorentz transformations. The quark model of Standard Model, with fractional charge struc- ture of nucleons enveloped by electronic clouds, mandates such non- isotropic charges. Dynamic Nuclear Orientation (DNO), via electronic spin and LS- coupling, allows to invert the population of low energy Gravitational attraction states, and achieve Gravity Control. The 1994 scientic experiment of Dr. Frederick Alzofon has con- rmed Gravity Control can be achieved via DNO. Other researchers have contributed in the same general direction of unifying Electromagnetism and Gravity, supporting the non-isotropic charge concept, including Paul LaViolette, author of Subquantum Ki- netics.

Within the background field formalism of quantum gravity, I show that if the quantum fluctuations are limited to diffeomorphic transformations, all the quantum corrections vanish on shell and the effective action is equivalent to the classical action. I also show that this choice of fields renders the path integral independent of the on-shell condition for the background field, and therefore incorporates a form of background independence. The proposed approach may provide insight into the development of a finite and background independent description of quantum gravity.

In the paper, with the help of various models, the thesis on the fundamental nature of the field form of matter in physics is considered. In the first chapter a model of special relativity is constructed, on the basis of which the priority of the massless form of matter is revealed. In the second chapter, a field model of inert and heavy mass is constructed and on this basis the mechanism of inertia and gravity of weighty bodies is revealed. In the third chapter, the example of geons shows the fundamental nature of a massless form of matter on the Planck scale. The three-dimensionality of the observable space is substantiated. In the fourth chapter, we consider a variant of solving the problem of singularities in general relativity using the example of multidimensional spaces. The last chapter examines the author's approach to quantum gravity, and establishes the basic equation of quantum gravity. The conclusions do not contradict the main thesis of the paper on the fundamental nature of the massless form of matter.

It is shown that the radial spectrum associated with a fuzzy sphere in a $noncommutative$ phase space characterized by the Yang algebra, leads $exactly$ to a Regge-like spectrum $G M^2_l = l = 1, 2,3, \ldots $, for $all$ positive values of $l$, and which is consistent with the extremal quantum Kerr black hole solution that occurs when the outer and inner horizon radius coincide $ r_+ = r_- = G M$. The condition $ G M_l^2 = l $ is tantamount to the mass-angular momentum relation $ M^2_l = l M_p^2 $ implying that the (extremal) horizon area is quantized in multiples of the minimal Planck area. Another important feature is the holographic nature of these results that are based in recasting the Yang algebra associated with an $8D$ noncommuting phase space, involving $ {\bf x}_\mu, {\bf p}_\nu, \mu, \nu = 0,1,2,3$, in terms of the $undeformed$ realizations of the Lorentz algebra generators $ J_{AB}$ corresponding to a $6D$-spacetime, and associated to a $12D$-phase-space with coordinates $ X_A, P_A; A = 0,1,2, \ldots, 5$. We hope that the findings in this work, relating the Regge-like spectrum $ l = G M^2 $ and the quantized area of black hole horizons in Planck bits, via the Yang algebra in Noncommutative phase spaces, will help us elucidate some of the impending issues pertaining the black hole information paradox and the role that string theory and quantum information will play in its resolution.

For a consistent picture of fundamental physics and cosmology, three first principles are proposed as the foundations. That is, quantum variational principle that provides the formalism, consistent observation principle that set physical constraints and symmetries, and spacetime inflation principle that determines physical contents (particle fields and interactions). Under these three principles, a series of supersymmetric mirror models are constructed to study various phases of the universe at different spacetime dimensions and the dynamics between the phases. In particular, mirror symmetry, as the orientation symmetry of the underlying geometry, plays a critical role in the new framework.

We have recently [1, 2] shown a possible method to unify gravity and quantum mechanics in a simple way that we have called collision space-time. Here, we demonstrate a special version of our theory when we set lp = 1 and c = 1. Mass, energy, Compton momentum, and the Schwarzschild radius are then all identical, and simply a collision frequency. A frequency below one is not observable and can be interpreted as a frequency quantum probability. One could easily make the mistake that this is simply setting G =hbar = c = 1 (Planck natural unit system); however this would possibly be inaccurate as we do not need either G or �� in our system even when not setting them to one. Furthermore, we can find the Planck length totally independent of G and ��, for any standardised length unit chosen. Setting c = 1 simply means one links space and time through the speed of light, and setting lp = 1 means one selects the Planck length as the fundamental length unit, and the Planck length we have argued for is the diameter of an indivisible particle. One of the beauties of our theory is that, in the output of many formulas we obtain from our theory, the integer part represents real observations (collisions) and fractions represent quantum probabilities. Therefore, we could say there is also almost a unification between numbers and physics, not only a unification of gravity and quantum mechanics.

In this essay the equivalence between mass/energy and spacetime is postulated, so that matter, energy and spacetime can be transformed into one another. This has major implications in the physics of Black Holes and in cosmology. It is argued that no central singularity arises inside a Black Hole, no remnant is left once it has evaporated and unitarity is conserved by means of gravitational radiation. The possible origin of the cosmological constant is briefly discussed.

Actions for strings and $p$-branes moving in octonionic-spacetime backgrounds and endowed with octonionic-valued metrics are constructed. An extensive study of the bosonic octonionic string moving in flat backgrounds, and its quantization, is presented. A thorough discussion follows pertaining whether or not the analysis leading to the $ D = 26$ critical dimension of the ordinary bosonic string is valid in the octonionic case. A remarkable numerical coincidence is found (without invoking supersymmetry) in that the total number of (real) degrees of freedom of $3$ fermion generations (involving massless Weyl fermions in $ 4D$) is $ 16 \times 4 \times 3 = 192$, and which matches the number of $ 8 \times 24 = 192$ real dimensions (degrees of freedom) corresponding to the $24$ transverse octonionic dimensions associated with the octonionic-worldsheet of a bosonic octonionic-string moving in $D = 26$ octonionic dimensions.

The relationship between gravitational potentials, black holes and the squared light speed c² is examined in this paper as well as the implications of the presented findings for the universal gravitational constant G and general relativity theory. It is common knowledge that the velocity limit in our universe is defined by light speed c and as shown in this work c² plays a similar role for the gravitational potential since c²/G is linked to the mass density of black holes and our local Hubble sphere. Furthermore, it is demonstrated that the rift between cosmology and quantum physics can possibly be reconciled by acknowledging the physical meaning of the Planck units which proposedly define the characteristics of a quantized space-time, including its gravitational impedance. This notion is also supported by the presented logarithmic relationships between the cosmological scale and the quantum scale. Moreover, the presented findings uncover a previously unknown physical meaning for the constituents of Dirac's mysterious large number hypothesis.

The possibility of ultra-high-speed interstellar travel is considered. The role of the Devil's advocate is played, purely for the sake of interest -- it is considered that ultra-high-speed interstellar travel is impossible.

We start with an elementary example of a nonsingular configuration using a trivial solution to massive gravity yielding a nonzero initial time step. Then we present a history of the cosmological constant issue from Einstein’s introduction—which did not work because his static universe solution to the Ricci Scalar problem and GR was unstable—to the radius of the universe being proportional to the inverse square root of the cosmological constant. We use two spacetime first integrals to isolate a nonperturbative cosmological constant solution at the surface of the start of expansion of the universe. A phenomenological solution to the cosmological constant involves scaling the radius of the present universe. Our idea is to instead solve the cosmological constant at the surface of the initial spacetime bubble, using the initially derived time step, ∆t, as input for the cosmological constant. This was done in a Zeldovich4 section for dark energy; solving the initial value of the cosmological constant supports one of the models of DE and why the universe reaccelerated a billion years ago. We depend on Katherine Freese’s Zeldovich4 talk of dark stars, which form supermassive black holes, to consume initially created DM, and Abhay Ashtekar’s nonsingular start to the universe as part of a solution to low l values in CMBR data. We conclude with a reference to a multiverse generalization of Penrose’s cyclic conformal cosmology as input to the initial nonsingular spacetime bubble.

In this paper, we will prove, based on reasoning as well as mathematical evidence and experimental obser- vations, why Newton gravity moves at the speed of light and is not instantaneous as previously thought. The misunderstanding that Newton gravity is instantaneous has constrained our progress in understanding gravity to its full extent. We will show that all of Newton’s gravitational phenomena contain the Planck length and the speed of gravity; this speed of gravity is identical to the speed of light. A series of gravitational phenomena that are considered to be non-Newtonian and most often explained by theory of general relativity actually contain no information about the speed of gravity. However, all observable gravity phenomena can be predicted from the Planck length and the speed of gravity alone, and we can easily extract both of them from gravitational phenomena with no knowledge of any physics constants. In addition, we can also measure the speed of light from electromagnetic phenomena and then extract the Planck length from any of Newton’s gravitational phenomena with no knowledge of G or h.

In this short note, we present the Gaussian law of gravitation, based on the concept that the mass is collision- time, see our paper Collision Space-Time, [1].

A brief review of the essentials behind the construction of a Chern-Simons-like brane action from the Large $N$ limit of Exceptional Jordan Matrix Models paves the way to the construction of actions for membranes and $p$-branes moving in octonionic-spacetime backgrounds endowed with octonionic-valued metrics. The main result is that action of a membrane moving in spacetime backgrounds endowed with an octonionic-valued metric is not invariant under the usual diffeomorphisms of its world volume coordinates $ \sigma^a \rightarrow \sigma'^a (\sigma^b) $, but instead it is invariant under the rigid $ E_{ 6 ( - 26) } $ transformations which preserve the volume (cubic) form. The star-product deformations of octonionic $p$-branes follow. In particular, we focus on the octonionic membrane along with the phase space quantization methods developed by \cite{Szabo} within the context of Nonassociative Quantum Mechanics. We finalize with some concluding remarks on Double and Exceptional Field theories, Nonassociative Gravity and $A_\infty, L_\infty$ algebras.

A New Robust Theory of Everything with Expected 10-100 ppb Anomalies in some Gravitational Experiments depending on the total ghost hypercharges of the proton-electron pair and on the total ghost hypercharges of the neutron. Here, the meaning of the word robust is the use of the concept of $n$-irreducible sequents and $n$-irreducible numbers to constraint the possible theories of everything into a single one with a maximized $n$-irreducible number. We try to write the definitions of the theory of everything in the most rigorous mathematical way and in a compatible way with every known experiments. A kind of Nobel Prize experiment is proposed for detecting anomaly between orbital parameters of identical metallic balls orbiting around Earth with different neutron-proton ratio. An anomaly between $10^{-8}-10^{-12}$ is expected and the current precision is $10^{-8.7}$.

We examine the associated wave of the electron, and we put in evidence the problem with its relative velocity. The velocity of an electron is always measured relative to the laboratory, which gives the correct behaviour of the electron concerning the law of Louis de Broglie. But, to agree with this law, there must exist some interaction between the electron and the laboratory, which allows the electron to modify its characteristics. The electron must therefore interact with a media connected to the laboratory. Such a media must be associated with the earth, following it in its path through the Universe. {\bf It follows that the relativity theories of A. Einstein are wrong.}

Simplified toy theories abound in theoretical physics. These toy models are ex- tremely useful. An example is N = 4 supersymmetric Yang–Mills theory. In this toy model alone, tens of thousands of papers have been published, some cited thousands of times. This essay proposes that physicists consider studying "N=4 General Relativity" as a toy model. This 'Only Gravity' toy model uses Einstein's field equations on their own in the hope that ignoring complicated interactions of gravity with other fields (electromagnetism, etc) and physical theories (quantum mechanics, QFT, etc) may paradoxically help us understand more about quantum gravity.

We will here show that there is one more relativistic wave equation rooted in the relativistic energy Compton moment relation, which should not be confused with the standard relativistic energy momentum relation. The standard momentum is, from a quantum perspective, rooted in the de Broglie wave. The de Broglie wave is not mathematically defined for rest-mass particles and has strange properties such as converging to infinity when the particle is almost at rest. As mentioned in the previous paper, the de Broglie wave is likely just a mathematical derivative of the true matter wave, which we have good reasons to think is the Compton wave. A wave equation that satisfies the relativistic energy Compton momentum relation will, in addition automatically satisfy the standard relativistic energy momentum relation, so there is no conflict between these two relations. The new one related to Compton is just the deeper reality and help explain why it gives simpler and more elegant relativistic wave equations, which are likely easier to interpret in terms of the physical reality.

Our present standard model is based on basic laws for forces which were mathematically introduced by matching equations with experimentally obtained curves. The basic laws are Coulomb, Ampere, Lorentz, Maxwell, Gravitation, etc. The equations were not deduced mathematically from the interactions of one postulated field, resulting the need to introduce for each particular manifestation of the force a different field, namely electric, magnetic, strong, weak and gravitation. In the present paper a model is presented where each known force is the product of a particular interaction of one field which consists of longitudinal and transversal angular momenta of a Fundamental Particle (FP). It shows that electrons and positrons neither attract nor repel each other when the distance between them tends to zero. This allows to represent muons, tauons and hadrons as swarms of electrons and positrons called quarks. The paper then concentrates on relativity showing that it is a speed and not a time-space problem, and that time and space are absolute variables. It also shows that photons are emitted with light speed from their source and move with speeds different than light speed relative to a moving reference system.

Using the brick wall method, we will calculate the entropy of Kerr-Newman black Hole and arrive at the already well established result. During the calculation, we will arrive at the generalized equation for FNSR and FSR mode of free energy, which can be used to evaluate the free energy of any black hole. And we will also show the detailed steps in our calculation to provide clarification about how we calculated it.

Using the brick wall method, we will calculate the entropy of Kerr-Newman AdS black Hole and arrive at the already well established result. During the calculation, we will be using the generalized equation for FNSR and FSR mode of free energy.

For more than hundred years, it has been assumed that one needs to know the Newton gravitational constant G, the Planck constant ̄h, and the speed of light c to find the Planck length. Here we demonstrate that the Planck length can be found without any knowledge of G, h, or c, simply by observing the change in the frequency of a laser beam in a gravity field at two altitudes. When this is done, we also show that the speed of light (gravity) easily can be extracted from any observable gravity phenomena. Further, we show that all observable gravity phenomena can be predicted using just these two constants, in addition to one variable that is dependent on the size of the gravity mass and the distance from the center of the gravity object. This lies in contrast to the standard theory, which holds that we need the three constants Max Planck suggested were the important universal constants, namely G, h, and c; in that formulation, we also need a variable for the mass size, and the radius. Based on our new findings, we get both a reduction in the number of constants required and a simplification of understanding gravity that is directly linked to the Planck scale. We discuss how this has a number of important implications that could even constitute a breakthrough in unifying quantum mechanics with gravity. Our analysis strongly indicates that standard physics uses two different mass definitions without being actively aware of it. The standard kg mass is used in all non-gravitational physics. Apparently, we are using the same mass in gravity, but we claim that the more complete mass is hidden in the multiplication of G and M. Based on this view, we will see that only two universal constants are needed, namely c and lp, to do all gravity predictions compared to the G, h, and c in the standard view of physics. In order to unify gravity with quantum mechanics, we need to use this “embedded” mass definition from gravity, which also impacts the rest of physics. Since 1922, a series of physicists have thought that the Planck length would play a major role in making progress in the understanding of gravity, particularly in the hope of unifying quantum mechanics with gravity. Although there have been a series of attempts to incorporate the Planck length in quantum gravity, little theoretical progress has been accomplished. However, with this recent discovery, we have reasons to think that a piece of the puzzle has emerged. We will continue our analysis and welcome other researchers to scrutinize our findings over time before drawing final conclusions.

The string model of gravitational force was proposed by author 40 years ago (Pardy, 1980; 1996). In this model the string forms the mediation of the gravitational interaction between two gravitating bodies. It reproduces the Newtonian results in the first-order approximation and it predicts in the higher-oder approximations the existence of oscillations of the massive bodies interacting by the string. In case of the moon it can be easily verified by the NASA laser measurements.

A derivation of continuously differentiable, fluctuating 3-dimensional vector fields as generalized Maxwell Fields leads to Identification of Einstein’s space as the result of a deformation of a Euclidean space and the fluctuating hypersurface of Einstein’s space as gravitational wave propagation. The consequence is the union of Maxwell field and Gravitational field which leads to 1. -the explanation of the photon and its formation by describing the detailed quantization process. 2. -the characterization of the photon resulting from the deformation movement defined in a point, which from here screws through space in a direction at the speed of light. These are discussions that are beyond the range of quantum mechanics and quantum field theory because of the uncertainty relation, although such connections seem qualitatively obvious. By the described unification electromagnetism is directly led back to the most fundamental terms of physics, space and time. Last but not least the importance of the Einstein-Equations for microphysics is proved. 2

The Geometrization of Quantum Mechanics proposed in this work is based on the postulate that the quantum probability density can $curve$ the classical spacetime. It is shown that the gravitational field produced by $smearing$ a point-mass $M_o$ at $ r = 0$ throughout all of space (in an spherically symmetric fashion) can be interpreted as the gravitational field generated by a self-gravitating anisotropic fluid droplet of mass density $ 4 \pi M_o r^2 \varphi^* ( r ) \varphi ( r ) $ and which is sourced by the $probability$ $cloud$ (associated with a spinless point-particle of mass $ M_o$) $permeating$ a $3$-spatial domain region $ {\cal D}_3 = \int 4 \pi r^2 dr $ at any time $ t $. Classically one may smear the point mass in any way we wish leading to arbitrary density configurations $ \rho (r ) $. However, Quantum Mechanically this is $not$ the case because the radial mass configuration $ M (r) $ must obey a key third order nonlinear differential equation (nonlinear extension of the Klein-Gordon equation) displayed in this work and which is the static spherically symmetric relativistic analog of the Newton-Schr\"{o}dinger equation. We conclude by extending our proposal to the Lagrange-Finsler and Hamilton-Cartan geometry of (co) tangent spaces and involving the relativistic version of Bohm's Quantum Potential. By further postulating that the quasi-probability Wigner distribution $W(x,p)$ $curves$ phase spaces, and by encompassing the Finsler-like geometry of the cotangent-bundle with phase space quantum mechanics, one can naturally incorporate the $noncommutative$ and non-local Moyal star product (there are also non-associative star products as well). To conclude, Phase Space is the arena where to implement the space-time-matter unification program. It is our belief this is the right platform where the quantization $of$ spacetime and the quantization $in$ spacetime will coalesce.

In this paper, we show how one can find the Planck length multiplied by the speed of light from a Newton force spring with no knowledge of the Newton gravitational constant G, the speed of light c, or the Planck constant h. This is remarkable, as for more than a hundred years, modern physics has assumed that one needs to know G, c, and the Planck constant in order to find any of the Planck units. We also show how to find other Planck units using the same method. To find the Planck time and the Planck length, one also needs to know the speed of light. To find the Planck mass and the Planck energy in their normal units, we need to know the Planck constant, something we will discuss in this paper. For these measurements, we do not need any knowledge of the Newton gravitational constant. It can be shown that the Planck length times the speed of light requires less information than any other Planck unit; in fact, it needs no knowledge of any fundamental constant to be measured. This is a revolutionary concept and strengthens the case for recent discoveries in quantum gravity theory completed by Haug [3].

By generically constraining the boundary term of the action of gravity, the formal structure of the observed types of matter fields (scalar, fermion/Dirac and spin 1) is obtained in the weak gravity limit, including their gauge behaviour, covering the standard model. By gravity, we mean any theory having the Gibbons-Hawking-York boundary term as its torsion-free weak gravity limit. The constraining term is assumed to be local, not explicitly coordinate-dependent and to be the boundary term of a bulk function (Lagrangian). In this way, the latter is fixed to a large extent, admitting couplings and mass terms. The formal matching with observed fields suggests that matter should be the consequence of gravity constraining, and quantum matter would result from constrained quantum gravity. This implies that it is possible to compute the value of 6.564.10^{-69} m^2 for the fundamental quantum constant of gravity - the smallest possible change of the boundary term. Also, the freedom to construct a fundamental quantum concept of gravity is strongly reduced, and the weak gravity limit is completely determined. For strong gravity, the boundary term - rather than the Hamiltonian - yields a key quantum counting operator.

Based on recent development in quantum physics we show how to extract the speed of gravity (light) from a Pendulum Clock. This with no knowledge off the so-called Newton's gravitational constant G. This is a very short preliminary note with the mathematical results. We will likely at a later point extend this paper with an in-depth discussion.

This short paper clarifies a few points discussed in earlier work. Under the neutrino CMB correspondence, low energy observables are analysed using quantum computation. Starting from the observed mu-tau symmetry, we discuss constraints on all neutrino masses and mixing parameters.

A brief review of the essentials of Asymptotic Safety and the Renormalization Group (RG) improvement of the Schwarzschild Black Hole that removes the $ r = 0$ singularity is presented. It is followed with a RG-improvement of the Kantowski-Sachs metric associated with a Schwarzschild black hole interior and such that there is $no$ singularity at $ t = 0$ due to the running Newtonian coupling $ G ( t )$ (vanishing at $ t = 0$). Two temporal horizons at $ t _- \simeq t_P$ and $ t_+ \simeq t_H$ are found. For times below the Planck scale $ t < t_P$, and above the Hubble time $ t > t_H$, the components of the Kantowski-Sachs metric exhibit a key sign $change$, so the roles of the spatial $z$ and temporal $t$ coordinates are $exchanged$, and one recovers a $repulsive$ inflationary de Sitter-like core around $ z = 0$, and a Schwarzschild-like metric in the exterior region $ z > R_H = 2 G_o M $. The inclusion of a running cosmological constant $ \Lambda (t) $ follows. We proceed with the study of a dilaton-gravity (scalar-tensor theory) system within the context of Weyl's geometry that permits to single out the expression for the $classical$ potential $ V (\phi ) = \kappa\phi^4$, instead of being introduced by hand, and find a family of metric solutions which are conformally equivalent to the (Anti) de Sitter metric. To conclude, an ansatz for the truncated effective average action of ordinary dilaton-gravity in Riemannian geometry is introduced, and a RG-improved Cosmology based on the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is explored where instead of recurring to the cutoff identification $ k = k ( t ) = \xi H ( t ) $, based on the Hubble function $ H (t)$, with $ \xi $ a positive constant, one has now $ k = k ( t ) = \xi \phi ( t ) $, when $ \phi $ is a positive-definite dilaton scalar field which is monotonically decreasing with time.

As first in this essay, I connected "uncomputability and unpredictability" with quantum consciousness, or more precisely, with a quantum decision. This means that I summarized my old model for quantum consciousness. Then, because consciousness is connected with information and because of panpsychism, I assumed that all physics is information. The essence of all physics is also space, time, and matter. The theory that will explain all this mathematically and will find connections between them is quantum gravity (QG). Because physics should also be information, this theory should be informational and also simple. I represent a scheme of a model for QG. Beside of informational aspect it is important that QG will explain one day, what matter, space, time, and relations between them are. These are mysteries, maybe even larger than consciousness, but probably it is connected with them. Probably, within five years the measurement of the masses of the neutrinos will be done, with it I will check my model for QG. This is also one of the rare measurements that will check some theory of QG.

The tessellation of space is considered for both the 2-sphere and the 3-sphere. As hypothesized in an earlier work, it is found that there is a dark matter density $\Omega_{DM} = 0.284 \pm 0.137$ associated with the curvature of the 3-sphere.

We here present {\bf The Daon Theory} it is the first real Theory of Everything, which means that all fundamental physics is explained, all fundamental constants are calculated, and all results agree with experiments. The explanations are simple and logical since we use 3D+time which leads to easy mathematics. We present here the explanation to all fundamental electromagnetic phenomena: Electricity, Magnetism, Induction, and Electro-Magnetic waves.

The {\bf Daon theory} is a new general theory of physics, it is a completely new way to approach physics and includes, in principle, all phenomena of nature. The theory is presented in a series of closely related papers treating Electromagnetism, Atomic physics, Relativity, Particle physics, Gravitation and Cosmology. The numerical value of the main natural constants and parameters are calculated, while the explanations for the various natural phenomena are simple and logical. All the results from this theory agree, as far as we know, with experimental data. In this part, we present some unknown forces acting within the atoms, giving the explanation to the strange behaviour of the electrons. We present a simulation program (ATOMOL) able to follow all charged particles within an atom, including their velocity, position and energy at any given moment. We explain the electron's associated wave, the fine structure constant, the constant of Planck and we explain and calculate the magnetic moment of the electron and the nucleus.

The {\bf Daon theory} is a new general theory of physics, it is a completely new way to approach physics and includes, in principle, all phenomena of nature. The theory is presented in a series of closely related papers treating Electromagnetism, Atomic physics, relativity, Particle physics, Gravitation and Cosmology. They should be red in this order for a complete understanding. The explanation for the various natural phenomena are simple and logical. All the results from this theory agree, as far as we know, with experimental data. In this document is presented an analysis of changes within an atom at high velocities. It is strongly recommended to first read \cite{1} and \cite{2} of the Daon Theory for a complete understanding.

Quantum gravity traditionally begins with path integrals for four dimensional spacetimes, where the subtlety is in smooth structures. From a motivic perspective, the same diagrams belong to ribbon categories for quantum computation, based on algebraic number fields. Here we investigate this divide using the principle of the neutrino CMB correspondence, which introduces a mirror pair of ribbon diagrams for each Standard Model state. Categorical condensation for gapped boundary systems in extended quantum double models extends the modular structure to encompass Kirby diagrams.

A model of the Universe as a dynamical homogeneous anisotropic self-gravitating fluid, consistent with Kantowski-Sachs homogeneous anisotropic cosmology and Black-Hole cosmology, is developed. Renormalization Group (RG) improved black-hole solutions resulting from Asymptotic Safety in Quantum Gravity are constructed which explicitly $remove$ the singularities at $t = 0$. Two temporal horizons at $ t _- \simeq t_P$ (Planck time) and $ t_+ \simeq t_H$ (Hubble time) are found. For times below the Planck time $ t < t_P$, and above the Hubble time $ t > t_H$, the components of the Kantowski-Sachs metric exhibit a key sign $change$, so the roles of the spatial $z$ and temporal coordinates $ t$ are $exchanged$, and one recovers a $repulsive$ inflationary de Sitter-like core around $ z = 0$, and a Schwarzschild-like metric in the exterior region $ z > R_H = 2 G_o M $. Therefore, in this fashion one has found a dynamical Universe $inside$ a Black Hole whose Schwarzschild radius coincides with the Hubble radius $ r_s = 2 G_o M = R_H$. For these reasons we conclude by arguing that our Universe could be seen as a Gravitating Vacuum State inside a Black-Hole.

Isaac Newton did not invent the gravity constant G, nor did he use it or need it. Newton’s original formula was F = Mm/r^2 and not the formula F = GMm/r^2 , which had evolved over time. Newton’s formula can easily be unified with quantum mechanics, while the modification to his formula can only be unified with quantum mechanics by introducing a very akward notation as shown in this paper. Modern physics indirectly uses two different definitions for mass without knowing it; one for gravity and another for the rest of physics. This, we will prove, has made it impossible to unify quantum mechanics with gravity. However, once we understand the cause of the problem, it can be fixed easily by going back to the key insight given by Newton, which leads to a beautiful simple unified theory, in both conception and notation. Alternatively, one can arrive at the same theory, but with unattractive notation that hides the beauty at the depth of reality. We will show a beautiful way to unify gravity and quantum mechanics and also an ugly way. Both are the essentially the same, but only one way, the Newton inspired way, gives the deep insight on matter, energy, time, space, and gravity and even quantum mechanics. Modern physics has ignored Newton’s insight on matter and altered the mass definition, and therefore Newton’s gravity formula was modified as well, such that a unified theory seemed to become impossible. Newton himself would probably not have approved of the gravity constant; it is a flaw on the foundation of his theory and his gravity formula. Still, when one understands what the gravity constant really represents, one can unify standard physics, by adding it in other places, as needed. As an example of its power, our new quantum gravity theory can predict galaxy rotation based on baryonic matter only. This strongly indicates that dark matter is an extraneous and awkward factor used in today’s standard gravity model in order to get an incomplete model to fit observations.

A brief introduction of the history of Born's Reciprocal Relativity Theory, Hopf algebraic deformations of the Poincare algebra, de Sitter algebra, and noncommutative spacetimes paves the road for the exploration of gravity in $curved$ phase spaces within the context of the Finsler geometry of the cotangent bundle $T^* M$ of spacetime. A scalar-gravity model is duly studied, and exact nontrivial analytical solutions for the metric and nonlinear connection are found that obey the generalized gravitational field equations, in addition to satisfying the $zero$ torsion conditions for $all$ of the torsion components. The $curved$ base spacetime manifold and internal momentum space both turn out to be (Anti) de Sitter type. The most salient feature is that the solutions capture the very early inflationary and very-late-time de Sitter phases of the Universe. A $regularization$ of the $8$-dim phase space action leads naturally to an extremely small effective cosmological constant $ \Lambda_{eff}$, and which in turn, furnishes an extremely small value for the underlying four-dim spacetime cosmological constant $ \Lambda$, as a direct result of a $correlation$ between $ \Lambda_{eff} $ and $ \Lambda$ resulting from the field equations. The rich structure of Finsler geometry deserves to be explore further since it can shine some light into Quantum Gravity, and lead to interesting cosmological phenomenology.

In this short lecture we describe the correspondence between tangles and associahedra tiles, where R occurs in the case of braid tangles, leading to a natural extension to ribbons. Such tangles come from the Temperley-Lieb algebra and were used by Bar-Natan to study Khovanov complexes in nice cobordism categories.

The associahedra appear in a line configuration space for the real Clebsch diagonal surface, which we relate to e6 in the magic star, with applications to mass generation.

According to the unified theory of dynamic space, the first (Universal) and the second (local) deformation of space is described, which change the geometric structure of the isotropic space. These geometric deformations created the dynamic space, the Universe, and the space holes (bubbles of empty space), the early form of matter. The neutron cortex is structured around these space holes with the electrically opposite elementary units (in short: units) at the light speed, as the third deformation of space (electrical and geometric deformation), resulting in the creation of surface electric charges (quarks), to which the particles spin is due. The constant kinetic energy of the particle spin is calculated at 100 million Joule. Thus, a single electron is enough to become the heart of a future energy machine.

In a paper in year 2011 the author implicitly predicted the masses of the neutrinos using some old empirical formulae. Now this prediction is explicitly written, mass of one neutrino is calculated as 21.44240(50) meV, respectively 21.36459(49) meV, dependent of the model. (The other masses of the neutrinos are connected with one of these values.) According to the upper bounds of neutrinos masses in 2005, and respectively in 2019, the author calculates that the upper bound of the lightest neutrino mass approached between 3 times to 20 times to the predicted value in 2019 according to 2005. At the same time, cosmologists predict that in the next five years we will have values of the neutrino masses, not only the lower and upper bounds. Thus this prediction can be tested, and maybe p-value for accident will not be large. Besides, the prediction of the gravitational constant with the same formulae is also mentioned.

This paper develops the theoretical ratio of the gravitational force to electromagnetic force between two electrons. The resulting ratio produces a gravitational constant with the precision of electromagnetic constants.

In quantum logic, the emergence of spacetime and related symmetries goes hand in hand with the emergence of the real and complex numbers themselves. In this paper, we show how finite fields are surprisingly sufficient for most physical questions, once we throw away classical geometrical models in favour of categorical axioms. In particular, generalised Pauli matrix algebras are closely related to braid and ribbon diagrams, and holographic information for mass localisation gains its intuition from algebras for anyon condensation. We discuss definitions of homology and cohomology associated to braids, recalling the twistor construction of massive solutions in H2.

In this new study we want to propose an updated heuristic model to compute and to interpret the dark energy content of our universe. To this purpose we include the mass-energy of the static gravitational field in Newtonian gravity, finding agreement with general relativity at large scales. We then compute its effect at very small distances also including quantum effects. From this analysis, we obtain an estimation of the smallest volume in empty space. Our result is compatible with loop quantum gravity and this enables the embedding in it. After that we show, how this can be used to compute a natural energy cutoff $k_c$ for all quantum fields and study its utility in computing the dark energy density and its implications on the content of fermionic and bosonic elementary fields. Indeed for the vacuum equation of state $w\,{=}\,p_{vac}/\rho_{vac}$ we obtain an expression depending on $\Delta N\,{=}\, N_f - N_b$, which represents the difference between the number of species of fermions and bosons. Finally comparing our result with the measured value of $w$, we discuss general constraints on the field content beyond the Standard Model of the elementary particles.

Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was F = Mm/r and not F = GMm/r. In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is to some degree well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is first when we combine Newton’s observation that matter and light ultimately consist of hard indivisible particles with new insight in atomism that we can truly begin to understand gravity. This leads to a quantum gravity theory that is unified with quantum mechanics where there is no need for G and even no need for Planck’s constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant almost holy and untouchable. Thus we have neglected to see an important aspect of mass, namely the indivisible particle that also Newton held in high regard. Second, we have built our version of quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength.

Haug [1] has recently introduced a new theory of unified quantum gravity coined “collision space-time.” From this new and deeper understanding of mass we can also understand how a grandfather pendulum clock can be used to measure the world shortest time interval, namely the Planck time [2, 3], indirectly. Such a clock can, therefore, also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time.” This basically proves that the Newton gravitational constant is not needed to find the Planck length or the Planck time; it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia in the current physics establishment towards new ideas that could significantly alter our perspective on the fundamentals, but this is not new in the history of science. Still, the idea that the Planck time can be measured totally independent of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics.

Despite the resounding experimental success of the Standard Model, the mystery of neutrino mass and neutrino oscillations must be approached from a framework for quantum gravity. Using well established results in condensed matter physics and in motivic mathematics, we present a new view of the quantum vacuum based on neutrino braid diagrams in quantum computation. The prediction of an effective 1.29 eV non local sterile state from the Koide matrix for neutrino masses fits known observational constraints.

This paper reproduces the dynamics of quantum mechanics with a four-dimensional spacetime manifold that is branched and embedded in a six-dimensional Minkowski space. Elementary fermions are represented by knots in the manifold, and these knots have the properties of the familiar particles. We derive a continuous model that approximates the behavior of the manifold's discrete branches. The model produces dynamics on the manifold that corresponds to the gravitational, strong, and electroweak interactions.

An alternative physical model for fundamental particles, fundamental forces & black holes is presented based on classical physics, an unconventional variant of quantum physics as well as holographic & fractal principles whereby the presented model is primarily based on work from Horst Thieme and Nassim Haramein. In this document their models are combined, refined and extended into a joint model that is wider in scope and which also adopts some elements from the work of Randell Mills and Erik Verlinde. The deduced equations produce a good number of interesting results and new understandings which might be perceived as controversial, though, with regard to contemporary physics. The presented content covers a broad range of topics in physics to demonstrate the model’s wide applicability and to spark more future research. In particular it is shown that entropy plays an even larger and more fundamental role in physics than currently acknowledged and that the Planck units are more than an arbitrary system of units.

From the holographic perspective in quantum gravity, topological field theories like Chern-Simons are more than toy models for computation. An algebraic construction of the CFT associated to Witten's j-invariant for 2+1 dimensional gravity aims to compute coefficients of modular forms from the combinatorics of quantum logic, dictated by axioms in higher dimensional categories, with heavy use of the golden ratio. This paper is self contained, including introductory material on lattices, and aims to show how the Monster group and its infinite module arise when the automorphisms of the Leech lattice are extended by special point sets in higher dimensions, notably the 72 dimensional lattice of Nebe.

A study of the simplest Jordan-Brans-Dicke-like action within the context of Weyl geometry, combined with the findings of Weinberg’s Asymptotic Safety program in quantum gravity, leads to a plethora of nice numerical results : (i) like singling out the quartic potential from all the others; (ii) having (Anti) de Sitter space as the most natural solution; (iii) furnishing the value of the observed vacuum energy density at the Hubble scale (3/8 pi G_N R_H^2) ~ 10^{−122} M_P^4 ; (iv) and a value of {3/8 pi) M^4_P for the vacuum energy density at the Planck scale; (v) interpreting the “Bang” of the Big Bang as the singularity of the Weyl gauge field of dilations at t = 0 ushering in the era of inflation, and (vi) allowing the possibility that our universe is a Black Hole whose horizon coincides with the cosmological Hubble horizon. It is warranted to explore deeper the interplay among Weyl geometry, Asymptotic safety and Maldacena’s AdS/CFT correspondence (holographic renormalization group flow). Also relevant is the work by Wetterich on the role of dilatation symmetry in higher dimensions and the vanishing of the cosmological constant. Last, but not least, we should also consider the implications of Penrose’ Conformal Cyclic Cosmology and Nottale’s Scale Relativity Theory with the key findings of this work.

The independent E/M waves are created, during the electron oscillations at an emission antenna. These waves do not compose the constant photon length, in contrast to the fundamental E/M waves of photon. Additionally, the Compton phenomenon is interpreted, while the atomic orbitals are standing waves the self-superposition of the motion wave of electrons.

We have recently presented a unified quantum gravity theory [23]. Here we extend on that work and present an even simpler version of that theory. For about hundred years, modern physics has not been able to build a bridge between quantum mechanics and gravity. However, a solution may be found here; we present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision space-time, which is equivalent to mass and energy. The beauty of our theory is that most of the main equations that currently exist in physics are not changed (in terms of predictions), except at the Planck scale. The Planck scale is directly linked to gravity and gravity is, surprisingly, actually a Lorentz symmetry as well as a form of Heisenberg uncertainty break down at the Planck scale. Our theory gives a dramatic simplification of many physics formulas without altering the output predictions. The relativistic wave equation, the relativistic energy momentum relation, and Minkowski space can all be represented by simpler equations when we understand mass at a deeper level. This not attained at a cost, but rather a reflection of the benefit in having gravity and quantum mechanics unified under the same theory.

This paper presents a model that bridges the gap between general relativity and quantum mechanics by providing a new understanding of space and time. The core principle of this formulation is impermanence, the fact that energy is never static, which has non-obvious consequences at the quantum level and leads to a formulation of quantum gravity. The results allow for a new interpretation of black holes and a resolution of the black hole information paradox. The model also presents the causes leading to the Big Bang as well as the Universe evolution, offering a new perspective on galaxy formation and a natural explanation to the origin of dark matter, dark energy and the matter-antimatter asymmetry.

Gravity is currently understood as a space-time curvature. If gravity was a force, it quantization would be much easier. Then what if gravity was a force able to bend space-time? We will see that gravity can be seen as such and what it would imply. We’ll then derive a new space-time bending equation thanks to a new principle equivalent to Einstein’s Equivalence Principle in low intensity fields. Thanks to quantum mechanics studies in curved space-time we can then blend gravity in quantum mechanics in a coherent way. Eventually, we'll see that applying these principles to cosmology, we can explain what we current call Dark Energy.

Based on a very simple model where mass, at the deepest level, is colliding indivisible particles and energy is indivisible particles not colliding, we get a new and simple model of matter that seems to be consistent with experiments. Gravity appears to be directly linked to collision time and also the space the collisions take up; we could call it collision space-time. This leads to a completely new quantum gravity theory that is able to explain and predict all major gravity phenomena without any knowledge of Newton’s gravitational constant or the mass size in the traditional sense. In addition, the Planck constant is not needed. Our model, combined with experimental data, strongly indicates that matter is granular and consists of indivisible particles that are colliding. Further, from experiments it is clear that the diameter of the indivisible indivisible particle is the Planck length. Our theory even predicts that there can be no time dilation in quasars, something that is consistent with observations and yet is inconsistent with existing gravity theories. Several modern quantum gravity models indicate that Lorentz symmetry is broken at the Planck scale, but there have been no signs of this occurring, despite extensive efforts to look for Lorentz symmetry break downs. We show that Lorentz symmetry break downs indeed happen and, to our own surprise, this is actually very easy to detect. In our model, it is clear that Lorentz symmetry break down is gravity itself. This seems contradictory, as Planck energies are very high energy levels, but we show that this must be seen in a new perspective. We also introduce a new quantum wave equation that tells us that gravity is both Lorentz symmetry break down and Heisenberg uncertainty break down at the Planck scale. Our wave equation in this sense includes gravity. For masses smaller than a Planck mass, probability will also dominate gravity; it is then a probability for Heisenberg uncertainty break down. At the Planck mass size and up, determinism dominates. For the first time, we have a quantum theory that unifies gravity with the quantum, all derived from a very simple model about the quantum. Our theory is simple, and we show that an indivisible particle is the fundamental unit of all mass and energy – a quantity that has been missing in physics all this time. Newton was one of the last great physicists who thought that such particle was essential, but it was naturally impossible for one man to solve the entire problem. This paper stands on the shoulders of giants like Newton, Einstein, Planck, and Compton to explore these long-standing questions. The beauty of our theory is that it keeps almost all existing and well-tested equations completely intact (unchanged) all the way to the Planck scale. Anything else would be a surprise; after all, some areas of physics have been extremely successful in predictions and have also been well-tested. Still, in our work, the Planck scale and all equations are united into one simple and powerful theory. Unlike standard physics, there are no inconsistencies in our theory. QM is unified with gravity, and even a simplified version of the Minkowski space- time is consistent with QM and gravity. A long series of mysteries in QM vanish, under our new interpretation.

A relation like Hubble equation is derived on a $(1+1)$-dimensional brane moving in the $AdS_{1+2}$-kerr space-time. The relation is used to obtain a Cardy-Verlinde formula on the brane.

We consider the string, the left end of which is fixed and the right end of the string is in periodic motion. We derive the quantum internal motion of this system.

The argument that modern string theory has become lost in math is compelling, controversial, and ever more timely. A perspective arguably of equal compulsion takes the view that the math is just fine, that string theory has become lost in physics. It's all about the wavefunction. Almost a century after Bohr and Copenhagen, ongoing proliferation of conflicting quantum interpretations of the unobservable wavefunction and its interactions attests to the profound confusion in philosophical foundations of basic quantum physics. Taking the octonion wavefunction to be comprised not of one-dimensional oscillators in eight-dimensional space, but rather the eight fundamental geometric objects of the Pauli algebra of 3D space - one scalar, three vectors, three bivector pseudovectors, and one trivector pseudoscalar - yields a long overdue and much needed coherent phenomenology.

The experimental search of standard model superpartners, and the derivation of the standard model from higher dimensional theories have been challenging for some time now. In this article these technologies are kept but they are applied to a simpler environment. A coherent scenario of particles based on Kaluza-Klein theory and unbroken supersymmetry is proposed. It offers an economic basis for constructing the standard model particles without the superpartner problem of the minimal supersymmetric standard model. With local supersymmetry one arrives at supergravity without Yang-Mills fields. A number of results in the literature would have to be reconsidered according to this model.

Here, the fundamental constants namely vacuum permeability and permittivity, which comprise the numerical definition of the speed of light in vacuum, are determined. They are found to be composites correlated to Planck’s constant, Wien’s constant and the mass energy of the cosmic microwave background. Derivations for both a new fundamental composite speed of light in vacuum and vacuum impedance are performed. Furthermore, this newly suggested definition is correlated to a confined quantized radiation spectrum of the cosmic particle horizon.

After a brief review of the thermal relativistic $corrections$ to the Schwarzschild black hole entropy, it is shown how the Stefan-Boltzman law furnishes large modifications to the evaporation times of Planck-size mini-black holes, and which might furnish important clues to the nature of dark matter and dark energy since one of the novel consequences of thermal relativity is that black holes do $not$ completely evaporate but leave a Planck size remnant. Equating the expression for the modified entropy (due to thermal relativity corrections) with Wald's entropy should in principle determine the functional form of the modified gravitational Lagrangian $ {\cal L } (R_{abcd}) $. We proceed to derive the generalized uncertainty relation which corresponds to the effective temperature $ T_{eff} = T_H ( 1 - { T^2_H \over T^2_P } )^{ - 1/2} $ associated with thermal relativity and given in terms of the Hawking ($T_H$) and Planck ($T_P$) temperature, respectively. Such modified uncertainty relation agrees with the one provided by string theory up to first order in the expansion in powers of $ { (\delta p)^2 \over M^2_P} $. Both lead to a minimal length (Planck size) uncertainty. Finally, an explicit analytical expression is found for the modifications to the purely thermal spectrum of Hawking radiation which could cast some light into the resolution of the black hole information paradox.

The quest to unify the four fundamental forces has been sought after for decades but has remained elusive to all physicists. The first clues to unification were given when information horizons were associated to radiation by Unruh and Hawking. This was then extended to be a discrete spectrum in nature by McCulloch. Here, it is suggested that the limitation, or confinement, of an allowed spectrum is relevant in order to compute all the fundamental forces. The maximum spectrum is defined by the size of the cosmic particle horizon and the Planck length. Notably, all fundamental forces can be computed by using the same core equation and can be extended to reflect the different information horizons and particle interaction scenarios. This result suggests that for unification, the radiation spectrum provides momentum space alterations to generate energy gradients. The force derivatives of the energy fields indicate numerical convergence to the observed fundamental forces.

We investigate the Friedmann equations and the Wheeler-DeWitt equations in three dimensional pure gravity under the Generalized Uncertainty Principle (GUP) effects. In addition we study the wave functions near the Big-Bang singularity as the solutions of the deformed Wheeler-DeWitt equation in momentum space. The resulting wave functions are represented as the Mathieu functions. The GUP is considered in the context of the Snyder non-commutative space.

A scenario of particles with unbroken supersymmetry has been proposed recently, a supersymmetric preon model. It offers an economic basis for constructing the standard model particles and going beyond it to supergravity. The model predicts that the standard model's superpartners do not exist in nature. The article is largely a review of selected papers. The model is tentatively explored towards quark and lepton structure. The supersymmetric Wess-Zumino and Starobinsky type of models of inflation are discussed. Both are found to agree well with the Plank 2018 CMB data, thus giving experimental support to supersymmetry on an energy scale of $10^{13}$ GeV. Some future directions are hinted.

Causality is the fundamental principle in the Einstein's theory of general relativity. We consider the theory of broken causality by the assumptions of stochastic nature to causal process. We see that the causality breaking of stochastic property brings the general relativity of broken causality, and this is equivalent to the theory of quantum gravity. We investigate some properties of quantum gravity in relation to the holographic principle. We calculate Shannon's entropy. In those investigations, we see the appearance of holographic principle at the first order in expansion of perturbation theory. The result indicates that the theory of stochastic causality, that we established, is the non-perturbative theory of quantum gravity.

The following derivation shows that the neutrino mass effectively replaces the Planck mass as a fundamental particle associated to Newton's Gravity Law. The neutrino mass is deduced from the cosmic microwave background and matches a previous obtained experimental value. Using a ratio of forces between two Planck mass pairs in comparison to two neutrino pairs, a proportion to the dimension of the Planck length and a Rindler horizon is formed. The work done on the two pairs are equivalent using this proportion. Additionally, it has been concluded that the cosmic diameter, as a particle horizon, can be written in terms of fundamental constants using Wien's displacement law and the Cosmic Microwave Background temperature.

Starting with a brief description of Born's Reciprocal Relativity Theory (BRRT), based on a maximal proper-force, maximal speed of light, inertial and non-inertial observers, we derive the $exact$ Thermal Relativistic $corrections$ to the Schwarzschild, Reissner-Nordstrom, Kerr-Newman black hole entropies, and provide a detailed analysis of the many $novel$ applications and consequences to the physics of black holes, quantum gravity, minimal area, minimal mass, Yang-Mills mass gap, information paradox, arrow of time, dark matter, and dark energy. We finalize by outlining our proposal towards a Space-Time-Matter Unification program where matter can be converted into spacetime quanta, and vice versa.

In this short memorandum, the curvature and dimension properties of the $2$-sphere surface of a 3-dimensional ball and the $2.x$-dimensional surface of a 3-dimensional fractal set are considered. Tessellation is used to approximate each surface, primarily because the $2.x$-dimensional surface of a 3-dimensional fractal set is otherwise non-differentiable (having no well-defined surface normals). It is found that the curvature of a closed surface {\it must} lead to fractional dimension. Notes are then given, including how this tessellation model applies to a toy Universe.

Important polytope sequences, like the associahedra and permutohedra, contain one object in each dimension. The more particles labelling the leaves of a tree, the higher the dimension required to compute physical amplitudes, where we speak of an abstract categorical dimension. Yet for most purposes, we care only about low dimensional arrows, particularly associators and braiding arrows. In the emerging theory of motivic quantum gravity, the structure of three dimensions explains why we perceive three dimensions. The Leech lattice is a simple consequence of quantum mechanics. Higher dimensional data, like the e8 lattice, is encoded in three dimensions. Here we give a very elementary overview of key data from an axiomatic perspective, focusing on the permutoassociahedra of Kapranov.

According to the unified theory of dynamic space the inductive-inertial phenomenon and its forces has been developed. These forces act on the electric units of the dynamic space, forming the grouping units (namely electric charges or forms of the electric field). So, by this inductive phenomenon and the phenomenon of motion the wave function will be calculated. This wave function, which essentially interprets the phenomena of motion waves replaces the Schrödinger's equation.

The report summarizes the current state of research of quantino-theory, which is an approach to explain fundamental physical phenomena based on Weber electrodynamics. The core concept of quantino-theory is a force-carrier model, which fulfils the postulates of special relativity without the spacetime. The field theory that follows out of this model does not turn for slow charge-carrier velocities into Maxwell electrodynamics but Weber electrodynamics. Based on the quantino-mechanism, numerous physical effects can be reinterpreted and explained. For example, it is possible to show that gravity is a thermodynamic electromagnetic relativistic effect of fourth order. Furthermore, quantino-theory seems to be an interesting approach to explain the reason for the existence of quantum mechanical effects, inertia and anti-matter. The report furthermore discusses the perihelion precession of the planet Mercury, the mass-energy-relation, photons and electromagnetic waves.

In the article, with the help of various models, the thesis about the fundamental nature of the field form of matter as the basis of elementary particles is considered. In the first chapter a model of special relativity is constructed, on the basis of which the priority of the massless form of matter is revealed. In the second chapter a field model of inert and heavy mass is constructed and the mechanism of inertness and gravity of weighty bodies is revealed. In the third chapter, the example of geons shows the fundamental nature of a massless form of matter on the Planck scale. The three-dimensionality of the observable space is substantiated. In the fourth chapter, we consider a variant of solving the problem of singularities in general relativity using the example of multidimensional spaces. The last chapter examines the author's approach to quantum gravity. The conclusions do not contradict the main thesis of the article on the fundamental nature of the massless form of matter.

We review briefly how {\bf R} $\otimes$ {\bf C} $\otimes$ {\bf H} $\otimes$ {\bf O}-valued Gravity (real-complex-quaterno-octonionic Gravity) naturally can describe a grand unified field theory of Einstein's gravity with a Yang-Mills theory containing the Standard Model group $SU(3) \times SU(2) \times U(1)$. In particular, the $ C \otimes H \otimes O$ algebra is explored deeper. It is found that it can furnish the gauge group {\bf [SU(4)]}$^4$ revealing the possibility of extending the Standard Model by introducing additional gauge bosons, heavy quarks and leptons, and a $fourth$ family of fermions with profound physical implications. An analysis of $ C \otimes H \otimes O$-valued gravity reveals that it bears a connection to Nonsymmetric Kaluza-Klein theories and complex Hermitian Matrix Geometry. The key behind these connections is in finding the relation between $ C \otimes H \otimes O$-valued metrics in $two$ $complex$ dimensions with metrics in $higher$ dimensional $real$ manifolds ($ D = 32 $ real dimensions in particular). It is desirable to extend these results to hypercomplex, quaternionic manifolds and Exceptional Jordan Matrix Models.

A physical approach to a category of motives must account for the emergent nature of spacetime, where real and complex numbers play a secondary role to discrete operations in quantum computation. In quantum logic, the cardinality of a set is initially replaced by a dimension of a linear space, making contact with the increasing dimensions in an operad. The operad of associahedra governs tree level scattering, and is closely related to the permutohedra and cube tiles, where cube vertices can encode components of a spinor in higher dimensional octonionic approaches. A study of rest mass generation begins with the cosmological infrared scale, set by the neutrino masses, and its related see-saw mechanism. We employ the anyonic ribbon spectrum for Standard Model states, and consider its relation to magic star algebras, giving a context for the Koide rest mass phenomenology of charged leptons and quarks.

We suggest united models and specific predictions regarding elementary particles, dark matter, dark energy, aspects of the cosmology timeline, and aspects of galaxy evolution. Results include specific predictions for new elementary particles and specific descriptions of dark matter and dark energy. Some modeling matches known elementary particles and extrapolates to predict other elementary particles, including bases for dark matter. Some models complement traditional quantum field theory. Some modeling features Hamiltonian mathematics and originally de-emphasizes motion. We incorporate results from traditional motion-centric and action-based Lagrangian math into our Hamiltonian-centric framework. Our modeling framework features mathematics for isotropic quantum harmonic oscillators.

It is argued how {\bf R} $\otimes$ {\bf C} $\otimes$ {\bf H} $\otimes$ {\bf O}-valued Gravity (real-complex-quaterno-octonionic Gravity) naturally can describe a Grand Unified Field theory of Einstein's gravity with a Yang-Mills theory containing the Standard Model group $SU(3) \times SU(2) \times U(1)$. In particular, it leads to a $[SU(4)]^4$ symmetry group revealing the possibility of extending the standard model by introducing additional gauge bosons, heavy quarks and leptons, and an extra $fourth$ family of fermions. We finalize by displaying the analog of the Einstein-Hilbert action for ${\bf R} \otimes {\bf C} \otimes {\bf H} \otimes {\bf O}$-valued gravity via the use of matrices, and which is based on ``coloring" the graviton; i.e. by attaching internal indices to the metric $g_{\mu \nu}$. In the most general case, $U(16)$ arises as the isometry group, while $U(8)$ is the isometry group in the split-octonion case.

According to the unified theory of dynamic space, the inductive-inertial phenomenon and its forces has been developed. These forces act on the electric units of the dynamic space, forming the grouping units (namely electric charges or forms of the electric field). The nature of the magnetic forces is explained, that are Coulomb's electric forces between these grouping units, created by the accelerated electron. So, Coulomb's Law for magnetism, the physical signicance of magnetic quantities and the so called strangeness of the fluctuation of nucleons magnetic dipole moment are interpreted. Additionally, due to in-phase motion of grouping units, a parallel common course of their electrons and a superposition picture of their motion waves are caused as in the double-slit experiment is displayed.

According to Noether's theorem, for every differentiable symmetry of action, there exists a corresponding conserved quantity. If we assume the stationary condition as a role of symmetry, there is a conserved quantity. By using the definition of the Komar mass, one can calculate the mass in a curved spacetime. If we consider charge as a conserved quantity, it means existence of symmetry, and we can consider one more axis. In this paper, we consider an extension to five dimensions by using results of the ADM formalism. In terms of (4+1) decomposition, with an alternative surface integral, we find the rotating and charged five-dimensional metric solution and check whether it gives the mass, charge, and angular momentum exactly.

The two-parameter quantum calculus used in the construction of Fibonacci oscillators is briefly reviewed before presenting the $ (p, q)$-deformed Lorentz transformations which leave invariant the Minkowski spacetime interval $ t^2 - x^2 - y^2 - z^2$. Such transformations require the introduction of three different types of exponential functions leading to the $(p, q)$-analogs of hyperbolic and trigonometric functions. The composition law of two successive Lorentz boosts (rotations) is $no$ longer additive $ \xi_3 \not= \xi_1 + \xi_2$ ( $ \theta_3 \not= \theta_1 + \theta_2$). We finalize with a discussion on quantum groups, noncommutative spacetimes, $\kappa$-deformed Poincare algebra and quasi-crystals.

According to the theory of dynamic space the inductive-inertial phenomenon and its forces will be developed, which act on the electric units of the dynamic space, forming the grouping units (namely electric charges or forms of the electric field). So, the nature of the magnetic forces is explained, that are Coulomb's electric forces between these grouping units, created by the accelerated electron. Additionally, it is proved the so called de Broglie's wave-particle is a motion wave (wave-like form) as a result the dynamics of the extremely fine texture of the particle motion.

A fundamental conservation and symmetry is proposed, as a unification between General Relativity (GR) and Quantum Theory (QT). Unification is then demonstrated across multiple applications. First, as applied to cosmological redshift z and energy density ρ. Then, a local system galaxy rotational curve is examined. Next, as applied to Quantum Mechanics’ ”time problem”: Absolute and relative notions of time are shown to be reconcilable, as well as renormalization values between scales. Finally, as applied to the Cosmological Constant: The discrepancy that exists between the vacuum energy density in GR at critical density: ρcr = 3H^2/8πG=1.88(H^2)x10−29g/cm^3, and the much greater zero-point energy delta value as calculated in quantum field theory (QFT) with a Planck scale ultraviolet cutoff: ρhep = M4c^3/h^3 =2.44x1091g/cm^3 is resolved to null orders of magnitude.

We revisit the construction of diffeomorphic but $not$ isometric solutions to the Schwarzschild metric. The solutions relevant to Black Holes are those which require the introduction of non-trivial areal-radial functions that are characterized by the key property that the radial horizon's location is $displaced$ continuously towards the singularity ($ r = 0 $). In the limiting case scenario the location of the singularity and horizon $merges$ and any infalling observer hits a null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the firewall problem and the complementarity controversy in black holes. Next we show how modified Newtonian dynamics (MOND) can be obtained from solutions to Finsler gravity, and which in turn, can also be modeled by metrics which are diffeomorphic but not isometric to the Schwarzschild metric. The key point now is that one will have to dispense with the asymptotic flatness condition, by choosing an areal radial function which is $finite$ at $ r = \infty$. Consequently, changing the boundary condition at $ r = \infty$ leads to MONDian dynamics. We conclude with some discussions on the role of scale invariance and Born's Reciprocal Relativity Theory based on the existence of a maximal proper force.

A brief tour of the developments of the Extended Relativity Theory in Clifford Spaces ($C$-space) is presented. These include : (i) Novel physical consequences like generalized dispersion relations, energy-dependent speed of light propagation, extended Lorentz transformations, relative locality, generalized Weyl-Heisenberg algebra and uncertainty relations, tensionless branes, superluminality, generalized velocities. (ii) Generalized areal, volume, $\cdots$ metrics and gravitational field equations in $C$-space. (iii) A unified description of particles, strings and branes. (iv) Clifford gravity based cosmology and dark energy. (v) Moyal deformations of Clifford gauge theories of gravity. (vi) N-ary algebras. We conclude with a brief discussion on symplectic Clifford algebras and generalized geometries.

The experimental fact that standard model superpartners have not been observed compels one to consider an alternative implementation for supersymmetry. The basic supermultiplet proposed here consists of a photon and a charged spin 1/2 preon field, and their superpartners. These fields are shown to yield the standard model fermions, Higgs fields and gauge symmetries. Supersymmetry is defined for unbound preons only. Quantum group SLq(2) representations are introduced to classify topologically scalars, preons, quarks and leptons.

In 2014, McCulloch showed, in a new and interesting way, how to derive a gravity theory from Heisenberg's uncertainty principle that is equivalent to Newtonian gravity. McCulloch utilizes the Planck mass in his derivation and obtains a gravitational constant of hbar*c/m_p^2. This is a composite constant, which is equivalent in value to Newton's gravitational constant. However, McCulloch has pointed out that his approach requires an assumption on the value of $G$, and that this involves some circular reasoning. This is in line with the view that the Planck mass is a derived constant from Newton's gravitational constant, while big G is a universal fundamental constant. Here we will show that we can go straight from the McCulloch derivation to measuring the Planck mass without any knowledge of the gravitational constant. From this perspective, there are no circular problems with his method. This means that we can measure the Planck mass without Newton's gravitational constant, and shows that the McCulloch derivation is a theory of quantum gravity that stands on its own. And further we show that we can easily measure the Schwarzschild radius of a mass without knowing its mass, or Newton's gravitational constant, or the Planck constant. The very essence of gravity is linked to the Planck length and the speed of light, but here we will claim that we do not need to know the Planck length itself. Our conclusion is that Newton's gravitational constant is a universal constant, but it is a composite constant of the form G=l_p^2*c^3/hbar where the Planck length and the speed of light are the keys to gravity. This could be an important step towards the development of a full theory of quantum gravity.

In this short paper we look at the Hawking temperature from a Newtonian perspective as well as a General Relativity perspective. If we are considering the Hawking temperature, and simply replace the gravitational field input in his 1974 formula with that of Newton, we will get a Hawking temperature of half of that of the well-known Hawking temperature formula. This is very similar to the case where Newton’s theory predicts half the light bending that GR does. Based on recent theoretical research on Newton’s gravitational constant, we also rewrite the Hawking temperature to give a somewhat different perspective without changing the output of the formula, that makes some of the Hawking formulas more intuitive.

In this paper we suggest that through working with the Planck mass and its link to other particles in a simple way, it possible to “convert” the Heisenberg uncertainty principle into a very simple quantum probabilistic model. We further combine this with key elements from special relativity theory and get an interesting quantum relativistic probability theory. Some of the key points presented here could help to eliminate negative and above unity (pseudo) probabilities that often are used in standard quantum mechanics. These fake probabilities may be rooted in a failure to understand the Heisenberg principle fully in relation to the Planck mass. When properly understood, the Heisenberg principle seems to give a probabilistic range of quantum probabilities that is sound. There are no instantaneous probabilities and the maximum probability is always unity. In our formulation, the Planck mass particle is always related to a probability of one. Thus, we have certainty at the Planck scale for the Planck mass particle, or for particles accelerated to reach Planck energy. We are also presenting a relativistic extension of the McCulloch Heisenberg-derived Newton equivalent gravity theory. Our relativistic version requires much less mass than the Newtonian theory to explain gravitational phenomena, and initial investigation indicates it is consistent with perihelion of Mercury.

Here we will present a probabilistic quantum gravity theory derived from Heisenberg’s uncertainty principle. Surprisingly, this theory is fully deterministic when operating with masses that are exactly divisible by the Planck mass. For masses or mass parts less than one Planck mass, we find that probabilistic effects play an important role. Most macroscopic masses will have both a deterministic gravity part and a probabilistic gravity part. In 2014, McCulloch derived Newtonian gravity from Heisenberg’s uncertainty principle. McCulloch himself pointed out that his theory only seems to hold as long as one operates with whole Planck masses. For those who have studied his interesting theory, there may seem to be a mystery around how a theory rooted in Heisenberg’s principle, which was developed to understand quantum uncertainty, can give rise to a Newtonian gravity theory that works at the cosmic scale (which is basically deterministic). However, the deeper investigation introduced here shows that the McCulloch method is very likely correct and can be extended to hold for masses that are not divisible by the Planck mass, a feature that we describe in more detail here. Our extended quantum gravity theory also points out, in general directions, how we can approach the set up of experiments to measure the gravitational constant more accurately.

The $nonlinear$ Bohm-Poisson-Schroedinger equation is studied further. It has solutions leading to $repulsive$ gravitational behavior. An exact analytical expression for the observed vacuum energy density is obtained. Further results are provided which include two possible extensions of the Bohm-Poisson equation to the full relativistic regime. Two specific solutions to the novel Relativistic Bohm-Poisson equation (associated to a real scalar field) are provided encoding the repulsive nature of dark energy. One solution leads to an exact cancellation of the cosmological constant, but an expanding decelerating cosmos; while the other solution leads to an exponential accelerated cosmos consistent with a de Sitter phase, and whose extremely small cosmological constant is $ \Lambda = { 3 \over R_H^2}$, consistent with current observations. We conclude with some final remarks about Weyl's geometry.

Mike McCulloch has derived Newton's gravity from Heisenberg's uncertainty principle in a very interesting way that we think makes great sense. In our view, it also shows that gravity, even at the cosmic (macroscopic) scale, is related to the Planck scale. Inspired by McCulloch, in this paper we are using his approach to the derivation to take another step forward and show that the gravitational constant is not always the same, depending on whether we are dealing with light and matter, or matter against matter. Based on certain key concepts of the photon, combined with Heisenberg's uncertainty principle, we get a gravitational constant that is twice that of Newton's when we are working with gravity between matter and light, and we get the (normal) Newtonian gravitational constant when we are working with matter against matter. This leads to a very simple theory of quantum gravity that gives the correct prediction on bending of light, i.e. the same as the General Relativity theory does, which is a value twice that of Newton's prediction. One of the main reasons the theory of GR has surpassed Newton's theory of gravitation is because Newton's theory predicts a bending of light that is not consistent with experiments.

In this paper we propose a new and simple theory of quantum gravity, inspired by Newton, that gives the same prediction of light bending as Einstein’s theory of general relativity. This new quantum gravity theory also predicts that non-light beams, that is to say beams of particles with rest-mass such as electron and proton beams, will only have half the bending of light as GR. In other words, this theory is testable. Based on this theory, we will suggest that it is a property of light that makes it bend twice as much as the amount that is predicted by Newton’s theory. This quantum gravity theory also seems to predict that for masses below the Planck mass, we are dealing with quantum probabilities and gravity force expectations. This may explain the difference between the strong and weak force – the difference is simply related to a probability factor at the Planck time scale. We are also suggesting a minor adjustment to the Newtonian gravitational acceleration field, which renders that field equal to the Planck acceleration at the Schwarzschild radius, and gives the same results as predicted by Newton when we are dealing with weak gravitational fields. This stands in contrast to standard Newtonian theory, which predicts a very weak gravitational acceleration field at the Schwarzschild radius for super-massive ob jects.

Born's Reciprocal Relativity Theory (BRRT) based on a maximal proper-force, maximal speed of light velocity, inertial and non-inertial observers is re-examined in full detail. Relativity of locality and chronology are natural consequences of this theory, even in flat phase space. The advantage of BRRT is that Lorentz invariance is preserved and there is no need to introduce Hopf algebraic deformations of the Poincare algebra, de Sitter algebra, nor noncommutative spacetimes. After a detailed study of the notion of $generalized$ force, momentum and mass in phase space, we explain that what one may interpret as ``dark matter'' in galaxies, for example, is just an effect of observing ordinary galactic matter in $different ~accelerating$ frames of reference than ours. Explicit calculations are provided that explain these novel relativistic effects due to the $accelerated$ expansion of the Universe, and which may generate the present-day density parameter value $ \Omega_{DM} \sim 0.25 $ of dark matter. The physical origins behind the numerical coincidences in Black-Hole Cosmology are also explored. We finalize with a rigorous study of the curved geometry of (co) tangent bundles (phase space) within the formalism of Finsler geometry, and provide a short discussion on Hamilton spaces.

The author shows examples where his opinion about fundamentality is different as opinion of the majority of physicists. He claims that special relativity alone gives that time runs only in rest matter. He claims that absolutely empty spacetime without rest matter cannot exist; one reason is also because time runs only in rest matter. Existence of dimensionless masses of the elementary particles also tells us about coupling between rest matter and spacetime. Dimensionless masses of the elementary particles are obtained when the masses of the elementary particles are combined with the gravitational constant, Planck's constant and the speed of light. The author insists that the principle of equivalence remains also in quantum physics, and that gravitational uncertainty principle is simple. Consciousness is still more fundamental than the elementary particles, but consciousness does not exist outside of elementary particles. The author advocates quantum consciousness, free-will, and suggests how to verify this experimentally.

In this paper we uncover the true power of Newton’s theory of gravity. Did you know that hidden inside Newton’s gravity theory is the speed of gravity, namely c? Physicists who claim that Newton’s gravitational force is instantaneous have not yet understood Newton’s gravity theory to its full extent. Did you know that the Newton’s theory of gravity, at a deeper level, is actually a theory of quantum gravity? Did you know that what is central for gravity is the Planck length and not the gravitational constant? To truly understand Newtonian gravity, we have to understand that Newton’s gravitational constant is actually a composite constant. Once we understand this, we will truly begin to understand what Newton’s theory of universal gravitation is all about.

We revisit the solutions to the nonlinear Bohm-Poisson (BP) equation with relevant cosmological applications. In particular, we obtain an exact analytical expression for the observed vacuum energy density and explain the origins of its repulsive gravitational nature. Further results are provided which include two possible extensions of the Bohm-Poisson equation to the full relativistic regime; how Bohm's quantum potential in four-dimensions could be re-interpreted as a gravitational potential in five-dimensions, and which explains why the presence of dark energy/dark matter in our 4D spacetime can only be inferred indirectly, but not be detected/observed directly. Solutions to the novel Bohm-Poisson-Schroedinger equation are provided encoding the repulsive nature of dark energy (repulsive gravity). We proceed with a discussion on Asymptotic safety, matter creation from the vacuum, and Finsler relativistic extensions of the Bohm-Poisson equation. Finally, we conclude with some comments about the Dirac-Eddington large numbers coincidences.

The primary consideration of this unifying field theory is the partial mapping of topology, within observations, as feedback loops. Specifically, the effective degrees of freedom (d.o.f.) resulting from such recursive exchanges. This modeling of observation as partial mapping seems well justified, as it is ubiquitous throughout nature's exchanges and propagation of information. Consider how the meridians of gnomonic projected light waves onto vision receptors are similarly distorted. Thus, PVRL extrapolates this same principle of constraining parameters in recursive feedback loops into the entire scope from QFT, (at flashpoint), to GR. PVRL proposes a multispace of transitioning Rn vector fields (similar to Hilbert space), coexisting like wavelengths in a prism. Progressing from quantum states, which are higher dimensional, outward to lower dimensional Macrospace (Note that backward causation is possible in quantum mechanics, but not possible in the constrained parameters of classic mechanics or GR). Familiar classic R4 spacetime is just one phase of this multispace. The mechanism which delineates between each state is PVRL: An iterated process of conscious binary gnomonic mapping of higher dimensional topology onto biased eigenstates. (and subsequent propagation within the quantum field). At each iteration, symmetry becomes more broken, and geometric parameters become more constrained (Polarity, bonding, separation, alignment and propagation). The inevitable outcome of such recursive feedback loops is a power law distribution (exponential tail), with increased entropy and complexity The resolution of the Cosmological Constant Problem is an understanding that scales approaching QFT are viewed in higher dimensional divergence, and that scales approaching GR are viewed in lower dimensional convergence. A Transitioning Rn space, from R5 at microscales, outward to R3 at the cosmic event horizon, with R4 spactime as an intermediate phase.

The author attempts to unify General Relativity with Quantum Mechanics. This involves the use of the Cartesian Axes as the building blocks of reality. A certain set is employed and this permeates the content of the article. The author can be contacted at jpeel01@hotmail.com.

The elementary algebra underlying the non local neutrino hypothesis is used to explain discrepancies in the value of Hubble's constant in terms of other physical constants, in the approximation of the R=ct semiclassical cosmology with Mach's principle. It is assumed that quantum gravity breaks the equivalence principle, in conjunction with a quantum Higgs mechanism, and this new view of the electroweak vacuum indicates an absence of dark matter and dark energy. We introduce mass quantisation in the Brannen-Koide scheme in this context.

Evolution of our universe with continuous production of matter by the vacuum, is described. The analysis is based on the quantum modification of the general relativity (Qmoger), supported by the cosmic data without fitting. Various types of matter are selected by the vacuum in accordance with stability of the developing universe. All laws of nature are emergent and approximate, including the conservation of energy. The (3+1)-dimensional space-time and gravity were selected first. Than came quantum condensate of gravitons (dark matter). Photons and other ordinary matter were selected much later during formation of galaxies, when the background condensate becomes gravitationally unstable. The effect of radiation on the global dynamics is described in terms of conservation of the enthalpy density. Mass of neutrino (as the first massive fermionic particle) is estimated, in accord with experimental bound. The electric dipole moment of neutrino is also estimated. The oscillations of neutrinos are explained in terms of interaction with background condensate. The phenomena of subjective experiences are also explained in terms of interaction of the action potentials of neurons with the background dipolar condensate, which opens a new window into the dark sector of matter. The Qmoger theory goes beyond the Standard Model and the Quantum Field Theory, but can be combined with their achievements. Key words: quantum modification of general relativity, emergence of the laws of nature, isenthalpic universe, oscillating neutrinos, subjective experiences and dark sector of matter.

The mirror neutrino hypothesis for quantum gravity has been used to resolve known cosmological problems using quantised inertia. In this note we clarify the theoretical principles, describe the true electroweak vacuum, and explain where conventional holographic scenarios go wrong.

The Brannen neutrino mass triplet extends Koide's rule for the charged leptons, which was used to correctly predict the tau mass. Assuming that Koide's rule is exact, we consider the fundamental 2/9 lepton phase, noting connections to the CKM matrix and arithmetic information. An estimate for the fine structure constant is included.

This paper discusses and applies a basis for modeling elementary forces and particles. We show that models based on isotropic quantum harmonic oscillators describe aspects of the four traditional fundamental physics forces and point to some known and possible elementary particles. We summarize results from models based on solutions to equations featuring isotropic pairs of isotropic quantum harmonic oscillators. Results include predictions for new elementary particles and possible descriptions of dark matter and dark energy.

Recently, solutions to the $nonlinear$ Bohm-Poisson (BP) equation were found with relevant cosmological applications. We were able to obtain an exact analytical expression for the observed vacuum energy density, and explain the origins of its $repulsive$ gravitational nature. In this work we considerably improve our prior arguments in support of our findings, and provide further results which include two possible extensions of the Bohm-Poisson equation to the full relativistic regime; explain how Bohm's quantum potential in four-dimensions could be re-interpreted as a gravitational potential in five-dimensions, and which explains why the presence of dark energy/dark matter in our $4D$ spacetime can only be inferred $indirectly$, but not be detected/observed directly. We conclude with some comments about the Dirac-Eddington large numbers coincidences.

Beginning with the observationally successful FLRW constraint of Riofrio, a classical alternative to $\Lambda$CDM, we introduce a mass gap correction to cosmology, incorporating a few aspects of the $\Lambda$CDM model, wherein both neutrinos and non local mirror neutrinos play a key role. Non local neutrinos are antineutrinos. The equivalence principle is mildly broken using McCulloch's approach to quantum inertia and a new holographic principle. There is no dark matter and no dark energy, and mirror neutrino states are informationally connected to the CMB. Consequences include (i) a present day temperature of $2.73$K arising as a mirror rest mass, (ii) an estimate of the observable mass of the universe and (iii) an effective sterile mass of $1.29$eV, permitted by current oscillation results.

Relativistic quantum gravity with the action including tems quadratic in the curvature tensor is analyzed. We derive new expressions for the crresponding Lagrangian and the graviton propagator. We argue that the considered model is a good candidate for the fundamental quantum theory of gravitation.

Recently, solutions to the $nonlinear$ Bohm-Poisson equation were found [2] with cosmological applications. We were able to obtain a value for the vacuum energy density of the same order of magnitude as the extremely small observed vacuum energy density, and explained the origins of its $repulsive$ gravitational nature. In this work we show how to obtain a value for the vacuum energy density which coincides $exactly$ with the extremely small observed vacuum energy density. This construction allows also to borrow the results over the past two decades pertaining the study of the Renormalization Group (RG) within the context of Weinberg's Asymptotic Safety scenario. The RG flow behavior of $ G $ shows that $ G $ $increases$ with distance, so that the magnitude of the repulsive force exemplified by $ - G < 0 $ becomes larger, and larger, as the universe expands. This is what is observed.

After applying the recently proposed Bohm-Poisson equation [1] to the observable Universe as a $whole$, and by introducing an ultraviolet (very close to the Planck scale) and an infrared (Hubble radius) scale, one can naturally obtain a value for the vacuum energy density which coincides $exactly$ with the extremely small observed vacuum energy density, and explain the origins of its $repulsive$ gravitational nature. Because Bohm's formulation of QM is by construction non-local, it is this non-locality which casts light into the crucial ultraviolet/infrared entanglement of the Planck/Hubble scales which was required in order to obtain the observed value of the vacuum energy density.

We use 3 equations as postulates: Pem referring to electromagnetism, Pgrav referring to gravity, and Pqm referring to quantum mechanic and defining the wave function. Combining Pem with "Sommerfeld's quantum rules" corresponds to the original quantum theory of Hydrogen, which produces the correct relativistic energy levels of atoms (Sommerfeld's and Dirac's theories of matter produces the same energy levels, and Schrodinger's theory produces the approximation of those energy levels). Pqm implies that the wave function is solution of both Schrodinger's and Klein-Gordon's equations in the non interacting case while, in the interacting case it implies "Sommerfeld's quantum rules": Pem and Pqm then produce the correct relativistic energy levels of atoms (the same as Dirac's energy levels). We check that the required degeneracy is justified by pure deduction, without any other assumption (Schrodinger's theory only justifies one half of the degeneracy). We observe the connection between Pqm, Quantum Field Theories and tunnel effect. From Pgrav we deduce an equation of motion very similar to general relativity (with accuracy 10^{-6} at the surface of the Sun), our postulate being explicitly an approximation. First of all, we discuss classical Kepler problems (Newtonian motion of the Earth around the Sun), explain the link between Kelpler's law of periods (1619) and Plank's law (1900) and observe the links between all historical models of atoms (Bohr, Sommerfeld, Pauli, Schrodinger, Dirac, Fock).

To construct quantum gravity we introduce the quantum gravity state as function of particle coordinates and functional of fields, We add metric as the new argument of state: $$ \Psi=\Psi(t,x_{1},...x_{n},\lbrace A^{\gamma}(x)\rbrace, \lbrace g_{\mu\nu}(x) \rbrace) $$ we calculate the cosmological constant assuming that the quantum state is a function of time and radius of universe (mini-superspace) $$ \Psi=\Psi(t,a) $$ To avoid infinities in the solutions, we substitute the usual equation for propagotor with initial value Cauchy problem, which has finite and unique solution, for example we substitute the equation for Dirac electron propagator $$ (\gamma^\mu p_\mu - mc)K(t,x,t_0,x_0)= \delta(\vec{x} - \vec{x_0})\delta(t-t_0) $$ which already has infinity at the start $t = t_0 $, with the initial value Cauchy problem $$ \begin{cases} (H - i \hbar\partial / \partial t)K(t,x,t_0,x_0)=0,\\ K(t,x,t_0,x_0) = \delta(\vec{x} - \vec{x_0}),\quad t=t_0, \end{cases} $$ which has finite and unique solution.

Neutrino mixing in a spectral model for QFT employs the Bogoliubov transformation, which is a quantum Fourier transform. We look at the Hopf algebras in this setting, from a more motivic perspective. Experimental results for mixing are considered.

We derive the canonical momentum of the gravity field. Then we use it to derive the path integral of the gravity field. The canonical momentum is represented in Lorentz group. We derive it from the holonomy U(A) of the connection A of Lorentz group. We derive the path integral of gravity field as known in quantum fields theory and discuss the situation of free gravity field (like electromagnetic field). We find that this situation is only in the background spacetime, weak gravity, the situation of low matter density. We search for a theory in which the gravity field is a dynamical at any energy in arbitrary curved spacetime. For that, we suggest a duality gravity-area. That duality lets to possibility to study both gravity and area as dynamical fields in arbitrary curved spacetime. We find that the area field exists in the space-like and the gravity field exists in the time-like. We find that the tensor product of gravity and area fields, in selfdual representation, satisfies the reality condition. We derive the static potential of exchanging gravitons in scalar and spinor fields, the Newtonian gravitational potential.

Through the introduction of a new principle of physics, we extend quantum mechanics by proposing three additional postulates. With them we construct a quantum theory where gravitation emerges from the thermodynamics of an entangled vacuum. This new quantum theory reproduces the observations of the $\Lambda$CDM model of cosmology, predicting the existence of massive vacua $ M_{\text{on}} = \sqrt{\dfrac{\hbar c}{G}}$ and $M_{\text{off}} = \sqrt{\dfrac{ \Lambda^{2} \hbar^{3}G}{c^{5}}}$. Finally, we propose an experiment for the formers direct detection.

From the quantum modification of general relativity (Qmoger), supported by cosmic data (without fitting), a new quantum scaling is derived. This scaling indicates a mechanism of formation new particles from the background matter. Based on this scaling, mass of neutrino is estimated in agreement with experimental bounds. The neutrino oscillations are explained in terms of interaction with the background quantum condensate of gravitons. Subjective experiences (qualia) and functioning of living cell are also connected with the background condensate.

New simple and exact analytical solutions of Einstein equations of general relativity (GR) and of Qmoger (quantum modification of GR) equations are obtained. These solutions corresponds to processes with invariant density of enthalpy (energy plus pressure). Interpretation of this solutions in terms of cosmic radiation and production of massive particles, as well as comparison with cosmic data (without fitting), are presented. It is suggested, that isenthalpic processes can be relevant also to excessive radiation from Jupiter and Saturn. Similar processes potentially can be used as a new source of energy on Earth.

In this paper, we show one theoretical possibility for cosmic rotation. We would like to appeal that: 1) A globally rotating universe is consistent with general relativity and quantum gravity. 2) As currently believed dark energy is having no observational evidence, it is better to search for cosmic rotational effects. In this context, one can see the main stream journal articles on cosmic axis of rotation and observational effects of cosmic rotation. Based on Mach's principle and quantum gravity, we imagine our universe as the best quantum gravity sphere and assume that, at any stage of cosmic evolution: 1) Planck scale Hubble parameter plays a crucial role. 2) Space-time curvature follows, ${GM_t}\cong{R_tc^2}$ where $M_t$ and $R_t$ represent the ordinary cosmic mass and radius respectively. 3) Cosmic thermal wavelength is inversely proportional to the ordinary matter density. 4) Magnitude of angular velocity is equal to the magnitude of Hubble parameter. Based on these assumptions, at $H_0\cong 70 \textrm{\,km/sec/Mpc\,},$ estimated current matter density is 0.04341$\left(\frac{3H_0^2}{8 \pi G}\right)$ and corresponding radius is 29 Gpc. Current cosmic rotational kinetic energy density is 0.667$\left(\frac{3H_0^2c^2}{8 \pi G}\right)$. We would like to emphasize that: 1) Currently believed mysterious dark energy can be identified with current cosmic rotational kinetic energy. 2) Currently believed `inflation' concept can be relinquished. With advanced science, engineering and technology and by considering the most recent observations on `cosmic axis of evil' and `axial alignment' of distance astronomical bodies, a unified model of quantum cosmology can be developed.

Understanding quantum gravity motivates string and loop theorists. Both employ geometric wavefunction models. Gravity enters strings by taking the one fundamental length permitted by quantum field theory to be not the high energy cutoff, rather the Planck length. This comes at a price - string theory cannot be renormalized, and the solutions landscape is effectively infinite. Loop theory seeks only to quantize gravity, with hope that insights gained might inform particle physics. It does so via interactions of two dimensional loops in three-dimensional space. While both approaches offer possibilities not available to Standard Model theorists, it is not unreasonable to suggest that geometric wavefunctions comprised of fundamental geometric objects of three-dimensional space are required for successful models, written in the language of geometric Clifford algebra.

There has been a crisis in theory regarding General Relativity and Quantum Mechanics. Here I propose a solution by saying there is a flexible structure to the universe and it is essentially the structure of the vacuum energy.

In this letter we describe a new concept of "pseudo-forces" that is obtained from a non-local geometrodynamic model. We argue that while the gravity force is described by the curvature of spacetime, the other three forces are, in fact, pseudo-forces that evolve from such geometrodynamic model.

To construct quantum gravity we formulate quantum electrodynamics in equivalent form with possibility to generalize, we calculate the сosmological constant assuming that the quantum state is a function of time and radius of universe.

In this paper we show how it is possible to measure the Planck length from a series of different measurements. One of these measurements is totally independent of big G, but requires particle accelerators far more powerful than the ones that we have today. However, a Cavendish-style experiment can be performed to find the Planck length with no knowledge of the value of big G. Not only that, the Cavendish style set-up gives half the relative measurement error in the Planck length compared to the measurement error in big G.

The basic building blocks of the universe have been debated for millennia. Recently advances have been made in string theory and variant schools of thought. Here I propose the notion that, at extremely small scales, information has a structure, and the information that determines a system is equivalent to it's momentum. This is achieved through an analogous mechanism to the Cartesian axes. These axes are aware of their position. This has many implications and I believe the mathematics regarding this will flourish.

Based on Mach's principle and quantum gravity, we imagine our universe as a best quantum gravitational sphere and assume that, at any stage of cosmic evolution: 1) Planck scale Hubble parameter plays a crucial role. 2) Space-time curvature follows, ${GM_t}\cong{R_tc^2}$ where $M_t$ and $R_t$ represent the ordinary cosmic mass and radius respectively. 3) Both, cosmic radius and expansion velocity, are proportional to the ratio of dark matter density and ordinary matter density. 4) Cosmic temperature is proportional to the ratio of ordinary matter density and critical density. With further research, a unified model of `quantum cosmology' with evolving dark energy or evolving vacuum energy can be developed.

I study the properties of a preon model for the substructure of the the standard model quarks and leptons. The goal is to establish both local and global group representations for the particles of the model. Knot theory algebra SLq(2) is shown to be applicable to the model. Teleparallel gravity is discussed with an interesting result to hadronic physics. A tentative glimpse on quantum gravity is indicated.

We revisit the construction of diffeomorphic but $not$ isometric metric solutions to the Schwarzschild metric. These solutions require the introduction of non-trivial areal-radial functions and are characterized by the key property that the radial horizon's location is $displaced$ continuously towards the singularity ($ r = 0 $). In the limiting case scenario the location of the singularity and horizon $merges$ and any infalling observer hits a null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. This construction allows to borrow the results over the past two decades pertaining the study of the Renormalization Group (RG) improvement of Einstein's equations which was based on the possibility that Quantum Einstein Gravity might be non-perturbatively renormalizable and asymptotically safe due to the presence of interacting (non-Gaussian) ultraviolet fixed points. The particular areal-radial function that eliminates the interior of a black hole, and furnishes a truly static metric solution everywhere, is used to establish the desired energy-scale relation $ k = k (r) $ which is obtained from the $k$ (energy) dependent modifications to the running Newtonian coupling $G (k) $, cosmological constant $\Lambda (k) $ and spacetime metric $g_{ij, (k) } (x)$. (Anti) de Sitter-Schwarzschild metrics are also explored as examples. We conclude with a discussion of the role that Asymptotic Safety might have in the geometry of phase spaces (cotangent bundles of spacetime); i.e. namely, in establishing a quantum spacetime geometry/classical phase geometry correspondence $g_{ij, (k) } (x) \leftrightarrow g_{ij} (x, E) $.

A model universe is analyzed with N protons and electrons where there are electromagnetic and spin interactions in the Hamiltonian is investigated in the context of quantum shape kinematics. We have found that quantum shape space exists for N≥4 particles and has 2N−7 functional degrees of freedom in the case of spin-1/2 particles. The emergence of space is associated with non-vanishing expectation value ⟨L^2⟩. We have shown that for odd N space always emerges, and for large even N space almost always emerges because ⟨L^2⟩≠0 for almost all states. In the limit N→∞ the density of states that yields ⟨L^2⟩=0 vanishes. Therefore we conclude that the space is almost always emergent in quantum shape kinematics.

Starting with the study of the geometry on the cotangent bundle (phase space), it is shown that the maximal proper force condition, in the case of a uniformly accelerated observer of mass $m$ along the $x$ axis, leads to a minimum value of $x$ lying $inside$ the Rindler wedge and given by the black hole horizon radius $ 2Gm$. Whereas in the uniform circular motion case, we find that the maximal proper force condition implies that the radius of the circle cannot exceed the value of the horizon radius $2Gm$. A correspondence is found between the black hole horizon radius and a singularity in the curvature of momentum space. The fact that the geometry (metric) in phase spaces is observer dependent (on the momentum of the massive particle/observer) indicates further that the matter stress energy tensor and vacuum energy in the underlying spacetime may admit an interpretation in terms of the curvature in momentum spaces. Consequently, phase space geometry seems to be the proper arena for a space-time-matter unification.

We use three postulates P1, P2a/b and P3 : Combining P1 and P2a with "Sommerfeld's quantum rules"; correspond to the original quan- tum theory of Hydrogen, which produces the correct relativistic energy levels for atoms (Sommerfeld's and Dirac's theories of matter produces the same energy levels, and Schrodinger's theory produces the approximation of those energy levels). P3 can be found in Schrodinger's famous paper introducing his equation, P3 being his first assumption (a second assumption, suppressed here, is required to deduce his equation). P3 implies that the wavefunction solution of both Schrodinger's and Klein-Gordon's equations in the non interacting case while, in the interacting case, it immediatly implies "Sommerfeld's quantum rules" : P1, P2a, and P3 then produce the correct relativistic energy levels of atoms, and we check that the required degeneracy is justied by pure deduction, without any other assumption (Schrodinger's theory only justies one half of the degeneracy). We observe that the introduction of an interaction in P1 is equivalent to a modication of the metric inside the wavefunction in P3, such that the equation of motion of a system can be deduced with two dierent methods, with or without the metric. Replacing the electromagnetic potential P2a by the suggested gravitationnal potential P2b, the equation of motion (deduced in two ways) is equivalent to the equation of motion of General Relativity in the low field approximation (with accuracy 10-6 at the surface of the Sun). We have no coordinate singularity inside the metric. Other motions can be obtained by modifying P2b, the theory is adaptable. First of all, we discuss classical Kepler problems (Newtonian motion of the Earth around the Sun), explain the link between Kelpler law of periods (1619) and Plank's law (1900) and observe the links between all historical models of atoms (Bohr, Sommerfeld, Pauli, Schrodinger, Dirac, Fock). This being done, we introduce P1, P2a/b, and P3 to then describe electromagnetism and gravitation in the same formalism.

1) Using the partition function for a system in thermodynamic equilibrium; and replacing the energy-Beta factor (Beta = 1/[Boltzmann constant x temperature]) by the imaginary parts of the nontrivial zeros Riemann's zeta function; It is obtained, a function that equals the value of elementary electric charge and the square root of the product of the Planck mass, the electron mass, and the constant of universal gravitation. 2) Using this same partition function (thermodynamic equilibrium) the Planck constant (Planck mass squared, multiplied by the constant of universal gravitation) is calculated with complete accuracy; As a direct function of the square of the quantized constant elementary electric charge. These two fundamental equations imply the existence of a repulsive acceleration of the quantum vacuum. As a direct consequence of this repulsive acceleration of the quantum vacuum; The repulsive energy of the quantum vacuum is directly derived from the general relativity equation for critical density. As a consequence of this repulsive acceleration, we establish provisional equations that allow us to calculate with enough approximation the speed of rotation within the galaxies; As well as the diameter of galaxies and clusters of galaxies. To obtain this results, completely accurate; several initial hypotheses are established. These hypotheses could say, that become physical-mathematical theorems, when they are demonstrated by empirical data. Among others, it is calculated accurately baryon density as well as the mass density. Hypothesis-axioms are demonstrated by their practical application for the empirical calculation of baryon density, antimatter-matter asymmetry factor, Higgs vacuum value, Higgs boson mass (mh1), and mass prediction of Quark stop, about 745-750 GeV. This boson would not have been discovered because its decay would be hidden by the almost equal masses of the particles involved in the decay. We think that this type of hidden decay is a general feature of supersymmetry. The physico-mathematical concept of quantum entropy (entropy of information) acquires a fundamental relevance in the axiomatization of the theories of unification. Another fundamental consequence is that time would be an emergent dimension in the part of the universe called real (finite limit velocities). In the part of the virtual universe and not observable; The time would be canceled, would acquire the value t = 0.This property would explain the instantaneity of the change of correlated observables of interlaced particles; And the instantaneous collapse of the wave function, once it is disturbed (measured, observed with energy transmission to the observed or measured system). To get a zero time, special relativity must be extended to hyperbolic geometries (virtual quantum wormholes). This natural generalization implies the existence of infinite speeds, on the strict condition of zero energy and zero time (canceled). This has a direct relationship with soft photons and soft gravitons with zero energy, from the radiation of a black hole; And that they would solve the problem of the loss of information of the black holes. The main equation of unification of electromagnetism and gravitation; It seems necessarily imply the existence of wormholes, as geometrical manifestation of hyperboloid of one sheet, and two sheets. In the concluding chapter we discuss this point; and others highly relevants. The relativistic invariance of elementary quantized electric charge is automatically derived.

I consider the standard model, together with a preon version of it, to search for unifying principles between quantum particles and general relativity. Argument is given for unified field theory being based on gravitational and electromagnetic interactions alone. Conformal symmetry is introduced in the action of gravity with the Weyl tensor. Electromagnetism is geometrized to conform with gravity. Conformal symmetry is seen to improve quantization in loop quantum gravity. The Einstein-Cartan theory with torsion is analyzed suggesting structure in spacetime below the Cartan scale. A toy model for black hole constituents is proposed. Higgs metastability hints at cyclic conformal cosmology.

After a very brief introduction to generalized gravity in Clifford spaces ($C$-spaces), generalized metric solutions to the $C$-space gravitational field equations are found, and inspired from the (Anti) de Sitter metric solutions to Einstein's field equations with a cosmological constant in ordinary spacetimes. $C$-space analogs of static spherically symmetric metrics solutions are constructed. Concluding remarks are devoted to a thorough discussion about Areal metrics, Kawaguchi-Finsler Geometry, Strings, and plausible novel physical implications of $C$-space Relativity theory.

I consider a preon model for quarks and leptons based on massless constituents having spin 1/2 and charge 1/3 or 0. The color and weak interaction gauge structures can be deduced from the three preon states. Argument is given for unified field theory being based on gravitational and electromagnetic interactions only. Conformal symmetry is introduced in the action of gravity with the Weyl tensor. Electromagnetism is geometrized to conform with gravity. Baryon number non-conservation mechanism is obtained.

New exact analytical solutions of Einstein and Qmoger (quantum modification of general relativity) equations are obtained in the context of an alternative to the Big Bang theory.

As it has been conjectured for a long time, dual orthogonal group-systems (DOGs) exhibit a non-static behaviour in the low temperature-limit. This article aims to explore the unitary transformations corresponding to the time-evolution of such systems in the limit of $\beta\rightarrow \infty$.

In this paper we look at the escape velocity for subatomic particles. We suggest a new and simple interpretation of what exactly the escape velocity represents at the quantum level. At the quantum level, the escape velocity leads to an escape probability that is likely to be more useful at the subatomic scale than the escape velocity itself. The escape velocity seems to make simple logical sense when studied in light of atomism. Haug [1] has already shown that atomism gives us the same mathematical end results as Einstein’s special relativity. Viewed in terms of general relativity and Newtonian mechanics, the escape velocity seems to be simple to understand. It also seems to explain phenomena at the quantum scale if one maintains an atomist’s point of view. This strengthens our hypothesis that everything consists of indivisible particles and void (empty space). From an atomistic interpretation, our main conclusion is that the standard escape velocity formula likely is the most accurate formula we can generate and it appears to hold all the way down to the Planck scale. An escape velocity of ve > c simply indicates that an indivisible particle cannot escape from a fundamental particle (for example an electron) without colliding with the indivisible particles making up the fundamental particle. To understand this paper in detail, I highly recommend reading the article The Planck Mass Finally Discovered [2] first.

In a recent paper, Haug [1] has rewritten many of Newton's and Einstein's gravitational results, without changing their output, into a quantized Planck form. However, his results only hold down to the scale of Planck mass size objects. Here we derive similar results for any mass less than or equal to a Planck mass. All of the new formulas presented in this paper give the same numerical output as the traditional formulas. However, they have been rewritten in a way that gives a new perspective on the formulas when working with gravity at the level of the subatomic world. To rewrite the well-known formulas in this way could make it easier to understand strength and weakness in Newton and Einstein gravitation formulas at the subatomic scale, potentially opening them up for new interpretations.

The current paper presents a new idea that it might lead us to the Grand Unified Theory. A concrete mathematical framework has been provided that could be appro- priate for one to work with. Possible answers were given concerning the problems of dark matter and dark energy as well as the “penetration” to vacuum dominant epoch, combining Quantum Physics with Cosmology through the existence of Higg’s boson. A value for Higg’s mass around 125.179345 Gev/c2 and a value for vacuum density around 4.41348x10−5Gev/cm3 were derived . Via Cartan’s theorem a proof regarding the number of bosons existing in nature (28) has been presented. Additionally, the full Lagrangian of our Cosmos (including Quantum Gravity) was accomplished.

We examine how a thermodynamic model of the boundary of 4d-manifolds can be used for an approach to quantum gravity, to keep the number of assumptions low and the quantum degrees of freedom manageable. We start with a boundary action leading to Einstein's Equations under a restriction due to additional information from the bulk. Optionally, a modified form with torsion can be obtained. From the thermodynamic perspective, the number of possible microscopic states is evaluated for every macroscopic configuration, and this allows to compute the transition probability between quantum states. The formalism does not depend on specific microscopic properties. The smoothness and the topological space condition of the manifold structure are viewed as a preferred representation of a macroscopic space on mathematical grounds. By construction, gravity may be interpreted as thermodynamic model which is forced to be out of equilibrium depending on the restrictions imposed by matter. Instead of an ill-behaved path integral description of gravity, we obtain a non-divergent concept of sums over microstates.

I consider a preon model for quarks and leptons based on constituents defined by mass, spin and charge. The preons form a finite combinatorial system for the standard model fermions. The color and weak interaction gauge structures can be deduced from the preon bound states. By applying the area eigenvalues of loop quantum gravity to black hole preons one gets a preon mass spectrum starting from zero. Gravitational baryon number non-conservation mechanism is obtained. Argument is given for unified field theory be based only on gravitational and electromagnetic interactions of preons.

We nalize the project initiated in [1, 2, 3, 4, 7, 8, 9, 10] by studying graviton theory in our setting. Given the results in [1, 3, 9, 10], there is not so much left to accomplish and we start by deepening our understanding of some points left open in [1, 10]. Perturbative niteness of the theory follows ad-verbatim from the analysis in [3, 9] and we do not bother here about writing it down explicitly. Rather, our aim is to provide for a couple of new physical and mathematical insights regarding the genesis of the structure of the quantal graviton theory.

A new approach to the theory of gravity is proposed. A second-rank tensor field is chosen to be the potential of the gravitational field. The gravitational field is related to the metric tensor of space--time, and all phenomena occur in curved space--time. A variational principle is established, and the gravitational field equations are derived. The energy--momentum density tensor of the gravitational field and its conservation law are obtained. The source of the gravitational field is the energy--momentum density of all kinds of matter, including the gravitational field itself. A Lagrangian of the gravitational field is proposed that correctly describes local observable gravitational phenomena in the second-order approximation. The energy density of the gravitational field is positive. Estimates are obtained for the gravitational energy defect, the difference between the inertial and gravitational masses of a body, and the effect of the external gravitational field on the mass of a body. The new approach to the description of the gravitational field and its energy provides additional incentives search possibilities of experimental verification of the phenomena of gravitation in strong fields.

We further investigate the new project initiated in [1, 2, 3, 4, 7, 8, 9] by generalizing non-abelian gauge theory to our setting. Given the results in [3, 9], there is not much left to do and we shall deepen our understanding of some points left open in [1] regarding the nature and presence of ghosts. Perturbative niteness of the theory follows ad-verbatim from the analysis in [3, 9] and we shall not bother here about writing it down explicitly. Rather, our aim is to provide for a couple of new physical and mathematical insights regarding the genesis of the structure of quantal non-abelian gauge theory.

We continue our investigation of the new project launched in [1, 2, 3, 4, 7, 8] by generalizing Quantum Electrodynamics, the theory of elec- trons and photons, to our setting. At first, we deal with the respective two point functions, define the correct interaction theory as a series of connected Feynman diagrams and finally, we show that for a certain class of spacetime metrics, each diagram is finite and a modified perturbation series is analytic.

In the light of a recent novel definition of a relativistic quantum theory [1, 3, 4], we ask ourselves the question what it would mean to make the gravitational field itself dynamical. This could lead to a couple of different viewpoints upon quantum gravity which we shall explain carefully; this paper expands upon some ideas in [2] and again confirms ones thought that we are still far removed from a (type one) theory of quantum gravity.

In a previous paper of this author [1] building upon insights reached in [2], we constructed the free theory on a rather general curved spacetime for spin-0, 1/2,1 particles and we wrote down the most general interaction vertices for the latter leading to the principle of local gauge invariance. In this paper, we further define the interacting theory and study the behavior of modified particle propagators, leading to a finite theory

The current paper presents an attempt to express the mass problem in a more con- crete mathematical scheme where all the Physical quantities could come naturally. The Standard Model and its extensions where investigated where SU(4) has appeared as a conclusion of this attempt.

In this short note, first we will show a few ways to rewrite Einstein's field equation without basically changing it. Then we speculate a bit more broadly on how to change the equation to make it hold at the quantum scale. More precisely, we modify it for bodies with masses less than the Planck mass.

This paper questions the assumption that the Schwarzschild radius actually represents a radius. It has recently been shown by Haug (2016) that the Schwarzschild radius for any object can simply be written as N2l_p, where N is the number of Planck masses into which we can ``hypothetically" pack an object of interest and l_p is the well known Planck length. The Schwarzschild radius seems to represent the length of the number of Planck mass objects we can ``hypothetically" pack a planet or star into and then we can place them in perfect alignment along a single strand (of single particles) in a straight line.

This is a short note to show how big G can be derived from dimensional analysis by assuming that the Planck length is much more fundamental than Newton's gravitational constant.

Every elementary particle or quantic entity may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts particle or wave to fully describe the behavior of quantum-scale objects. In this paper, we show that X-particles of dark energy can create the wave appearance of a quantum-scale particle, and argue that the particle is indeed a particle. Our theory is deterministic and local, and is based on classical mechanics. Double-slit experiment and quantum entanglement are explained by the X-particle interpretation.

As an origin of dark energy, an X-particle with repulsive force proportional to energy density has been proposed [1]. In this paper, we will develop the X-particle theory further, and postulate how dark energy could form a ubiquitous gravitational field and inertial reference of frames, and why they might be the reason for the uncertainty principle. Like photon, an X-particle has only relativistic mass, and acts like a particle that has a definite position and momentum. It creates spaces between them by forces of gravitational attraction and repulsion. However, unlike photon that travels in space, an X-particle only needs to pass signals to its neighboring particles to form the ubiquitous gravitational field. This model could explain how gravitational signals propagate at the speed of light, how their values are stored in X-particles, and why the uncertainty principle could arise from this.

I consider a statistical mechanical model for black holes as atoms of spacetime with the partition function sum taken over area eigenvalues as given by loop quantum gravity. I propose a unied structure for matter and spacetime by applying the area eigenvalues to a black hole composite model for quarks and leptons. Gravitational baryon number non-conservation mechanism is predicted. Argument is given for unified field theory be based on gravitational and electromagnetic interactions only. The non-Abelian gauge interactions of the standard model are briefly discussed.

Modifications of the Weyl-Heisenberg algebra $ [ { \bf x}^i, {\bf p}^j ] = i \hbar g^{ij} ( {\bf p } ) $ are proposed where the classical limit $g_{ij} ( p ) $ corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the $ 2D$ de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty $ \Delta x $. The first uncertainty relation of this hierarchy has the same functional form as the $stringy$ modified uncertainty relation with a Planck scale minimum value for $ \Delta x = L_P $ at $ \Delta p = p_{Planck} $. We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric $ g_{ ( \mu \nu ) } $ and nonsymmetric $ g_{ [ \mu \nu ] } $ metric components of a Hermitian complex metric $ g_{ \mu \nu} = g_{ ( \mu \nu ) } + i g_{ [ \mu \nu ] } $, such $ g_{ \mu \nu} = (g_{ \nu \mu})^*$. Yang's noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of $ L_P^2$ emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.

In this paper I will first show that Coulomb's electrostatic force formula is mathematically exactly the same as Newton's universal gravitational force at the very bottom of the rabbit hole --- that is for two Planck masses. Still, the electrostatic force is much stronger than the gravity force when we are working with any non-Planck masses. We show that the difference in strength between the gravity and the electromagnetism is likely due to the fact that electromagnetism can be seen as aligned matter (``superimposed" gravity), and standard gravity is related to non-aligned matter (waves). Mathematically the difference between gravity and electromagnetism is simply linked to a joint probability factor; this is probably one for aligned matter (electromagnetism) and is close to zero for gravity. Actually, the dimensionless gravitational coupling constant is directly related to this gravitational probability factor. Based on this new view, we claim to have unified electromagnetism and gravity. This paper could have major implications for our entire view on physics from the largest to the smallest scales. For example, we show that electron voltage and ionization can basically be calculated from the Newtonian gravitational escape velocity when it is adjusted to take aligned matter (electromagnetism) into account. Up until now, we have had electromagnetism and gravity; from now on there is GravityElectroMagnetism!

In this paper we are rewriting the gravitational coupling constant in a slightly different form than has been shown before (without changing its value). This makes it simpler to understand what is meant and what is not meant by a “dimensionless gravitational coupling constant.

We present results of applying our divergence-free effective action quantum field theory techniques to a scalar model with gravity-like, non-polynomial interactions characterized by a dimensional coupling constant. This treatment would give a clear perspective regarding the viability of applying the divergence-free approach to quantum gravity. Issues regarding the masslessness of the effective graviton, while the virtual counterpart is massive, as well as, regarding the invariance of the basic Lagrangian, are discussed.

In this paper we rewrite the gravitational constant based on its relationship with the Planck length and, based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein's gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. Numerically this only has implications at the quantum scale; for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein's gravitation are potentially linked with the quantum world.

After reviewing the basics of the geometry of the cotangent bundle of spacetime, via the introduction of nonlinear connections, we build an action and derive the generalized gravitational field equations in phase spaces. A nontrivial solution generalizing the Hilbert-Schwarzschild black hole metric in spacetime is found. The most relevant physical consequence is that the metric becomes momentum-dependent (observer dependent) which is what one should aim for in trying to $quantize$ geometry (gravity) : the observer must play an important role in any measurement (observation) process of the spacetime he/she lives in.

A variety of quantum gravity models (including spin foams) can be described using a path integral formulation. A path integral has a well-known statistical mechanical interpretation in connection with a canonical ensemble. In this sense, a path integral describes the thermodynamic equilibrium of a local system in a thermal bath. This interpretation is in contrast to solutions of Einstein's Equations which depart from local thermodynamical equilibrium (one example is shown explicitly). For this reason, we examine an extension of the path integral model to a (locally) non-equilibrium description. As a non-equilibrium description, we propose to use a global microcanonical ensemble with constraints. The constraints reduce the set of admissible microscopic states to be consistent with the macroscopic geometry. We also analyse the relation between the microcanonical description and a statistical approach not based on dynamical assumptions which has been proposed recently. This analysis is of interest for the test of consistency of the non-equilibrium description with general relativity and quantum field theory.

I propose first a simple model for quantum black holes based on a harmonic oscillator describing the black hole horizon covered by Planck length sized squares carrying soft hair. Secondly, I discuss a more involved statistical model with the partition function sum taken over black hole stretched horizon constituents which are black holes themselves. Attempting a unified quantum structure for spacetime, black holes and matter, I apply the statistical model picture also to matter particles using a composite model for quarks and leptons.

In the framework of the Joos-Weinberg 2(2S+1)- theory for massless particles, the dynamical invariants have been derived from the Lagrangian density which is considered to be a 4-vector. A la Majorana interpretation of the 6-component ``spinors`", the field operators of S=1 particles, as the left- and right-circularly polarized radiation, leads us to the conserved quantities which are analogous to those obtained by Lipkin and Sudbery. The scalar Lagrangian of the Joos-Weinberg theory is shown to be equivalent to the Lagrangian of a free massless field, introduced by Hayashi. As a consequence of a new ``gauge" invariance this skew-symmetric field describes physical particles with the longitudinal components only. The interaction of the spinor field with the Weinberg's 2(2S+1)-component massless field is considered. New interpretation of the Weinberg field function is proposed. KEYWORDS: quantum electrodynamics, Lorentz group representation, high-spin particles, bivector, electromagnetic field potential. PACS: 03.50.De, 11.10.Ef, 11.10.Qr, 11.17+y, 11.30.Cp

After a cursory introduction of the basic ideas behind Born's Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain $nonholonomic$ modifications of Riemann--Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the $8D$ cotangent bundle $ T^*M$ of spacetime is explicitly constructed and based on the gauge group $ SO (6, 2) \times_s R^8$ which acts on the tangent space to the cotangent bundle $ T_{ ( {\bf x}, {\bf p}) } T^*M $ at each point $ ({\bf x}, {\bf p})$. Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, QFT in accelerated frames, {\bf T}-duality, double field theory, and generalized geometry.

The phenomenological model proposed in this note indicates that the black hole radiation consists of two components: the standard thermal Hawking radiation and an additional non-thermal baryonic/leptonic component due to quantum number neutralization by the no-hair theorem. The particle radiation grows relatively stronger than the Hawking radiation with increasing black hole mass, and it can be tested in principle.

I raise some issues when one combines the dynamical causal sequential growth dynamics with the static approach towards quantum field theory. A proper understanding of these points is mandatory before one attempts to unite both approaches. The conclusions we draw however appear to transcend causal set theory and apply to any theory of spacetime and matter which involves topology change.

Further evidence is provided why a $ Cl ( 5, C ) $ gauge field theory in four dimensions furnishes the $simplest$ Grand Unification model of Gravity and the Standard Model. In essence we have four copies of $ Cl ( 4, R )$, one copy per each axis-direction in our observed $ D = 4$-dim spacetime.

Accelerated strings in tangent bundle backgrounds are studied in further detail than it has been done in the past. The worldsheet associated with the accelerated open string described in this work envisages a continuum family of worldlines of accelerated points. It is when one embeds the two-dim string worldsheet into the tangent bundle $ TM$ background (associated with a uniformly accelerated observer in spacetime) that the effects of the maximal acceleration are manifested. The induced worldsheet metric as a result of this embedding has a $null$ horizon. It is the presence of this null horizon that limits the acceleration values of the points inside string. If the string crosses the null horizon some of its points will exceed the maximal acceleration value and that portion of the string will become causally disconnected from the rest of string outside the horizon. It is explained why our results differ from those in the literature pertaining the maximal acceleration modifications of the Rindler metric. We also find a modified Rindler metric which has a true curvature singularity at the location of the null horizon due to a finite maximal acceleration. One of the salient features of studying the geometry of the tangent bundle is that the underlying spacetime geometry becomes $observer ~dependent$ as Gibbons and Hawking envisioned long ago. We conclude with some remarks about generalized QFT in accelerated frames and the black hole information paradox.

We investigate the most general Lagrangian in the Minkowski space for the symmetric tensor field of the second rank. Then, we apply the Higgs mechanism to provide the mass to the appropriate components.

I propose a phenomenological model for the decay of black holes near Planck mass. The decay takes place via a quantum state between general relativity and a grand unified field theory like SO(10). This group is favored also by a no-scale SUGRA GUT model for Starobinsky inflation by other authors

This work is based on modification of the general relativity, which includes effects of production /absorption of matter by the vacuum. The theory (without fitting parameters) is in good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding universe). In this theory, there is no Big Bang at the beginning, but some local bangs during the evolution are probable. Also, there is no critical density of the universe and, therefore, no dark energy. Based on exact Gaussian solution for the scale factor, it is shown that an effective age of the universe is about 327 billion years. Production of primary dark matter particles have started 43 billion years later. It is shown that characteristic distance between particles is 30 times smaller than the thermal de Brogle wavelength, so that quantum effects, including formation of the Bose-Einstein condensate, can dominate. "Ordinary" matter was synthesized from dark matter in galaxies. Supplementary exact solutions are obtained for various ranges of parameters. From the theory we get an interface between dark and ordinary matter (IDOM), which very likely exist not only in cosmos, but everywhere, including our body and our brain. Key words: cosmology; age of the universe; dark matter; interface between dark and ordinary matter.

This work is based on modification of the general relativity with two additional terms in the Einstein equations. The additional terms give macroscopic description of the quantum effects of production /absorption of matter by the vacuum. The theory (without fitting parameters and without hypothesis of inflation) is in good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding universe). In this theory, there is no Big Bang at the beginning, but some local bangs during the evolution are probable. Also, there is no critical density of the universe and, therefore, no dark energy (no need in the cosmological constant). Based on exact Gaussian solution for the scale factor, it is shown that an effective age of the universe is about 327 billion years. Production of primary dark matter particles (possibly, gravitons) have started 43 billion years later. It is shown that characteristic distance between particles is much smaller than the thermal de Brogle wavelength, so that quantum effects, including formation of the Bose-Einstein condensate, can dominate, even for high temperature. "Ordinary" matter was synthesized from dark matter (with estimated small electric dipole moment (EDM)) in galaxies. Supplementary exact solutions are obtained for various ranges of parameters. From the theory we get an interface between dark and ordinary matter (IDOM), which very likely exist not only in cosmos, but everywhere, including our body and our brain. Key words: modification of general relativity; cosmology; age of the universe; dark matter (gravitons); interface between dark and ordinary matter.

The search for a consistent theory of quantum gravity has motivated the development of radically different approaches. This seeks consists of constructing a mathematical apparatus that encapsulates both concepts of quantum theory and general relativity. However, none approach has been definitive and the problem remains open. As the quantization of the metric is an alternative, this paper shows how a metric operator may be explicitly obtained by introducing a temporal operator, defining an induced metric and invoking some spacetime symmetries. This makes it possible to relate the effective acoustic metric to the model proposed here. The metric operator equations are expressed in terms of a hamiltonian operator describing the degrees of freedom of quantum vaccum whose dynamics gives rise to the metric field. These findings may help understand and study the quantum vacuum at Planck scale, consisting of one more tool for the community working on quantization of gravity.

The current paper presents a new idea that it might lead us to the Grand Unified Theory. A concrete mathematical framework has been provided that could be appro- priate for one to work with. Possible answers were given concerning the problems of dark matter and dark energy as well as the \penetration" to vacuum dominant epoch, combining Quantum Physics with Cosmology through the existence of Higg's boson. A value for Higg's mass around 125,179345 Gev/c^2 and a value for vacuum density around 4,41348x10^-5Gev/cm^3 were derived . Via Cartan's theorem a proof regarding the number of bosons existing in nature (28) has been presented. Additionally, the full Lagrangian of our Cosmos (including Quantum Gravity) was accomplished.

After reviewing the basic ideas behind Born's Reciprocal Relativity theory, the geometry of the (co) tangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain $nonholonomic$ modifications of Riemann--Cartan gravity within the context of Finsler geometry. The curvature tensors in the (co) tangent bundle of spacetime are explicitly constructed leading to the analog of the Einstein vacuum field equations. The geometry of Hamilton Spaces associated with curved phase spaces follows. An explicit construction of a gauge theory of gravity in the $8D$ co-tangent bundle $ T^*M$ of spacetime is provided, and based on the gauge group $ SO (6, 2) \times_s R^8$ which acts on the tangent space to the cotangent bundle $ T_{ ( x, p) } T^*M $ at each point $ ({\bf x}, {\bf p})$. Several gravitational actions associated with the geometry of curved phase spaces are presented. We conclude with a discussion about the geometrization of matter, QFT in accelerated frames, {\bf T}-duality, double field theory, and generalized geometry.

The field of an electromagnetic (E) dipole has been examined using general relativistic (R) and quantum mechanical (Q) points of view, and an E=Q=R equivalence principle presented whereas the curvature of the electromagnetic streamlines of the field are taken to be evidence of the distortion of spacetime, and hence of the presence of a gravitational field surrounding the dipole. Using a quasi-refractive index function N, with the streamlines and equipotential surfaces as coordinates, a new dipole relativistic metric is described, replacing Schwarzschild’s for a point mass. The same principle equates the curvature and other physical features of the field with fundamental quantum concepts such as the uncertainty principle, the probability distribution and the wave packet. The equations of the dipole field therefore yield the three fields emerging naturally one from the other and unified without resorting to any new dimensions. It is speculated whether this model can be extended to dipolar matter-antimatter pairs.

Explicit deformations of the Lorentz (Conformal) algebra are performed by recurring to Clifford algebras. In particular, deformations of the boosts generators are possible which still retain the form of the Lorentz algebra. In this case there is an invariant value of the energy that is set to be equal to the Planck energy. A discussion of Clifford-Hopf $\kappa$-deformed quantum Poincare algebra follows. To finalize we provide further deformations of the Clifford geometric product based on Moyal star products associated with noncommutative spacetime coordinates.

We discuss the gravitational collapse of a photon. It is shown that when the photon gets Planck energy, it turns into a black hole (as a result of interaction with the object to be measured). It is shown that three-dimensional space is a consequence of energy advantage in the formation of the Planck black holes. New uncertainty relations established on the basis of Einstein’s equations. It is shown that the curvature of space-time is quantized.

To extend the standard model to Planck scale energies I propose a phenomenological model of quantum black holes and dark matter. I assume that inside any black hole there is a core object of length scale L_Planck. The core is proposed to replace the singularity of general relativity. A simple phenomenological schematic model is presented for the core as quantum fields of SO(10) grand unified theory. A survey is made of calculational models that could support or supplement the present scheme and of theoretical frameworks for future developments.

The shared background independence of spacetime algebra and the impedance approach to quantization, coupled with the natural gauge invariance of phase shifts introduced by quantum impedances, opens the possibility that identifying the geometric objects of the impedance model with those of spacetime algebra will permit a more intuitive understanding of the equivalence of gauge theory gravity in flat space with general relativity in curved space.

To complete the standard model I propose a phenomenological model of quantum black holes and dark matter. I assume that at the center of any black hole there is a Kerr (Schwarzschild) core object of size Planck length. The core replaces the general relativity singularity of the black hole. A simple phenomenological model is presented for the core. During very early inflation the overlapping wave functions of the cores caused rapid expansion of the universe. Gravitons condensated around the cores to form primordial black holes which evolve into dark matter in the big bang together with the standard model particles.

We propose a model of microscopic black holes and dark matter to reinforce the standard model. We assume that at the center of a black hole there is a spin 1/2 neutral core field. The core is proposed to replace the singularity of the hole. During Starobinsky inflation gravitons condensate around the core to form a primordial quantum black holes which evolve naturally into abundant dark matter universe.

This paper uses a small set of mathematical principles to describe a very wide swath of physics. These principles define a new theory of quantum gravity called the theory of infinite complexity. The main result is that Einstein's equation for general relativity can be derived from unrelated, mathematically novel quantum phenomena. That the theory takes no free parameters should be considered strong evidence in favor of a real connection between physics and mathematics.

A Moyal deformation of a Clifford $ Cl (3, 1) $ Gauge Theory of (Conformal) Gravity is performed for canonical noncommutativity (constant $\Theta^{\mu \nu }$ parameters). In the very special case when one imposes certain constraints on the fields, there are $no$ first order contributions in the $\Theta^{\mu \nu }$ parameters to the Moyal deformations of Clifford gauge theories of gravity. However, when one does $not$ impose constraints on the fields, there are first order contributions in $\Theta^{\mu \nu }$ to the Moyal deformations in variance with the previous results obtained by other authors and based on different gauge groups. Despite that the generators of $U(2,2), SO(4,2), SO(2,3)$ can be expressed in terms of the Clifford algebra generators this does $not$ imply that these algebras are isomorphic to the Clifford algebra. Therefore one should not expect identical results to those obtained by other authors. In particular, there are Moyal deformations of the Einstein-Hilbert gravitational action with a cosmological constant to first order in $\Theta^{\mu \nu }$ . Finally, we provide a mechanism which furnishes a plausible cancellation of the huge vacuum energy density.

We propose a model scheme of microscopic black holes. We assume that at the center of the hole there is a spin 1/2 core field. The core is proposed to replace the singularity of the hole. Possible frameworks for non-singular models are discussed briefly.

Geometric algebra is universal, encompassing all the tools of the mathematical physics toolbox, is background independent, and is the foundation of gauge theory gravity. Similarly, impedance is a fundamental concept of universal validity, is background independent, and the phase shifts generated by impedances are at the foundation of gauge theory. Impedance may be defined as a measure of the amplitude and phase of opposition to the flow of energy. Generalizing quantum impedances from photon and quantum Hall to all forces and potentials generates a network of both scale dependent and scale invariant impedances. This essay conjectures that these quantum impedances can be identified with the gauge fields of gauge theory gravity, scale dependent with the translation field and scale invariant with rotation.

Extraordinary mathematicality of physics is also shown by dimensionlessness of Planck spacetime and mass. At the same time the Planck granularity of spacetime also shows that physics can be simulated by a binary computer. So physics is informational. But mathematics is not everything in physics, consciousness cannot be solely explained by mathematics. The reason that quantum gravity (QG) does not yet exist is the lack of knowledge about spacetime as background. Quantum mechanics is not complete, because foundational principle is not yet known, and because consciousness and QG are not yet explained. The free will and quantum randomness are similar unexplained phenomena. Even philosophy is important in physics, because what mathematics cannot describe in physics is ontology. And, intuition affects what is mainstream physics. Simplicity and clearness of physics and mathematics of physics are important not only for beginners, but also for the development of the fundamental physics. Uncertainty principle is so simple that maybe it could be derived without the use of wave functions. On the simplicity and clearness of fundamental physics it can be done a lot.

We find that having the scale factor close to zero due to a given magnetic field value in an early universe magnetic field affects how we would interpret Mukhanov’s chapter on “self reproduction” of the universe in in his reference. The stronger an early-universe magnetic field is, the greater the likelihood of production of about 20 new domains of size 1/H, with H the early-universe Hubble constant, per Planck time interval in evolution. We form DM from considerations as to a minimum time step, and then generate DM via axions. Through Ng’s quantum infinite statistics, we compare a DM count, giving entropy. The remainder of the document is in terms of DE as well as comparing entropy in galaxies versus entropy in the universe, through a lens of Mistra’s quantum theory of the big bang

Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, theoretical motivation for this venture is the old papers of Ogievetskiı and Polubarinov, Hayashi, and Kalb and Ramond. They proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. We also proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism. They are consistent with the general relativity. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph. PACS number: 03.65.Pm , 04.50.-h , 11.30.Cp

Kaluza's 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is inspiration for many modern attempts to develop new physical theories. Here an alternative approach is presented that more fully unifies gravity and electromagnetism. Emphasis is placed on admitting important electromagnetic fields not present in Kaluza's original theory without constraints, and on deriving a Lorentz force law. This is done by identifying 5D momentum with a kinetic charge. By doing so the usual assumption of Ricci flatness corresponding to sourceless electromagnetic fields is replaced by the weaker constraint of vanishing 5D momentum outside of charge models. A weak field limit is also used. An electromagnetic limit is imposed by assuming a constant scalar field. A further extended postulate set involving a super-energy divergence law and a conformal factor is also suggested that allows for a varying scalar field, within what then becomes a type of geometrical conformal gauge theory.

It is proposed how the Extended Relativity Theory in $C$-spaces (Clifford spaces) allows a unified formulation of point particles, strings, membranes and $p$-branes, moving in ordinary target spacetime backgrounds, within the description of a single $polyparticle$ moving in $C$-spaces. The degrees of freedom of the latter are provided by Clifford polyvector-valued coordinates (antisymmetric tensorial coordinates). A correspondence between the $p$-brane ($p$-loop) wave functional ``Schroedinger-like" equations of Ansoldi-Aurilia-Spallucci and the polyparticle wave equation in $C$-spaces is found via the polyparticle/$p$-brane duality/correspondence. The crux of exploiting this correspondence is that it might provide another unexplored avenue to quantize $p$-branes (a notoriously difficult and unsolved problem) from the more straightforward quantization of the polyparticle in $C$-spaces, even in the presence of external interactions. We conclude with some comments about the $compositeness$ nature of the polyvector-valued coordinate operators in terms of ordinary $p$-brane coordinates via the evaluation of $n$-ary commutators.

The notion of induced second quantization is introduced as an unavoidable aspect of the induction procedure for metric and spinor connection, which is the key element of TGD. Induced second quantisation provides insights about the QFT limit, about generalizes Feynman diagrammatics, and about TGD counterpart of second quantization of strings which appear in TGD as emergent objects. Zero energy ontology (ZEO) naturally restricts the anti-commutation relations inside causal diamonds defining quantum coherence regions so that the counterintuitive implication that all identical particles of the Universe are in totally symmetric/antisymmetric state is avoided. The relation of statistics to negentropic entanglement and the new view about position measurement provided by ZEO are discussed.

Twistors Grassmannian formalism has made a breakthrough in N=4 supersymmetric gauge theories and the Yangian symmetry suggests that much more than mere technical breakthrough is in question. Twistors seem to be tailor made for TGD but it seems that the generalisation of twistor structure to that for 8-D imbedding space H=M⁴× CP₂ is necessary. M⁴ (and S⁴ as its Euclidian counterpart) and CP₂ are indeed unique in the sense that they are the only 4-D spaces allowing twistor space with Kähler structure. The Cartesian product of twistor spaces P₃=SU(2,2)/SU(2,1)× U(1) and F₃ defines twistor space for the imbedding space H and one can ask whether this generalized twistor structure could allow to understand both quantum TGD and classical TGD defined by the extremals of Kähler action. In the following I summarize the background and develop a proposal for how to construct extremals of Kähler action in terms of the generalized twistor structure. One ends up with a scenario in which space-time surfaces are lifted to twistor spaces by adding CP₁ fiber so that the twistor spaces give an alternative representation for generalized Feynman diagrams. There is also a very closely analogy with superstring models. Twistor spaces replace Calabi-Yau manifolds and the modification recipe for Calabi-Yau manifolds by removal of singularities can be applied to remove self-intersections of twistor spaces and mirror symmetry emerges naturally. The overall important implication is that the methods of algebraic geometry used in super-string theories should apply in TGD framework. The physical interpretation is totally different in TGD. The landscape is replaced with twistor spaces of space-time surfaces having interpretation as generalized Feynman diagrams and twistor spaces as sub-manifolds of P₃× F₃replace Witten's twistor strings.

This paper is a sequel to ``Doppler Boosting a de Broglie Electron from a Free Fall Grid Into a Stationary Field of Gravity''. We Doppler boost a de Broglie particle from a free fall grid onto a stationary field of gravity. This results in an identification of the two Doppler boost options with an electron energy double-valueness similar to electron spin. It seems that, within the limitations of our approach to gravity, we found a bottom up version of a possible theory of Quantum Gravity, on that connects the de Broglie hypothesis to gravity. This paper finishes and adapts ``Towards a 4-D Extension of the Quantum Helicity Rotator with a Hyperbolic Rotation Angle of Gravitational Nature'' for the quantum gravity part. We try to boost the de Broglie particle's quantum wave equation from the free fall grid to the stationary grid. We find that this is impossible on the Klein-Gordon level, the Pauli level and the Dirac level. But when we double the Dirac level and thus realize a kind of a Yang-Mills doublet level, we can formulate a doublet version of the Weyl-Dirac equation that can be Doppler boosted from the free fall grid into the stationary grid in a central field of gravity. In the end we add a quantitative prediction for the gravitational Doppler shift of the matter wave or probability density of an electron positron pair. Our free fall grid to stationary grid approach is ad-hoc and does not present a fundamental theory, but is a pragmatic attempt to formulate quantum mechanics outside the Poincaré group environment and beyond Lorentz symmetry.

This paper is a sequel to ``Frequency Gauged Clocks on a Free Fall Grid and Some Gravitational Phenomena''. We Doppler boost a de Broglie particle from a free fall grid onto a stationary field of gravity. First we do this for a photon and then for a particle with non-zero rest-mass. This results in an identification of the two Doppler boost options with electron spin or with electron energy double-valueness. It seems that, within the limitations of our approach to gravity, we found a bottom up version of a possible theory of Quantum Gravity, on that connects the de Broglie hypothesis to gravity. This paper realizes the connection between our papers ``Frequency Gauged Clocks on a Free Fall Grid and Some Gravitational Phenomena'' and ``Towards a 4-D Extension of the Quantum Helicity Rotator with a Hyperbolic Rotation Angle of Gravitational Nature''.

This paper will present various techniques for visualizing a split real even E8 representation in 2 and 3 dimensions using an E8 to H4 folding matrix. This matrix is shown to be useful in providing direct relationships between E8 and the lower dimensional Dynkin and Coxeter-Dynkin geometries contained within it, geometries that are visualized in the form of real and virtual 3 dimensional objects. A direct linkage between E8, the folding matrix, fundamental physics particles in an extended Standard model, quaternions, and octonions is introduced, and its importance is investigated and described.

This review aims to show the Light cone gauge quantization of strings. It is divided up into three parts. The first consists of an introduction to bosonic and superstring theories and a brief discussion of Type II superstring theories. The second part deals with different configurations of D-branes, their charges and tachyon condensation. The third part contains the compactification of an extra dimension, the dual picture of D-branes having electric as well as magnetic field and the different dualities in string theories. In ten dimensions, there exist five consistent string theories and in eleven dimensions there is a unique M-Theory under these dualities, the different superstring theories are the same underlying M-Theory.

Some of the novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) are presented. In particular, generalized photon dispersion relations which allow for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, while breaking the $extended$ Lorentz symmetry in $C$-spaces. We analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of ``extended events" one finds a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. We finalize with a discussion of the modified dispersion relations, rainbow metrics and generalized uncertainty relations in $C$-spaces which are extensions of the stringy uncertainty relations.

We recently improved the famous result of Parikh and Wilczek, who found a probability of emission of Hawking radiation which is compatible with a non-strictly thermal spectrum, showing that such a probability of emission is really associated to two non-strictly thermal distributions for boson and fermions. Here we finalize the model by finding the correct value of the pre-factor of the Parikh and Wilczek probability of emission. In fact, that expression has the ∼ sign instead of the equality. In general, in this kind of leading order tunnelling calculations, the exponent arises indeed from the classical action and the pre-factor is an order Planck constant correction. But in the case of emissions of Hawking quanta, the variation of the Bekenstein-Hawking entropy is order 1 for an emitted particle having energy of order the Hawking temperature. As a consequence, the exponent in the Parikh and Wilczek probability of emission is order unity and one asks what is the real significance of that scaling if the pre-factor is unknown. Here we solve the problem assuming the unitarity of the black hole (BH) quantum evaporation and considering the natural correspondence between Hawking radiation and quasi-normal modes (QNMs) of excited BHs , in a “Bohr-like model” that we recently discussed in a series of papers. In that papers, QNMs are interpreted as natural BH quantum levels (the “electron states” in the “Bohr-like model”). Here we find the intriguing result that, although in general it is well approximated by 1, the pre-factor of the Parikh and Wilczek probability of emission depends on the BH quantum level n. We also write down an elegant expression of the probability of emission in terms of the BH quantum levels.

It is an intuitive but general conviction that black holes (BHs) result in highly excited states representing both the “hydrogen atom” and the “quasi-thermal emission” in quantum gravity. Here we show that such an intuitive picture is more than a picture, discussing a model of quantum BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. Our model has important implications on the BH information puzzle and on the non-strictly random character of Hawking radiation. It is also in perfect agreement with existing results in the literature, starting from the famous result of Bekenstein on the area quantization. This paper improves, clarifies and finalizes some recent results that, also together with collaborators, we published in various peer reviewed journals. Preliminary results on the model in this paper have been recently discussed in an Invited Lecture at the 12th International Conference of Numerical Analysis and Applied Mathematics.

The exploration of the novel physical consequences of the Extended Theory of Gravity in $C$-spaces (Clifford spaces) is continued. One of the most salient physical feature of the extended gravitational theory in $C$-spaces is that one can generate an $effective$ stress energy tensor mimicking the effects of ``dark" matter/energy. In particular, it is found that the presence of the cosmological constant, along with a plausible mechanism to explain its extremely small value and/or its cancellation, can be understood entirely from a purely Clifford algebraic and geometric perspective. For this reason we believe that this theory may have important consequences in Cosmology and further research in Gravitation and Particle Physics.

The hierarchy of phases with effective value of Planck constant coming as an integer multiple of the ordinary Planck constant and interpreted as dark matter is crucial in the TGD inspired model of living matter. The challenge is to identify physical mechanisms forcing the increase of effective Planck constant h_eff (whether to call it effective or not is to some extent matter of taste). The work with certain potential applications of TGD led to a discovery of a new mechanism possibly achieving this. The method would be simple: apply constant torque to a rotating system. I will leave it for the reader to rediscover how this can be achieved. The importance of the result is that it provides strong mathematical motivations for zero energy ontology (ZEO), causal diamonds (CDs), and hierarchy of (effective) Planck constants . Quite generally, the results apply to systems with external energy feed inducing generalized force acting in some compact degrees of freedom. Living matter represents basic example of this kind of system. Amazingly, ATP synthase enzyme contains generator with a rotating shaft: a possible TGD based interpretation is that the associated torque forces the generation of large h_eff phases.

A generalization of twistor Grassmannian approach defines a very promising vision about the construction of generalized Feynman diagrams. Since particles are replaced with 3-D surfaces and since string like objects emerge naturally in TGD framework, one expects that scattering amplitudes define a generalization of twistor Grassmannian amplitudes with a generalized Yangian symmetry. The realization of this approach has been however plagued by long-standing problems. SUSY in some form seems to be strongly supported by theoretical elegance and TGD indeed suggests a good candidate for a broken SUSY realized in terms of covariantly constant right-handed neutrino and not requiring Majorana spinors. Separate conservation of baryon and lepton number imply that super-generators carry quark or lepton number. This has been the main obstacle in attempts to construct stringly amplitudes. In this article it is found that this obstacles can be overcome and that stringy approach is forced both by the TGD view about physical particles and by the cancellation of UV and IR divergences. Also the planarity restriction emerges automatically in stringy approach. Absolutely essential ingredient is that fundamental fermions can be regarded as massless on-shell fermions having non-physical helicity with propagator replaced with its inverse: this representation follows by perfoming the integration over the virtual four-momentum squared using residue calculus.

Physicists M. Tajmar and C. J. Matos and their collaborators working in ESA (European Satellite Agency) have made an amazing claim of having detected strong gravimagnetism with gravimagnetic field having a magnitude which is about 20 orders of magnitude higher than predicted by General Relativity. </p><p> Tajmar et al have proposed the gravimagnetic effect as an explanation of an anomaly related to the superconductors. The measured value of the mass of the Cooper pair is slightly larger than the sum of masses whereas theory predicts that it should be smaller. The explanation would be that actual Thomson field is larger than it should be because of gravimagnetic contribution to quantization rule used to deduce the value of Thomson field. The required value of gravimagnetic Thomson field is however 28 orders of magnitude larger than General Relativity suggests. TGD inspired proposal is based on the notion of gravitational Planck constant assignable to the flux tubes connecting to massive objects. It turns out that the TGD estimate for the Thomson field has correct order of magnitude. The identification h_eff = h_gr at particle physics and atomic length scales emerges naturally. </p><p> A vision about the fundamental role of quantum gravitation in living matter emerges. The earlier hypothesis that dark EEG photons decay to biophotons with energies in visible and ultraviolet range receives strong quantitative support. Also a mechanism for how magnetic bodies couple bio-chemistry emerges. The vision conforms with Penrose's intuitions about the role of quantum gravity in biology.

The earlier attempts to understand the relationship between TGD and GRT have been in terms of solutions of Einstein's equations imbeddable to M⁴ ×CP₂ instead of introducing GRT space-time as a fictive notion naturally emerging from TGD as asimplified concept replacing many-sheeted space-time. This resolves also the worries related to Equivalence Principle. TGD can be seen as a "microscopic" theory behind TGD and the understanding of the microscopic elements becomes the main focus of theoretical and hopefully also experimental work some day. </p><p> The understanding of Kähler Dirac action has been second long term project. How can one guarantee that em charge is well-defined for the spinor modes when classical W fields are present? How to avoid large parity breaking effects due to classical Z⁰ fields? How to avoid the problems due to the fact that color rotations induce vielbein rotation of weak fields? The common answer to these questions is restriction of the modes of induced spinor field to 2-D string world sheets (and possibly also partonic 2-surfaces) such that the induced weak fields vanish. This makes string picture a part of TGD.

The construction of Kähler geometry of WCW ("world of classical worlds") is fundamental to TGD program. I ended up with the idea about physics as WCW geometry around 1985 and made a breakthrough around 1990, when I realized that Kähler function for WCW could correspond to Kähler action for its preferred extremals defining the analogs of Bohr orbits so that classical theory with Bohr rules would become an exact part of quantum theory and path integral would be replaced with genuine integral over WCW. The motivating construction was that for loop spaces leading to a unique Kähler geometry. The geometry for the space of 3-D objects is even more complex than that for loops and the vision still is that the geometry of WCW is unique from the mere existence of Riemann connection. </p><p> This article represents the updated version of the construction providing a solution to the problems of the previous construction. The basic formulas remain as such but the expressions for WCW super-Hamiltonians defining WCW Hamiltonians (and matrix elements of WCW metric) as their anticommutator are replaced with those following from the dynamics of the modified Dirac action.

An updated view about M⁸-H duality is discussed. M⁸-H duality allows to deduce M⁴× CP₂ via number theoretical compactification. One important correction is that octonionic spinor structure makes sense only for M⁸ whereas for M⁴× CP₂ complefixied quaternions characterized the spinor structure. </p><p> Octonions, quaternions, quaternionic space-time surfaces, octonionic spinors and twistors and twistor spaces are highly relevant for quantum TGD. In the following some general observations distilled during years are summarized. </p><p> There is a beautiful pattern present suggesting that H=M⁴× CP₂ is completely unique on number theoretical grounds. Consider only the following facts. M⁴ and CP₂ are the unique 4-D spaces allowing twistor space with Kähler structure. Octonionic projective space OP₂ appears as octonionic twistor space (there are no higher-dimensional octonionic projective spaces). Octotwistors generalise the twistorial construction from M⁴; to M⁸ and octonionic gamma matrices make sense also for H with quaternionicity condition reducing OP₂ to to 12-D G₂/U(1)× U(1) having same dimension as the the twistor space CP₃× SU(3)/U(1)× U(1) of H assignable to complexified quaternionic representation of gamma matrices. </p><p> A further fascinating structure related to octo-twistors is the non-associated analog of Lie group defined by automorphisms by octonionic imaginary units: this group is topologically six-sphere. Also the analogy of quaternionicity of preferred extremals in TGD with the Majorana condition central in super string models is very thought provoking. All this suggests that associativity indeed could define basic dynamical principle of TGD. </p><p> Number theoretical vision about quantum TGD involves both p-adic number fields and classical number fields and the challenge is to unify these approaches. The challenge is non-trivial since the p-adic variants of quaternions and octonions are not number fields without additional conditions. The key idea is that TGD reduces to the representations of Galois group of algebraic numbers realized in the spaces of octonionic and quaternionic adeles generalizing the ordinary adeles as Cartesian products of all number fields: this picture relates closely to Langlands program. Associativity would force sub-algebras of the octonionic adeles defining 4-D surfaces in the space of octonionic adeles so that 4-D space-time would emerge naturally. M⁸-H correspondence in turn would map the space-time surface in M⁸ to M⁴× CP₂.

This piece of text was written as an attempt to provide a popular summary about TGD. This is of course mission impossible since TGD is something at the top of centuries of evolution which has led from Newton to standard model. This means that there is a background of highly refined conceptual thinking about Universe so that even the best computer graphics and animations fail to help. One can still try to create some inspiring impressions at least. This chapter approaches the challenge by answering the most frequently asked questions. Why TGD? How TGD could help to solve the problems of recent day theoretical physics? What are the basic princples of TGD? What are the basic guidelines in the construction of TGD? </p><p> These are examples of this kind of questions which I try to answer in using the only language that I can talk. This language is a dialect of the language used by elementary particle physicists, quantum field theorists, and other people applying modern physics. At the level of practice involves technically heavy mathematics but since it relies on very beautiful and simple basic concepts, one can do with a minimum of formulas, and reader can always to to Wikipedia if it seems that more details are needed. I hope that reader could catch the basic principles and concepts: technical details are not important. And I almost forgot: problems! TGD itself and almost every new idea in the development of TGD has been inspired by a problem.

One manner to see TGD is as a solution of the energy problem of General Relativity in terms of sub-manifold gravity. The translations act now as translations of 8-D imbedding space M⁴×CP₂ rather than in space-time itself and four-momentum can be identified as Noether charge. The detailed realization of this vision however involves several conceptual delicacies. What does Equivalence Principle mean in this framework: equivalence of gravitational and inertial momenta or just Einstein's equations or their generalization? What is the precise definition of inertial and gravitational four-momenta? What does quantum classical correspondence mean and could Equivalence Principle reduce to it? p-Adic mass calculations and the notion of generalised conformal invariance provide strong constraints on the attempts to answer these questions. This article provides the most recent view about the most plausible looking answer to these questions. Twistor Grassmann approach relies on the Yangian variant of 4-D conformal symmetry generalizing in TGD framework to Yangian variants of huge conformal symmetry algebras due to the effective 2-dimensionality of light-like 3-surfaces. This suggest also a generalization of four-momentum bringing in multilocal contributions analogous to interaction energy and also this is discussed in some detail.

The book is devoted to the applications of p-adic length scale hypothesis and dark matter hierarchy. <OL> <LI>p-Adic length scale hypothesis states that primes p≈ 2^k, k integer, in particular prime, define preferred p-adic length scales. Physical arguments supporting this hypothesis are based on the generalization of Hawking's area law for blackhole entropy so that it applies in case of elementary particles. <LI>A much deeper number theory based justification for this hypothesis is based on the generalization of the number concept fusing real number fields and p-adic number fields among common rationals or numbers in their non-trivial algebraic extensions. This approach also justifies the notion of multi-p-fractality and allows to understand scaling law in terms of simultaneous p≈ 2^k- and 2-fractality. <LI>Certain anomalous empirical findings inspire in TGD framework the hypothesis about the existence of entire hierarchy of phases of matter identifiable as dark matter. The levels of dark matter hierarchy are labeled by the values of dynamical quantized Planck constant. The justification for the hypothesis provided by quantum classical correspondence and the fact the sizes of space-time sheets identifiable as quantum coherence regions can be arbitrarily large. </OL> The organization of the book is following. <OL> <LI>The first part of the book is devoted to the description of elementary particle massivation in terms of p-adic thermodynamics. <LI>In second part is devoted to the detailed calculation of masses of elementary particles and hadrons, and to various new physics suggested or predicted by the resulting scenario. </OL>

The book is devoted to hyper-finite factors and hierarchy of Planck constants. <OL> <LI>Configuration space spinors indeed define a canonical example about hyper-finite factor of type II₁. The work with TGD inspired model for quantum computation led to the realization that von Neumann algebras, in particular hyper-finite factors of type II₁ could provide the mathematics needed to develop a more explicit view about the construction of M-matrix. This has turned out to be the case to the extent that a general master formula for M-matrix with interactions described as a deformation of ordinary tensor product to Connes tensor products emerges. <LI>The idea about hierarchy of Planck constants emerged from anomalies of biology and the strange finding that planetary orbits could be regarded as Bohr orbits but with a gigantic value of Planck constant. This lead to the vision that dark matter corresponds to ordinary particles but with non-standard value of Planck constant and to a generalization of the 8-D imbedding space to a book like structure with pages partially characterized by the value of Planck constant. Using the intuition provided by the inclusions of hyper-finite factors of type II₁ one ends up to a prediction for the spectrum of Planck constants associated with> M⁴; and CP₂ degrees of freedom. This inspires the proposal that dark matter could be in quantum Hall like phase localized at light-like 3-surfaces with macroscopic size and behaving in many respects like black hole horizons. </OL>

I take a very exciting and revival excurse on a hypothesis that has risen in the midst of General Relativity and Quantum field description (in the form of the electromagnetic wave). The Emeritus Dr. Cooperstock has derived the absence of energy harvesting from the gravitational waves using wave description of light, however latter MUST be seen as photon gas. Let me show this necessity in the paper. The paper explains the known result of Dr. Cooperstock, hereby defending the previous authors (which the Dr. Cooperstock criticizes). I show, that they do not contradict the Dr. Cooperstock result, but very strongly support it. Also presented my attempt to generalize the Dr. Cooperstock result to more nonlinear, more higher precision.

Some novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) were explored recently. In particular, generalized photon dispersion relations allowed for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, but breaking the $extended$ Lorentz symmetry in $C$-spaces. In this work we analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of ``extended events" one finds a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. A generalized Weyl-Heisenberg algebra, involving polyvector-valued coordinates and momenta operators, furnishes a realization of an extended Poincare algebra in $C$-spaces. In addition to the Planck constant $\hbar$, one finds that the commutator of the Clifford scalar components of the Weyl-Heisenberg algebra requires the introduction of a $dimensionless$ parameter which is expressed in terms of the ratio of two length scales : the Planck and Hubble scales. We finalize by discussing the concept of ``photons", null intervals, effective temporal variables and the addition/subtraction laws of generalized velocities in $C$-space.

The present reading is part of our on-going attempt at the foremost endeavour of physics since man began to comprehend the heavens and the earth. We present a much more improved unified field theory of all the Forces of Nature i.e. the gravitational, the electromagnetic, the weak and the strong nuclear forces. The proposed theory is a radical improvement of Professor Herman Weyl's supposed failed attempt at a unified theory of gravitation and electromagnetism. As is the case with Professor Weyl's theory, unit vectors in the resulting/proposed theory vary from one point to the next, albeit, in a manner such that they are compelled to yield tensorial affinities. In a separate reading, the Dirac equation is shown to emerge as part of the description of the these variable unit vectors. The nuclear force fields -- i.e., electromagnetic, weak and the strong -- together with the gravitational force field are seen to be described by a four vector field, which forms part of the body of the variable unit vectors and hence the metric of spacetime. The resulting theory very strongly appears to be a logically consistent and coherent unification of classical and quantum physics and at the same time a grand unity of all the forces of Nature. Unlike most unification theories, the present proposal is unique in that it achieves unification on a four dimensional continuum of spacetime without the need for extra-dimensions.

In the model of low-energy quantum gravity by the author, the ratio ${H(z) / (1+z)}$ should be equal to the Hubble constant. Here, the weighted average value of the Hubble constant has been found using 29 observed values of the Hubble parameter $H(z)$: $<H_{0}>\pm \sigma_{0}=(64.40 \pm 5.95) \ km \ s^{-1} \ Mpc^{-1}. $

A Clifford-Gravity based model is exploited to build a generalized action (beyond the current ones used in the literature) and arrive at relevant numerical results which are consistent with the presently-observed de Sitter accelerating expansion of the universe driven by a very small vacuum energy density $ \rho_{obs} \sim 10^{ -120} (M_P)^4 $ ($ M_P $ is the Planck mass) and provide promising dark energy/matter candidates in terms of the $16$ scalars corresponding to the degrees of freedom associated with a $ Cl(3,1)$-algebra valued scalar field $ {\bf \Phi} $ in four dimensions.

Grand unification can be considered as a virtual crossword ideas, hypotheses and theories. Compose and solve this crossword, we develop new ideas and hypotheses, which intersect with each other. The idea of space consisting of unit cells allows us to relate gravitation to the ability of unit cells to change volume, and electromagnetism to the ability of unit cells to internal movement. The ability of unit cells to form short-range order suggests that photons, leptons, mesons and baryons have structure of regular and semiregular polyhedra. Applied to dark matter, new model of elementary particles leads to the conclusion that elements of DM are non-relativistic nuclei consisting of neutrinos or antineutrinos. It is alleged that neutrinos are capable to form short-lived Cooper pairs most of which immediately decay appearing oscillation, and other fuse into nuclei of deutrinium, the lightest element of DM.

Black hole (BH) quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In this specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and non-strictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, this work exemplifies a series of imperative corrections that eventually permits a BH's horizon area spectrum to be generalized from strictly thermal to non-strictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the identified results are significant because quasi-normal modes (QNM) and "effective states" characterize the transitions between the established levels of the non-strictly thermal spectrum.

Knot physics describes the geometry of particles and fields. In a previous paper we described the topology and geometry of an electron. From the geometry of an electron we can construct a mathematical model relating its charge to its spin angular momentum. From experimental data, the spin angular momentum is hbar/2. Therefore the mathematical model provides a comparison of electron charge to Planck’s constant, which gives the fine structure constant alpha. We find that using only electromagnetic momentum to derive the fine structure constant predicts a value for 1/alpha that is about two orders of magnitude too small. However, the equations of knot physics imply that the electromagnetic field cusp must be compensated by a geometric field cusp. The geometric cusp is the source of a geometric field. The geometric field has momentum that is significantly larger than the momentum from the electromagnetic field. The angular momentum of the two fields together predicts a fine structure constant of 1/alpha = 136.85. Compared to the actual value of 1/alpha = 137.04, the error is 0.13%. Including the effects of virtual particles may reduce the error further.

Spacetime is assumed to be a branched 4-dimensional manifold embedded in a 6-dimensional Minkowski space. The branches allow quantum interference, each individual branch is a history in the sum-over-histories. A n-manifold embedded in a n+2-space can be knotted. The metric on the spacetime manifold is inherited from the Minkowski space and only allows a particular variety of knots. We show how those knots correspond to the observed particles with corresponding properties. We derive a Lagrangian. The Lagrangian combined with the geometry of the manifold produces gravity, electromagnetism, weak force, and strong force.

It is argued that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete, is described by continuous mathematics. Moreover, no ultimate physical theory can be based on continuous mathematics because, as follows from G\"{o}del's incompleteness theorems, any mathematics involving the set of all natural numbers has its own foundational problems which cannot be resolved. In the first part of the paper inconsistencies in standard approach to quantum theory are discussed and the theory is reformulated such that it can be naturally generalized to a formulation based on discrete and finite mathematics. Then the cosmological acceleration and gravity can be treated simply as {\it kinematical} manifestations of de Sitter symmetry on quantum level ({\it i.e. for describing those phenomena the notions of dark energy, space-time background and gravitational interaction are not needed}). In the second part of the paper motivation, ideas and main results of a quantum theory over a Galois field (GFQT) are described. In contrast to standard quantum theory, GFQT is based on a solid mathematics and therefore can be treated as a candidate for ultimate quantum theory. The presentation is non-technical and should be understandable by a wide audience of physicists and mathematicians.

English(traduction): Here mention that gravity is not a variety of Riemann space is following patterns Similar to the special theory of relativity as to time warp refers . We show that the Euclidean continuum is a mathematical entelequia, and therefore has a curved surface and a single point of a plane tangent to said surface . The infinitesimal character disappears to make way for spacetime quanta, which depend on the distance to the center of the attractor mass and the magnitude of it. Regarding the gemini speed. Perceive the distorted astronomical periods. Explaining and severity depends on the set of all the stars that populate the universe. It is argued that solar radiation is due to the expansion of the universe, also mentioning the peculiarities the Sun. It explains that both local gravity, as the trajectory of a photon are few and obey forminvariantes space and time, based on all stars. It is stated that the time dilation factor in the TRE is a consequence of the sets of star, both with inertia as electric potential. And finally , the possibility of an even ours but added compound Universe antimatter. Being the last over time because of the flux density of electric field. The details of an experiment made ??with a time dilation charged sphere can be found in Appendix C. Spanish (original): Aquí se hace mención a que la gravedad no es una variedad del espacio de Riemann, siguiendo unos patrones similares a los de la teoría de la relatividad especial en cuanto a deformación del tiempo se refiere. Se demuestra que el continuo euclidiano es una entelequia matemática, y, por tanto, una superficie curva tiene un y un solo punto de un cierto plano, tangente a dicha superficie. El carácter infinitesimal desaparece para dejar paso a cuantos de espaciotiempo, que dependen de la distancia al centro de la masa atractora y de la magnitud de ésta. En cuanto a la velocidad géminis. Percibimos los períodos astronómicos distorsionados. Explicando como la gravedad depende del conjunto de todas las estrellas que pueblan el Universo. Se argumenta que la radiación solar es debida a la expansión del Universo, mencionando además las peculiaridades del Sol. Se explica que tanto la gravedad local, como la trayectoria de un fotón son forminvariantes y obedecen a cuantos de espacio y de tiempo, en función de todas las estrellas. Se expone que el factor de dilatación temporal de la TRE es consecuencia de los conjuntos de estrellas, tanto con inercia como con potencial eléctrico. Y, por último, se añade la posibilidad de que exista un Universo parejo al nuestro pero compuesto de antimateria. Siendo la causa última del transcurso del tiempo la densidad de flujo de Campo eléctrico. En el Apéndice C se recogen los detalles de un experimento de dilatación temporal hecho con una esfera cargada.

An analysis of some of the applications of Clifford Space Relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.

We improve our earlier work in [14] and derive the minimal length string/membrane uncertainty relations by imposing momentum slices in flat Clifford spaces. The Jacobi identities associated with the modified Weyl-Heisenberg algebra require noncommuting spacetime coordinates, but commuting momenta, and which is compatible with the notion of curved momentum space. Clifford Phase Space Relativity requires the introduction of a maximal scale which can be identified with the Hubble scale and is a consequence of Born's Reciprocal Relativity Principle.

This paper presents a proof of the fundamental connection between the zeros of the Riemann function and quantum mechanics. Two results that unify gravity and electromagnetism, by exact calculation, both the elementary electric charge and mass of the electron. These two results depend directly on the sum of the imaginary parts of the zeros of the Riemann function, exactly following the Hilbert-Polya conjecture. This summatory, is the exponential sums of all the negative values ​​of the imaginary part of all zeros of the Riemann function.The main consequences are: scales of the Planck length gravity becomes repulsive, through the interaction of the gravitinos. Special relativity is a special case of a generalization, in which the geometry of a wormhole (hyperbolic geometry) implies that the energy of the tachyon states is zero, only if the velocity at the outer surface of the wormhole is infinite, or what is the same: an observer at rest can not distinguish an infinite speed of zero velocity, both are equivalent. There is not mere speculation; since only under this assumption the mass of the electron as a function of the non-trivial zeros of the Riemann zeta function is calculated. Time ceases to exist, takes the value zero. These wormholes would explain the quantum entanglement, as well as resolve the paradox of information loss in black holes. Fundamental constants used in this calculation are: elementary charge, gravitational Newton constant, Planck mass, mass of the electron, and fine structure constant for zero momentum.

Recently, novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) were explored and which provided a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. An elegant $nonlinear$ momentum-addition law was derived that tackled the ``soccer-ball'' problem in DSR. Generalized photon dispersion relations allowed also for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, but breaking the $extended$ Lorentz symmetry in $C$-spaces. This does $not$ occur in DSR nor in other approaches, like the presence of quantum spacetime foam. In this work we show why a $minimal$ length (say the Planck scale) follows naturally from the Extended Relativity principle in Clifford Spaces. Our argument relies entirely on the Physics behind the extended notion of Lorentz transformations in $ C$-space, and $does ~not$ invoke quantum gravity arguments, nor quantum group deformations of Lorentz/Poincare algebras, nor other prior arguments displayed in the Physics literature. The Extended Relativity Theory in Clifford $Phase$ Spaces requires also the introduction of a $maximal$ scale which can be identified with the Hubble scale. It is found also that $ C$-space physics favors a choice of signature $ ( -, +, +, .... , + ) $.

We argue that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete and even finite, is described by classical mathematics involving the notions of infinitely small, continuity etc. Moreover, since classical mathematics has its own foundational problems which cannot be resolved (as follows, in particular, from G\"{o}del's incompleteness theorems), the ultimate physical theory cannot be based on that mathematics. In the first part of the work we discuss inconsistencies in standard quantum theory and reformulate the theory such that it can be naturally generalized to a formulation based on finite mathematics. It is shown that: a) as a consequence of inconsistent definition of standard position operator, predictions of the theory contradict the data on observations of stars; b) the cosmological acceleration and gravity can be treated simply as {\it kinematical} manifestations of quantum de Sitter symmetry, {\it i.e. the cosmological constant problem does not exist, and for describing those phenomena the notions of dark energy, space-time background and gravitational interaction are not needed}. In the second part we first prove that classical mathematics is a special degenerate case of finite mathematics in the formal limit when the characteristic $p$ of the field or ring in the latter goes to infinity. {\bf This implies that mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit and infinitely small/large and the notions constructed from them (e.g. continuity, derivative and integral) are needed only in calculations describing nature approximately}. In a quantum theory based on finite mathematics, the de Sitter gravitational constant depends on $p$ and disappears in the formal limit $p\to\infty$, i.e. gravity is a consequence of finiteness of nature. The application to particle theory gives that the notion of a particle and its antiparticle is only approximate and, as a consequence: a) the electric charge and the baryon and lepton quantum numbers can be only approximately conserved; b) particles which in standard theory are treated as neutral (i.e. coinciding with their antiparticles) cannot be elementary. We argue that only Dirac singletons can be true elementary particles and discuss a conjecture that classical time $t$ manifests itself as a consequence of the fact that $p$ changes, i.e. $p$ and not $t$ is the true evolution parameter.

I propose a simple model for quarks and leptons in order to analyze what could be the building blocks of the Standard Model of particles. I start with the least number of elementary fields and generate using the Nambu--Jona-Lasinio model light masses for the subconstituent fermions. The NJL coupling constant turns out to be of the order of the gravitational coupling constant.

Novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) are explored. The latter theory provides a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. Furthermore, an elegant $nonlinear$ momentum-addition law is derived in order to tackle the ``soccer-ball'' problem in DSR. Neither derivation in $C$-spaces requires a $curved$ momentum space nor a deformation of the Lorentz algebra. While the constant (energy-independent) speed of photon propagation is always compatible with the generalized photon dispersion relations in $C$-spaces, another important consequence is that these generalized photon dispersion relations allow also for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, while breaking the $extended$ Lorentz symmetry in $C$-spaces. This does $not$ occur in DSR nor in other approaches, like the presence of quantum spacetime foam. We conclude with some comments on the quantization program and the key role that quantum Clifford-Hopf algebras might have in the future developments since the latter $q$-Clifford algebras naturally contain the $ \kappa$-deformed Poincare algebras which are essential ingredients in the formulation of DSR.

In this note, we preliminarily discuss the possibility that the expression \alpha_{em}^{-1}=4\pi^{3}+\pi^{2}+\pi has a physical interpretation and can even be helpful in model building. If one interprets this expression in terms of the volumes of l_{p} - sized three-cycles on G_{2} holonomy manifolds and requires that it also comprises effects of the running of the coupling, one can obtain the desired value, but only in a setup which is clearly different from the standard model of particle physics (SM). An understanding of the nature of the link between such putative model and SM is needed. Studying this issue could possibly shed some light on existing problems in model building within string theory (ST), particularly the hierarchy problem. Numerological “success”, which can be achieved if one interprets the formula in terms of volumes of three-cycles on the compactification manifold, as we intend to do here, cannot change the fact that discussion in this note represents merely a heuristic estimate of the feasibility of further research in a certain direction.

We propose a model of quark and lepton subconstituents which extends the Standard Model of particles to the Planck scale and beyond. We perform a Gedanken experiment by scattering a probe deep inside a mini black hole. We assume the result is that at the core of the hole there is a spin 1/2 (or 0) constituent field, grayon, in Minkowski space. The grayon is proposed to replace the singularity of the hole. The grayon interactions are assumed to provide bound states of three grayons which form the quarks and leptons.

Part two of the Origins of Matter and Gravity paper. We show a group of equations that appear to represent target values for the mass, radius, and number of elementary particles in the universe: the values of an 'ideal particle'. Quanta and particles are not static; they change with time. The angular momentum of the universe is continually increasing, and this requires a dynamical response to conserve angular momentum. The creation, collapse, and coalescence of quanta conserves angular momentum, resulting in the creation of particles of matter. Matter is condensed space. The increase in the gravitational potential energy of particles matches the accretion rate of energy predicted by this model. This gives a simple, universe-wide mechanism for the creation of matter, and is the reason all elementary particles, of a kind, are identical. The centripetal force of a particle of matter matches the gravitational force; they are the same entity. Gravity is the ongoing accretion of the quanta of space by particles of matter.

A Clifford $ Cl ( 5, C ) $ Unified Gauge Field Theory formulation of Conformal Gravity and $ U (4 ) \times U ( 4 ) \times U(4) $ Yang-Mills in $ 4D$, is reviewed, along with its implications for the Pati-Salam group $ SU (4) \times SU(2)_L \times SU(2)_R$, and $Trinification$ GUT models of $3$ fermion generations based on the group $ SU (3)_C \times SU (3)_L \times SU(3)_R$. We proceed with a brief review of a unification program of $4D$ Gravity and $SU(3) \times SU (2) \times U (1)$ Yang-Mills emerging from $8D$ pure Quaternionic Gravity. A realization of $E_8$ in terms of the $Cl(16) = Cl (8) \otimes Cl(8)$ generators follows, as a preamble to Tony Smith's $E_8$ and $ Cl(16) = Cl(8) \otimes Cl(8)$ unification model in $8D$. The study of Chiral Fermions and Instanton Backgrounds in $ {\bf CP}^2, {\bf CP}^3$ related to the problem of obtaining $3$ fermion generations is thoroughly studied. We continue with the evaluation of the coupling constants and particle masses based on the geometry of bounded complex homogeneous domains and geometric probability theory. An analysis of neutrino masses, Cabbibo-Kobayashi-Maskawa quark-mixing matrix parameters and neutrino-mixing matrix parameters follows. We finalize with some concluding remarks about other proposals for the unification of Gravity and the Standard Model, like string, $M, F$ theory and Noncommutative and Nonassociative Geometry.

The well known expectations to unify general relativity with quantum mechanics did not give some essential results up to now. If quantum gravity has such a poor set of tiny effects as in existing models, it may not be of great interest for physics. But there is another approach to quantum gravity, in which it seems to be a common ground of general relativity and quantum mechanics rather than their consequence. Important features of the author's model of low-energy quantum gravity, such as the quantum mechanism of classical gravity, the quantum mechanism of redshift and the specific relaxation of any photonic flux, are described here. In the model, the Newton and Hubble constants may be computed, but the latter is not connected with any expansion. The model fits SN1a and GRB observations very well without dark energy. Some possibilities to verify the model in ground-based experiments are discussed.

In this paper we present an anachronistic pre-YM and pre-GR attempt to formulate an alternative mathematical physics language in order to treat the problem of the electron in twentieth century physics. We start the construction of our alternative to the Minkowski-Laue consensus by putting spin in the metric. This allows us to simplify Lorentz transformations as metric transformations with invariant coordinates. Using the developed formalism on the Pauli-Dirac level,we expand the quantum helicity operators into helicity rotators and then extend them from the usual 3-D expressions to 4-D variants. We connect the resulting 4-D Dirac-Weyl hyperbolic rotators to mathematical expressions that are very similar to their analogues in the pre General Relativity attempts towards a relativistic theory of gravity. This relative match motivates us to interpret the 4-D hyperbolic rotation angle as possibly gravitational in nature. At the end we apply the 4D hyperbolic rotator to the Dirac equation and investigate how it might change this equation and the related Lagrangian. We are curious to what extend the result enters the realm of quantum gravity and thus might be beyond pre-GR relativistic theories of gravity of Abraham, Nordstr{\"o}m, Mie and Einstein.

A question about how non-planar Feynman diagrams could be represented in twistor Grassmannian approach inspired a re-reading of the recent article by <A HREF="http://arxiv.org/pdf/1212.5605v1.pdf">recent article</A> by Nima Arkani-Hamed et al. This inspired the conjecture that non-planar twistor diagrams correspond to non-planar Feynman diagrams and a concrete proposal for realizing the earlier proposal that the contribution of non-planar diagrams could be calculated by transforming them to planar ones by using the procedure applied in knot theories to eliminate crossings by reducing the knot diagram with crossing to a combination of two diagrams for which the crossing is replaced with reconnection.

The original motivation of this work was related to Platonic solids. The playing with Einstein's equations and the attempts to interpret them physically forced the return to an old interpretational problem of TGD. TGD allows enormous vacuum degeneracy for Kähler action but the vacuum extremals are not gravitational vacua. Could this mean that TGD forces to modify Einstein's equations? Could space-time surfaces carrying energy and momentum in GRT framework be vacua in TGD context? Of course, also in GRT context cosmological constant means just this and an experimental fact, is that cosmological constant is non-vanishing albeit extremely small. </p><p> Trying to understand what is involved led to the realization that the hypothesis that preferred extremals correspond to the solutions of Einstein-Maxwell equations with cosmological constant is too restricted in the case of vacuum extremals and also in the case of standard cosmologies imbedded as vacuum extremals. What one must achieve is the vanishing of the divergence of energy momentum tensor of Kähler action expressing the local conservation of energy momentum currents. The most general analog of Einstein's equations and Equivalence Principle would be just this condition giving in GRT framework rise to the Einstein-Maxwell equations with cosmological constant. The vanishing or light-likeness of Kähler current guarantees the vanishing of the divergence for the known extremals. </p><p> One can however wonder whether it could be possible to find some general ansätze allowing to satisfy this condition. This kind of ansätze can be indeed found and can be written as kG+∑ Λ_iP_i=T, where Λ_i are cosmological "constants" and P_i are mutually orthogonal projectors such that each projector contribution has a vanishing divergence. One can interpret the projector contribution in terms of topologically condensed matter, whose energy momentum tensor the projectors code in the representation kG=-∑Λ_iP_i+T. Therefore Einstein's equations with cosmological constant are generalized. This generalization is not possible in General Relativity, where Einstein's equations follow from a variational principle. This kind of ansätze can be indeed found and involve the analogs of cosmological constant, which are however not genuine constants anymore. Therefore Einstein's equations with cosmological constant are generalized. This generalization is not possible in General Relativity, where Einstein's equations follow from a variational principle. </p><p> The suggested quaternionic preferred extremals and preferred extremals involving Hamilton-Jacobi structure could be identified as different families characterized by the little group of particles involved and assignable to time-like/light-like local direction. One should prove that this ansatz works also for all vacuum extremals. This progress - if it really is progress - provides a more refined view about how TGD Universe differs from the Universe according to General Relativity and leads also to a model for how the cosmic honeycomb structure with basic unit cells having size scale 10⁸ ly could be modelled in TGD framework.

The article by Tim Adamo titled <A HREF="http://arxiv.org/pdf/1308.2820.pdf">"Twistor actions for gauge theory and gravity"</A> considers the formulation of N=4 SUSY gauge theory directly in twistor space instead of Minkowski space. The author is able to deduce MHV formalism, tree level amplitudes, and planar loop amplitudes from action in twistor space. Also local operators and null polygonal Wilson loops can be expressed twistorially. This approach is applied also to general relativity: one of the challenges is to deduce MHV amplitudes for Einstein gravity. The reading of the article inspired a fresh look on twistors and a possible answer to several questions (I have written two chapters about twistors and TGD giving a view about development of ideas). </p><p> Both M⁴ and CP₂ are highly unique in that they allow twistor structure and in TGD one can overcome the fundamental "googly" problem of the standard twistor program preventing twistorialization in general space-time metric by lifting twistorialization to the level of the imbedding space containg M⁴ as a Cartesian factor. Also CP₂ allows twistor space identifiable as flag manifold SU(3)/U(1)× U(1) as the self-duality of Weyl tensor indeed suggests. This provides an additional "must" in favor of sub-manifold gravity in M⁴× CP₂. Both octonionic interpretation of M⁸ and triality possible in dimension 8 play a crucial role in the proposed twistorialization of H=M⁴× CP₂. It also turns out that M⁴× CP₂ allows a natural twistorialization respecting Cartesian product: this is far from obvious since it means that one considers space-like geodesics of H with light-like M⁴ projection as basic objects. p-Adic mass calculations however require tachyonic ground states and in generalized Feynman diagrams fermions propagate as massless particles in M⁴ sense. Furthermore, light-like H-geodesics lead to non-compact candidates for the twistor space of H. Hence the twistor space would be 12-dimensional manifold CP₃× SU(3)/U(1)× U(1). </p><p> Generalisation of 2-D conformal invariance extending to infinite-D variant of Yangian symmetry; light-like 3-surfaces as basic objects of TGD Universe and as generalised light-like geodesics; light-likeness condition for momentum generalized to the infinite-dimensional context via super-conformal algebras. These are the facts inspiring the question whether also the "world of classical worlds" (WCW) could allow twistorialization. It turns out that center of mass degrees of freedom (imbedding space) allow natural twistorialization: twistor space for M⁴× CP₂ serves as moduli space for choice of quantization axes in Super Virasoro conditions. Contrary to the original optimistic expectations it turns out that although the analog of incidence relations holds true for Kac-Moody algebra, twistorialization in vibrational degrees of freedom does not look like a good idea since incidence relations force an effective reduction of vibrational degrees of freedom to four. The Grassmannian formalism for scattering amplitudes generalizes practically as such for generalized Feynman diagrams. The Grassmannian formalism for scattering amplitudes generalizes for generalized Feynman diagrams: the basic modification is due to the presence of CP₂ twistorialization required by color invariance and the fact that 4-fermion vertex -rather than 3-boson vertex- and its super counterparts define now the fundamental vertices.

A formula, derived from general relativity, is given that can be used to generate a cosmological mass spectrum. The spectrum values come out as kilograms and are determine by two input parameters galactic epoch birth time, t_b, and a scale factor theta_0.

In the sixties Ogievetskiı and Polubarinov proposed the concept of notoph, whose helicity properties are complementary to those of photon. Later, Kalb and Ramond (and others) developed this theoretical concept. And, at the present times it is widely accepted. We analyze the quantum theory of antisymmetric tensor fields with taking into account mass dimensions of notoph and photon. It appears to be possible the description of both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it, and we obtain the spin-2 relativistic equations, which are consistent with the general relativity. The importance of the 4-vector field (and its gauge part) is pointed out. Thus, we present the full theory which contains the photon, the notoph (the Kalb-Ramond field) and the graviton. The relations of this theory with the higher spin theories are established. In fact, we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with scalar-tensor theories of gravitation and f(R) are discussed. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they will be probably seen in experiments in the next few years. PACS number: 03.65.Pm , 04.50.-h , 11.30.Cp

An $extended$ Orthogonal-Symplectic Clifford Algebraic formalism is developed which allows the novel construction of a graded Clifford gauge field theory of gravity. It has a direct relationship to higher spin gauge fields, bimetric gravity, antisymmetric metrics and biconnections. In one particular case it allows a plausible mechanism to cancel the cosmological constant contribution to the action. The possibility of embedding these Orthogonal-Symplectic Clifford algebras into an infinite dimensional algebra, coined $Super$-Clifford Algebra is described. Finally, some physical applications of the geometry of $Super$-Clifford spaces to Generalized Supergeometries, Double Field Theories, $ U$-duality, $11D$ supergravity, $M$-theory, and $ E_7, E_8, E_{11}$ algebras are outlined.

The non-strictly continuous character of the Hawking radiation spectrum generates a natural correspondence between Hawking radiation and black hole (BH) quasi-normal modes (QNM). In this work, we generalize recent results on this important issue to the framework of Kerr BHs (KBH). We show that for the KBH, QNMs can be naturally interpreted in terms of quantum levels. Thus, the emission or absorption of a particle is in turn interpreted in terms of a transition between two different levels. At the end of the paper, we also generalize some concepts concerning the "effective state" of a KBH.

Some important consequences of the model of low-energy quantum gravity by the author are described, which give a possibility to re-interpret such cosmological observations as redshifts of remote objects and the dimming of Suprnovae 1a without any expansion of the Universe and without dark energy, but as manifestations of quantum gravity.

Imagine for a moment an endless diamond, completely solid and pristine. No flaws or gaps in the structure. Suppose at some point in the density of the material something strange occurs in that a deformation appears out of nowhere which splits into two waves. Should these two waves interact again with each other, the deformation disappears. However should they separate enough then one of the waves, which we shall call the baryon wave, is stable by itself. This wave has the strange property that it is a traveling decrease in density of the diamond. There is no "other" material, only the decrease in something we shall have to think of as the vacuum (energy) density. The wave apparently has the ability to pass through or combine into structures with other baryon waves but has no ability to disappear back into a pristine diamond if there is no second deformation wave present, which we do not cover in this essay. Suppose that a certain combination of these first waves were to become sentient. Would they be able to detect that they are a moving wave or would their perceptions lead them to a misunderstanding of how these waves effect the very substance that they are traveling within and so not realize there exists another class of solutions for tensors (scalars, vectors and so on)? Is there a way to determine that the actual density is a fairly good model for their universe? If so, what mathematics would be required in order to describe it much better than other models which the sentient waves have based on their physical perceptions? It is due to this question that we present our proposed answer of a modication of calculus. In order to fully describe the baryon wave, the dimensions they create with their presence, the limited radius distortions they cause and even the substance itself we must re-evaluate our understanding of calculus in order to model them as the derivatives of finite Action area integrals. We propose that in order to understand how the universe stores information, we must have a foundational basis for these areas, and in order to understand how it processes information we must ensure that we have within the literature all classes of its derivatives (directional derivatives, divergence, etc.). We do not go into details in this essay, but our proposed future path is to accomplish this via a modification of Gunnar Nordstroem's gravitational theory, an early competing model to General Relativity worked on by Nordstroem, Einstein and Fokker (see [1] for a recent review). This model was discarded by Einstein and others since it did not predict gravitational lensing, a problem which our modication would seem to have the possibility of remedying (see final assertions). Therefore in this essay we introduce our different view point of calculus, named "Area" Calculus in order to distinguish the concept from the mainstream variety which we will refer to as "Single Function" Calculus.

There are two types of fundamental quantum gravitational mass amplitude states that are denoted by the subscripts D and P. The D amplitudes lead to Einstein's usual general relativity mass density functions. The P amplitudes lead to Einstein's additional pressure mass densities, 3P/c². Both of these densities appear in the stress energy momentum tensor of general relativity. Here they appear as solutions to a non-linear Schrödinger equation and carry three quantising parameters (l_D,m) and (l_P,m), The l_D,l_P values are subsets of the usual electronic quantum variable l which is here denoted by l' to avoid confusion. The m parameter is exactly the same as the electronic quantum theory m, there the z component of angular momentum. In this paper, these parametric relations are briefly displayed followed by an account of the connection to the spherical harmonic functions symmetry system that is necessarily involved. Taken together, the two types of mass density can be integrated over configuration space to give quantised general relativity galactic masses in the form of cosmological mass spectra as was shown in previous papers. Here this aspect has been extended to ensure that every galaxy component of the spectra has a quantised black hole core with a consequent quantised surface area. This is achieved by replacing the original free core radius parameter r_ε with the appropriate Schwarzschild radius associated with the core mass. Explanations are given for the choices of two further, originally free, parameters, t_b, θ₀. The main result from this paper is a quantum classification scheme for galaxies determined by the form of their dark matter spherical geometry.

In recent years, the notion that information may be the basis for reality, rather than the other way around, has become more popular. Here we consider the issue within the context of a general relation between the role of physical objects against the background in shaping the pattern of distinctions that can then be translated into information. It is found that from this perspective, in classical physics substance is more fundamental than information, while in general relativity they are on an equal footing. Quantum superposition and collapse, on the other hand, introduce new considerations. A foundational principle is introduced to give an explanation for quantum superposition, and from this principle it becomes evident that to the extent that one frames the nature of quantum objects in terms of this dichotomy, in quantum theory information is more fundamental. This implies that the description of quantum objects in a superposition is dependent on features of the background, as these features set boundary conditions on such manifestations. Thus, if this principle really does underlie quantum mechanics, it means that the term "background independent quantum theory" has to be considered a contradiction, which has implications for the search for a quantum theory of gravity.

It is broadly believed that everything in the universe is found to be made from a few basic building blocks called fundamental particles, governed by four fundamental forces. However, physicists such as John Archibald Wheeler suggested that information is fundamental to the physics of the universe. According to this it from bit doctrine, all things physical are information-theoretic in origin. This doctrine is based in the old Copenhagen interpretation of quantum mechanics; an interpretation which is internally inconsistent and no applicable to the cosmos as a whole. Modern consistent interpretations of quantum mechanics eliminate the old myths about measurement processes and observers' consciousness and reintroduce the idea of a wholly physical reality, invalidating the it from bit doctrine. Utilizing a new phase space formulation of quantum mechanics developed recently by the author, the concepts of bit and it are reconsidered. We introduce the new states D as quantum bits and the new Hamiltonians H as quantum its. The new concepts of it and bit introduced in this work have a well-defined and rigorous definition, unlike Wheeler's concepts. Moreover, the new concepts apply on situations where the traditional wavefunction theory does not work. The it H is not derivable from the bit D and, as a consequence, the old it from bit doctrine gets substituted by the new it and bit. After showing why the physical entropy used in the science of thermodynamics is not a measure of the ignorance of human observers, the final part of this Essay is devoted to emphasize the importance that the bit acquires in modern science when confronted to the delicious multiplicity of the far-from-equilibrium regimes, where the certainty of Newtonian and Schrödinger motion begin to fade in favour of a complex non-geometrical, 'living', conception of Nature: an it and bit conception.

An octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket defined earlier by Yamazaki. The ternary infinitesimal gauge transformations do obey the key $closure$ relations $ [ \delta_1, \delta_2] = \delta_3 $. An invariant action for the octonionic-valued gauge fields is displayed after solving the previous problems in formulating a non-associative octonionic ternary gauge field theory. These octonionc ternary gauge field theories constructed here deserve further investigation. In particular, to study their relation to Yang-Mills theories based on the $G_2$ group which is the automorphism group of the Octonions and their relevance to Noncommutative and Nonassociative Geometry.

We extend the construction of Born's Reciprocal Relativity theory in ordinary phase spaces to an extended phase space based on Quaternions. The invariance symmetry group is the (pseudo) unitary quaternionic group $ U ( N_+, N_-, {\bf H} ) $ which is isomorphic to the unitary symplectic group $ USp( 2N_+, 2 N_-, {\bf C} )$. It is explicitly shown that the quaternionic group $ U ( N_+, N_-, {\bf H} ) $ leaves invariant both the quadratic norm (corresponding to the generalized Born-Green interval in the extended phase space) and the tri-symplectic $ 2 $-form. The study of Octonionic, Jordan and ternary algebraic structures associated with generalized spacetimes (and their phase spaces) described by Gunaydin and collaborators is reviewed. A brief discussion on $n$-plectic manifolds whose Lie $ n$-algebra involves multi-brackets and $n$-ary algebraic structures follows. We conclude with an analysis on the role of higher-order Finsler geometry in the construction of extended relativity theories with an upper and lower bound to the higher order accelerations (associated with the higher order tangent and cotangent spaces).

Much of the introductory section of this paper is devoted to displaying some previously obtained formulae, incorporating a change of notation and variables and giving some explanation of the relation of the work to Newtonian gravitation theory. This section all refers to a quantisation of gravity concentrated on and limited to galaxies with totally spherically symmetric cores and halos. Only the radial variable r is involved and the emphasis is on the dark matter concept. All the following sections are devoted to generalising the theory to additionally incorporate a dependence of galactic structure on the and spherical angular coordinates. The theory is derived using Schr¨odinger quantum theory in much the same way as it was used in developing the theory of atomic structure. The theoretical structure to be developed in this papers is a hybrid formulation involving three fundamental theoretical facets, general relativity, Schr¨odinger quantum mechanics and a new theoretical version of isothermal gravity self equilibrium. The combined structure has only become possible because of the discovery of an infinite discrete set of equilibrium states associated with this later theory, the l parameter states. The configuration space structure of these states has been found to be available in Schr¨odinger theory from a special inverse square law potential which appears to supply an inverse cube self attraction to the origin that maintains galaxies in an isolated steady state self gravity quantum condition.

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state” (Verbatim from ref. 2). This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we ex- plicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schröedinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

Einstein dealt a lethal blow to Weyl's unified theory by arguing that Weyl's theory was at the very least, it was beautiful and at best, un-physical, because its concept of variation of the length of a vector from one point of space to the other meant that certain absolute quantities, such as the ``fixed" spacing of atomic spectral lines and the Compton wavelength of an Electron for example, would change arbitrarily as they would have to depend on their prehistories. This venomous criticism of Einstein to Weyl's theory remains much alive today as it was on the first day Einstein pronounced it. We demonstrate herein that one can overcome Einstein's criticism by recasting Weyl's theory into a new Weyl-kind of theory were the length of vectors are preserved as is the case in Riemann geometry. In this new Weyl theory, the Weyl gauge transformation of the Riemann metric and the electromagnetic field are preserved

A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a $spatial$ singularity at the origin $ r = 0 $ is found. These solutions are parametrized by a real valued parameter $ \lambda$ (ranging from $ 0 $ to $ \infty$) and such that the radial horizon's location is $displaced$ continuously towards the singularity ($ r = 0 $) as $ \lambda $ increases. In the limit $ \lambda \rightarrow \infty$, the location of the singularity and horizon $merges$ leading to a $null$ singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. Another salient feature of these solutions is that it leads to a modification of the Newtonian potential consistent with the effects of the generalized uncertainty principle (GUP) associated to a minimal length. The field equations due to a delta-function point-mass source at $ r = 0 $ are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions $ D \ge 3 $. The study of the Nonperturbative Renormalization Group flow of the metric $ g_{\mu v} [ k ] $ in terms of the momentum scale $ k $ and its relationship to these family of metrics parametrized by $ \lambda$ deserves further investigation.

It is shown that small quantum effects of the model of low-energy quantum gravity by the author give a possibility of another interpretation of cosmological observations without an expansion of the Universe and dark energy.

We extend the construction of Born's Reciprocal Phase Space Relativity to the case of Clifford Spaces which involve the use of $polyvectors$ and a $lower/upper$ length scale. We present the generalized polyvector-valued velocity and acceleration/force boosts in Clifford Phase Spaces and find an $explicit$ Clifford algebraic realization of the velocity and acceleration/force boosts. Finally, we provide a Clifford Phase-Space Gravitational Theory based in gauging the generalization of the Quaplectic group and invoking Born's reciprocity principle between coordinates and momenta (maximal speed of light velocity and maximal force). The generalized gravitational vacuum field equations are explicitly displayed. We conclude with a brief discussion on the role of higher-order Finsler geometry in the construction of extended relativity theories with an upper and lower bound to the higher order accelerations (associated with the higher order tangent and cotangent spaces). We explain how to find the procedure that will allow us to find the $n$-ary analog of the Quaplectic group transformations which will now mix the $X, P, Q, .......$ coordinates of the higher order tangent (cotangent) spaces in this extended relativity theory based on Born's reciprocal gravity and $n$-ary algebraic structures.

In this paper, we have made an attempt to discuss the role of octonions in superstring theory (i.e. a theory of everything to describe the unification of all four types of forces namely gravitational, electromagnetic, weak and strong) where, we have described the octonion representation of the superstring(SS) theory as the combination of four complex (C) spaces namely associated with the gravitational (G-space), electromagnetic (EM-space), weak (W-space) and strong (S-space) interactions. We have discussed the octonionic differential operator, octonionic valued potential wave equation, octonionic field equation and other various quantum equations of superstring theory in simpler, compact and consistent manner. Consequently, the generalized Dirac-Maxwell’s equations are studied with the preview of superstring theory by means of octonions.

In this paper, we have made an attempt to discuss the role of octonions in gravity and dark matter where, we have described the octonion space as the combination of two quaternionic spaces namely gravitational G-space and electromagnetic EM-space. It is shown that octonionic hot dark matter contains the photon and graviton (i.e. massless particles) while the octonionic cold dark matter is associated with the W-;Z (massive) bosons.

A preon model for standard model particles is proposed based on spin 1/2 fermion and spin 0 boson constituents. The preons are quantum mechanical strings. Implications to the number of generations, heavy boson states, and dark matter are briefly considered.

The recent progress in the understanding of preferred extremals of Kaehler action leads to the conclusion that they satisfy Einstein-Maxwell equations with cosmological term with Newton's constant and cosmological constant predicted to have a spectrum. One particular implication is that preferred extremals have a constant value of Ricci scalar. The implications of this are expected to be very powerful since it is known that D>2-dimensional manifolds allow a constant curvature metric with volume and other geometric invariants serving as topological invariants. Also the the possibly discrete generalization of Ricci flow playing key role in manifold topology to Maxwell flow is very natural, and the connections with the geometric description of dissipation, self-organization, transition to chaos and also with coupling constant evolution are highly suggestive. A further fascinating possibility inspired by quantum classical correspondence is quantum ergodicity (QE): the statistical geometric properties of preferred extremals code for various correlations functions of zero energy states defined as their superpositions so that any preferred extremal in the superposition would serve as a representative of the zero energy state. QE would make possible to deduce correlation functions and S-matrix from the properties of single preferred extremal.

Whether right-handed neutrinos generate a supersymmetry in TGD has been a long standing open question. N=1 SUSY is certainly excluded by fermion number conservation but already N=2 defining a "complexification" of N=1 SUSY is possible and could generate right-handed neutrino and its antiparticle. These states should however possess a non-vanishing light-like momentum since the fully covariantly constant right-handed neutrino generates zero norm states. So called massless extremals (MEs) allow massless solutions of the modified Dirac equation for right-handed neutrino in the interior of space-time surface, and this seems to be case quite generally in Minkowskian signature for preferred extremals. This suggests that particle represented as magnetic flux tube structure with two wormhole contacts sliced between two MEs could serve as a starting point in attempts to understand the role of right handed neutrinos and how N=2 or N=4 SYM emerges at the level of space-time geometry. The following arguments inspired by the article of Nima Arkani-Hamed et al about twistorial scattering amplitudes suggest a more detailed physical interpretation of the possible SUSY associated with the right-handed neutrinos. The fact that right handed neutrinos have only gravitational interaction suggests a radical re-interpretation of SUSY: no SUSY breaking is needed since it is very difficult to distinguish between mass degenerate spartners of ordinary particles. In order to distinguish between different spartners one must be able to compare the gravitomagnetic energies of spartners in slowly varying external gravimagnetic field: this effect is extremely small.

In zero energy ontology (ZEO) lattices in the 3-D hyperbolic manifold defined by H³ (t²-x²-y²-z²=a²) (and known as hyperbolic space to distinguish it from other hyperbolic manifolds emerge naturally. The interpretation of H³ as a cosmic time=constant slice of space-time of sub-critical Robertson-Walker cosmology (giving future light-cone of M^4 at the limit of vanishing mass density) is relevant now. ZEO leads to an argument stating that once the position of the "lower" tip of causal diamond (CD) is fixed and defined as origin, the position of the "upper" tip located at H³ is quantized so that it corresponds to a point of a lattice H³/G, where G is discrete subgroup of SL(2,C) (so called Kleinian group). There is evidence for the quantization of cosmic redshifts: a possible interpretation is in terms of hyperbolic lattice structures assignable to dark matter and energy. Quantum coherence in cosmological scales would be in question. This inspires several questions. How does the crystallography in H³ relate to the standard crystallography in Eucdlidian 3-space E³? Are there general results about tesselations H³? What about hyperbolic counterparts of quasicrystals? In this article standard facts are summarized and some of these questions are briefly discussed.

The blackhole information paradox is often believed to have solution in terms of holography stating in the case of blackholes that blackhole horizon can serve as a holographic screen representing the information about the surrounding space as a hologram. The situation is however far from settled. The newest challenge is so called firewall paradox proposed by Polchinsky et al. These paradoxes strengthen the overall impression that the blackhole physics indeed represent the limit at which GRT fails and the outcome is recycling of old arguments leading nowhere. Something very important is lacking. On the other hand, some authors like Susskind claim that the physics of this century more or less reduces to that for blackholes. I however see this endless tinkering with blackholes as a decline of physics. If super string had been a success as a physical theory, we would have got rid of blackholes. If TGD is to replace GRT, it must also provide new insights to blackholes, blackhole evaporation, information paradox and firewall paradox. This inspired me to look for what blackholes and blackhole evaporation could mean in TGD framework and whether TGD can avoid the paradoxes. This kind of exercises allow also to sharpen the TGD based view about space-time and quantum and build connections to the mainstream views.

We continue with the study of Clifford-space Gravity and find some solutions to the Clifford space ($ C$-space) generalized gravitational field equations which are obtained from a variational principle based on the generalization of the Einstein-Hilbert-Cartan action. The $C$-space connection requires $torsion$ and the field equations in $C$-space are $not$ equivalent to the ordinary gravitational equations with torsion in higher $2^D$-dimensions. We find specific metric solutions in the most simple case and discuss their difference with the metrics found in ordinary gravity.

As every circuit designer knows, the flow of energy is governed by impedance matching. Classical or quantum impedances, mechanical or electromagnetic, fermionic or bosonic, topological,... To understand the flow of energy it is essential to understand the relations between the associated impedances. The connection between electromagnetism and gravitation can be made explicit by examining the impedance mismatch between the electrically charged Planck particle and the electron. This mismatch is shown to be the ratio of the gravitational and electromagnetic forces between these particles

The geometry of the Schwarzschild black hole is compared to the geometry of the signal space from Shannon's mathematical theory of communication. One result of these considerations is that the black hole is found to leak in a way that does not introduce an information loss paradox.

Summary of articles [1, 2] is shown, and a new approach to quantum gravity is presented. It is based on suppositions that masses of black holes can be smaller than Planck's mass, that dimensionless masses of particles or black holes are a first hint toward development of quantum gravity. It is shown a new way to develop principle of uncertainty, and this principle is more fundamental than wave function. Virtual gravitons are based on a wave function and if it does not exist, they also do not exist. Thus, it is excluded contradiction that "virtual photons exist in background space-time".At the same time all is based on the principle that "gravity is not a force".

This elementary text is for anyone interested in combinatorial methods in modern axiomatic particle physics. It focuses on the role of knots in motivic arithmetic, and the connection to category theoretic structures. Phenomenological aspects of rest mass quantum numbers are also discussed.

We continue with the study of Clifford-space Gravity and analyze further the Clifford space ($ C$-space) generalized gravitational field equations which are obtained from a variational principle based on the generalization of the Einstein-Hilbert-Cartan action. One of the main features is that the $C$-space connection requires $torsion$ in order to have consistency with the Clifford algebraic structure associated with the curved $C$-space basis generators. Hence no spin matter is required to induce torsion since it already exists in the vacuum. The field equations in $C$-spaces associated to a Clifford algebra in $D$-dimensions are $not$ equivalent to the ordinary gravitational equations with torsion in higher $2^D$-dimensions. The most physically relevant conclusion, besides the presence of torsion in the vacuum, is the contribution of the $higher$ grade metric components $g^{\mu_1 \mu_2 ~\nu_1 \nu_2}, g^{\mu_1 \mu_2 \mu_2~\nu_1 \nu_2 \nu_3 }, ~.....$ of the $C$-space metric to dark energy/dark matter.

R. Kiehn has proposed what he calls Topological Thermodynamics (TTD) as a new formalism of thermodynamics. The basic vision is that thermodynamical equations could be translated to differential geometric statements using the notions of differential forms and Pfaffian system. That TTD differs from TGD by a single letter is not enough to ask whether some relationship between them might exist. Quantum TGD can however in a well-defined sense be regarded as a square root of thermodynamics in zero energy ontology (ZEO) and this leads leads to ask seriously whether TTD might help to understand TGD at deeper level. The thermodynamical interpretation of space-time dynamics would obviously generalize black hole thermodynamics to TGD framework and already earlier some concrete proposals have been made in this direction. This raises several questions. Could the preferred extremals of Kähler action code for the square root of thermodynamics? Could induced Kähler gauge potential and Kähler form (essentially Maxwell field) have formal thermodynamic interpretation? The vacuum degeneracy of Kähler action implies 4-D spin glass degeneracy and strongly suggests the failure of strict determinism for the dynamics of Kähler action for non-vacuum extremals too. Could thermodynamical irreversibility and preferred arrow of time allow to characterize the notion of preferred extremal more sharply? It indeed turns out that one can translate Kiehn's notions to TGD framework rather straightforwardly. Kiehn's work 1- form corresponds to induced Kähler gauge potential implying that the vanishing of instanton density for Kähler form becomes a criterion of reversibility and irreversibility is localized on the (4-D) "lines" of generalized Feyman diagrams, which correspond to space-like signature of the induced metric. Heat produced in given generalized Feynman diagram is just the integral of instanton density and the condition that the arrow of geometric time has definite sign classically fixes the sign of produced heat to be positive. In this picture the preferred extremals of Kähler action would allow a trinity of interpretations as non-linear Maxwellian dynamics, thermodynamics, and integrable hydrodynamics.

A fundamental assumption embedded in our current worldview is that there exists an as yet undiscovered `theory of everything', a final unified framework according to which all interactions in nature are but different manifestations of the same underlying thing. This paper argues that this assumption is wrong because our current distinct fundamental theories of nature already have mutually exclusive domains of validity, though under our current worldview this is far from obvious. As a concrete example, it is shown that if the concepts of mass in general relativity and quantum theory are distinct in a specific way, their domains become non-overlapping. The key to recognizing the boundaries of the domains of validity of our fundamental theories is an aspect of the frame of reference of an observer which has not yet been appreciated in mainstream physics. This aspect, called the dimensional frame of reference(DFR), depends on the number of length dimensions that constitute an observer frame. Edwin Abbott's Flatland is used as point of departure from which to provide a gentle introduction to the applications of this idea. Finally, a metatheory of nature is proposed to encompass the collection of theories of nature with mutually exclusive domains of validity.

This essay considers eight basic physical assumptions which are not fundamental: (i) spacetime as the arena for physics, (ii) unitarity of the dynamics, (iii) microscopic time-reversibility, (iv) the need for black hole thermodynamics, (v) state vectors as the general description of quantum states, (vi) general relativity as a field theory, (vii) dark matter as real matter, (viii) and cosmological homogeneity. This selection ranges from micro-physics to cosmology, but is not exhaustive.

During years several approaches to what preferred extremals of Kähler action and solutions of the modified Dirac equation could be have been proposed and the challenge is to see whether at least some of these approaches are consistent with each other. It is good to list various approaches first. <OL> <LI> For preferred extremals generalization of conformal invariance to 4-D situation is very attractive approach and leads to concrete conditions formally similar to those encountered in string model. The approach based on basic heuristics for massless equations, on effective 3-dimensionality, and weak form of electric magnetic duality is also promising. An alternative approach is inspired by number theoretical considerations and identifies space-time surfaces as associative or co-associative sub-manifolds of octonionic imbedding space. <LI> There are also several approaches for solving the modified Dirac equation. The most promising approach is assumes that the solutions are restricted on 2-D stringy world sheets and/or partonic 2-surfaces. This strange looking view is a rather natural consequence of number theoretic vision. The conditions stating that electric charge is conserved for preferred extremals is an alternative very promising approach. </OL> The question whether these various approaches are mutually consistent is discussed. It indeed turns out that the approach based on the conservation of electric charge leads under rather general assumptions to the proposal that solutions of the modified Dirac equation are localized on 2-dimensional string world sheets and/or partonic 2-surfaces. Einstein's equations are satisfied for the preferred extremals and this implies that the earlier proposal for the realization of Equivalence Principle is not needed. This leads to a considerable progress in the understanding of super Virasoro representations for super-symplectic and super-Kac-Moody algebra. In particular, the proposal is that super-Kac-Moody currents assignable to string world sheets define duals of gauge potentials and their generalization for gravitons: in the approximation that gauge group is Abelian - motivated by the notion of finite measurement resolution - the exponents for the sum of KM charges would define non-integrable phase factors. One can also identify Yangian as the algebra generated by these charges. The approach allows also to understand the special role of the right handed neutrino in SUSY according to TGD.

A preon model is proposed based on spin 1/2 fermion and spin 0 boson constituents. They interact via a massive scalar field which is tentatively considered a phenomenological model of quantum gravity. Implications to generations, heavy boson states and dark matter are briefly discussed.

In this paper, we focus on the calculation of the supersymmetric term for obtaining the mass of the lightest Higgs boson. Thus will provide the scale of supersymmetry. Similarly, entering the exact angle β, ,will allow us to calculate the masses of the remaining four Higgs bosons , mA , mH0 , mH ± and the stop mass 422.9 Gev. Was used for this, the well-known model of a one-dimensional string, or a dimensional box. We believe that the results obtained consistent with the observation, carry a string model mathematically satisfactory of a n-dimensional string, well known to all physicists. The main novelty of this model is the introduction of dimensionless ratios between the Planck length and the length n dimensional, as the length of the string. An extension of the Heisenberg principle to extra dimensions, will derive a principle of equivalence between mass, time and space so that it showed that the mass is actually another dimension. This principle of equivalence, so described, anger further and allow the equivalence between spin, probability, fluctuations and dimensions. Successive breaking symmetries-topology geometry involved, appears to be the cause of the distinguishability between spins, number of particles, dimensions, etc.; to the observer

A modified framework for special relativity is proposed in which mass is incorporated in the temporal components of the Minkowski metric and a particle may convert between massive and massless states. The speed of such a particle therefore changes between subluminal and luminal. The well-known equations for relativistic energy of massive and massless particles do not conflict with the notion that a massive particle can convert all of its mass into energy, thereby removing the problem of requiring infinite energy to reach the speed of light barrier. This enables the production of gravitons, which in collisions transfer their momentum and energy to matter, thereby giving rise to the gravitational force. The conversion of particles between massive and massless states suggests that time, and hence the universe, is eternal.

Clifford-space Gravity is revisited and new results are found. The Clifford space ($ C$-space) generalized gravitational field equations are obtained from a variational principle and which is based on an extension of the Einstein-Hilbert-Cartan action. One of the main results of this work is that the $C$-space connection requires torsion in order to have consistency between the Clifford algebraic structure and the zero nonmetricity condition $ \nabla_K g^{MN} = 0 $. A discussion on the cosmological constant and bi-metric theories of gravity follows. We continue by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan (LLC) higher curvature gravity with torsion. We finalize by pointing out that $ C$-space gravity involves higher-spins beyond spin $ 2 $ and argue why one could view the LLC higher curvature actions, and other extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions, as mere $effective$ actions after integrating the $C$-space gravitational action with respect to all the poly-coordinates, except the vectorial ones $ x^\mu$.

he general consensus feeling amongst researchers is that it is generally difficult to obtain a position space Lorentz invariant Doubly Special Relativity (DSR) theory. In this reading, we propose such a theory. The Lorentz transformations are modified such that the resultant theory has not one, but two invariants -- the speed of light c = 2.99792458e 8 m/s, and a minimum length. Actually, we achieve our desire by infusing Heisenberg's quantum mechanical uncertainty principle into the fabric of Minkowiski spacetime. In this new theory, it is seen that under extreme quantum conditions, it should be possible to exceed the light-speed-barrier without any limit. It should be stated that this theory has been developed more as a mathematical exercise to obtain a physically reasonable as is possible a position space DSR theory that is Lorentz invariant. In the low energy regime, the theory gives the same predictions as Einstein's Special Theory of Relativity (STR).

Clifford-space Gravity is revisited and new results are found. A derivation of the proper expressions for the connections (with $torsion$) in Clifford spaces ( $C$-spaces) is presented. The introduction of hyper-determinants of hyper-matrices are instrumental in the derivation of the $ C$-space generalized gravitational field equations from a variational principle and based on the extension of the Einstein-Hilbert-Cartan action. We conclude by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan higher curvature gravity with torsion and extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions. Introducing nonmetricity furnishes higher curvature extensions of metric affine theories of gravity.

A rigorous construction of Clifford-space Gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the expressions for the connections with $torsion$ in Clifford spaces ( $C$-spaces). The $ C$-space generalized gravitational field equations are derived from a variational principle based on the extension of the Einstein-Hilbert-Cartan action. We continue by arguing how Lanczos-Lovelock-Cartan higher curvature gravity with torsion can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions. In essence, the Lanczcos-Lovelock-Cartan curvature tensors appear as Ricci-like traces of certain components of the $ C$-space curvatures. Torsional gravity is related to higher-order corrections of the bosonic string-effective action. In the torsionless case, black-strings and black-brane metric solutions in higher dimensions $ D > 4 $ play an important role in finding specific examples of solutions to Lanczos-Lovelock gravity.

Extensions of Clifford algebra are presented. Applications in physics, especially with regard to the flavor structure of Standard Model, are discussed. Modified gravity is also suggested.

A rigorous construction of Clifford-space Gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the generalized connections in Clifford spaces ( C-space) in terms of derivatives of the C-space metric. We continue by arguing how Lanczos-Lovelock higher curvature gravity can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on f ( R ), f ( R_{\mu \nu} ), .... actions, for polynomial-valued functions. Black-strings and black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples.

The unification of Einstein's field equations with Quantum field theory is a problem of theoretical physics. Many models for solving this problem were done, i.e. the String Theory or Loop quantum gravity were introduced to describe gravity with quantum theory. The main problem of this theories is that they are mathematically very complicated. In this research text, there is given another description of gravity unified with Quantum field theory. In this case, gravity is described so that for weak gravitational fields the (semi)classical gravity desciption is equivalent.

We argue that the entropic origin of gravitation correctly reproduced general relativity and quantum mechanics, with a particular treatment, where entropic gravity can be viewed as Maxwell's theory of gravity and thermodynamics. And this application will give us more detailed knowledge on the origin of gravity

Considering the `molar electron mass' an attempt is made to study the 4 interactions in a unified manner. Charged leptons, nucleons and (integral charge) quark masses were fitted in a unified scheme. Based on the modified SUSY, Higgs charged fermion, its boson and the quark baryon and quark meson masses were fitted. Finally an attempt is made to fit and predict the new excited levels of the bottom and anti bottom mesons.

In this paper we show as the lightest Higgs boson, is directly linked to the existence of seven dimensions compacted Kaluza-Klein type, and four extended. The model of a particle in a box allows us to calculate, using the extra dimensions as entries in the well-known equations of this model, the mass of the lightest Higgs boson. This estimate coincides with complete accuracy with that obtained in our previous work, "God and His Creation: The Universe", using the well known quantum mechanical model of a particle in a spherically symmetric potential. Both load match and result in a mass for the lightest Higgs boson of 126.23 Gev - 126.17 Gev

Considering the `molar electron mass' an attempt is made to understand the strong, weak and gravitational interactions in a unified approach. Muon \& tau rest masses, nuclear characteristic size, proton size, nucleon rest masses and magnetic moments were fitted. Obtained SEMF energy coefficients are 16.28, 19.36, 0.7681, 23.76 and 11.88 MeV respectively.

Considering the Avogadro number as a scaling factor an attempt is made to understand the origin of the strong, weak and electromagnetic interactions in a unified approach. Nuclear characteristic size, proton size, nucleon rest masses and magnetic moments were fitted. It is noticed that, nuclear binding energy can be understood with the `molar electron mass' and `fermi energy' concepts.

Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit, $F_C \cong \left(\frac{c^{4} }{G} \right)$. Nuclear weak force magnitude is $F_W \cong \frac{F_C}{N^2}$ where $N$ is the Avogadro number. Relation between the nuclear strong force and weak force magnitudes can be expressed as $\sqrt{\frac{F_S}{F_W}} \cong 2 \pi \ln \left(N^2\right).$ It is noticed that there exists simple relations in between the nuclear strong force, weak force and the force on the revolving electron in the Bohr radius of the Hydrogen atom. An attempt is made to couple the strong coupling constant with these 3 forces.

A unification model of 4D gravity and SU(3) x SU(2) x U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP^2 = SU (3)/U(2) symmetric space . We proceed to explore the nonlinear connection A^a_\mu ( x, y ) formalism used in Finsler geometry to show how ordinary gravity in D = 4 + 2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU (5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S^2 . This is an appealing result because SU (5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU (3) x SU (2) x U(1) \subset SU ( 5 ) \subset SU ( \infty ) .

Kaluza’s 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is inspiration for many modern attempts to develop new physical theories. For a number of reasons the theory is incomplete and generally considered untenable. An alternative approach is presented that includes torsion, unifying gravity and electromagnetism in a Kaluza-Cartan theory. Emphasis is placed on admitting important electromagnetic fields not present in Kaluza’s original theory, and on the Lorentz force law. This is investigated via a non-Maxwellian kinetic def- inition of charge related to Maxwellian charge and 5D momentum. Two connections and a new cylinder condition are used. General covariance and global properties are investigated via a reduced non-maximal atlas. Conserved super-energy is used in place of the energy conditions for 5D causality. Explanatory relationships between matter, charge and spin are present.

Nucleon behaves as if it constitutes molar electron mass. In a unified way nucleon's mass, size and other characteristic properties can be studied with this idea. If strong interaction is really $10^{39}$ times stronger than the strength of gravity, this proposal can be given a chance. Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit, $F_C \cong \left(\frac{c^{4} }{G} \right)$. It can be considered as the upper limit of the cosmic string tension. Weak force magnitude $F_W$ can be considered as the characteristic nuclear weak string tension. Until the measurement of $\left(F_C \;\&\; F_W\right)-$ it can be assumed that $\frac{F_C}{F_W}\cong N^2$ where $N$ is Avogadro like number.

Dirac singletons are exceptional irreducible representations (IRs) of the so(2,3) algebra found by Dirac. As shown in a seminal work by Flato and Fronsdal, the tensor product of singletons can be decomposed into massless IRs of the so(2,3) algebra and therefore each massless particle (e.g. the photon) can be represented as a composite state of singletons. This poses a fundamental problem of whether only singletons can be treated as true elementary particles. However, in standard quantum theory (based on complex numbers) such a possibility encounters difficulties since one has to answer the following questions: a) why singletons have not been observed and b) why the photon is stable and its decay into singletons has not been observed. We show by direct calculations that in a quantum theory over a Galois field (GFQT), the decomposition of the tensor product of singletons IRs contains not only massless IRs but also special massive IRs which have no analogs in standard theory. In the case of supersymmetry we explicitly construct a complete set of IRs taking part in the decomposition of the tensor product of supersingletons. Then in GFQT one can give natural explanations of a) and b).

The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of Planck's natural units in a future physical theory of spacetime is only a plausible, yet by no means certain, assumption. The purpose of this article is to clearly separate fact from belief in this connection.

This article deals with empty spacetime and the question of its physical reality. By "empty spacetime" we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects -- themselves intrinsic to the concept of field -- might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation -- as well as conceptual overthrow -- of this geometric ether.

This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the pseudo-Riemannian manifold of general relativity is considered a flawed description of spacetime and it is attempted to replace it by theoretical constructs of a different character, ontologically prior to it. However, despite its claims to the contrary, pregeometry is found to surreptitiously and unavoidably fall prey to the very mode of description it endeavours to evade, as evidenced in its all-pervading geometric understanding of the world. The question remains as to the deeper reasons for this human, geometric predilection--present, as a matter of fact, in all of physics--and as to whether it might need to be superseded in order to achieve the goals that frontier theoretical physics sets itself at the dawn of a new century: a sounder comprehension of the physical meaning of empty spacetime.

In this paper we demonstrate how the universe has to be caused or created by an intelligent being: God. And as the multiverse theory, mainly based on the random generation of states infinite universe is very poorly posed from the mathematical point of view, and how this failure leads to the demonstration of its impossibility. The anthropic principle called not taken into account, it is a mere philosophical statement without any physical-mathematical foundation, and therefore lacking the minimum necessary scientific validity. The main parameters are obtained: density of baryons, vacuum energy density, mass of the lightest Higgs boson, neutrino mass, mass of the graviton, among others. Deducting finally naturally within the theory, the inflation factor of the universe. Similarly, the theory implies necessarily the "creation" of matter

In the cosmic Euclidean volume, inverse of the fine structure ratio is equal to the natural logarithm of ratio of number of (electrons or positrons) and the Avogadro number. Bohr radius of hydrogen atom, quanta of the angular momentum and the strong interaction range - are connected with the large scale structure of the massive universe. In the accelerating universe, as the space expands, in hydrogen atom, distance between proton and electron increases and is directly proportional to the size of the universe. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. `Rate of decrease in fine structure ratio' is a measure of cosmic rate of expansion. Considering the integral nature of number of protons (of any nucleus), integral nature of `hbar' can be understood.

The basic challenge of quantum TGD is to give a precise content to the notion of generalization Feynman diagram and the reduction to braids of some kind is very attractive possibility inspired by zero energy ontology. The point is that no n>2-vertices at the level of braid strands are needed if bosonic emergence holds true. <OL> <LI> For this purpose the notion of algebraic knot is introduced and the possibility that it could be applied to generalized Feynman diagrams is discussed. The algebraic structrures kei, quandle, rack, and biquandle and their algebraic modifications as such are not enough. The lines of Feynman graphs are replaced by braids and in vertices braid strands redistribute. This poses several challenges: the crossing associated with braiding and crossing occurring in non-planar Feynman diagrams should be integrated to a more general notion; braids are replaced with sub-manifold braids; braids of braids ....of braids are possible; the redistribution of braid strands in vertices should be algebraized. In the following I try to abstract the basic operations which should be algebraized in the case of generalized Feynman diagrams. <LI> One should be also able to concretely identify braids and 2-braids (string world sheets) as well as partonic 2-surfaces and I have discussed several identifications during last years. Legendrian braids turn out to be very natural candidates for braids and their duals for the partonic 2-surfaces. String world sheets in turn could correspond to the analogs of Lagrangian sub-manifolds or two minimal surfaces of space-time surface satisfying the weak form of electric-magnetic duality. The latter opion turns out to be more plausible. Finite measurement resolution would be realized as symplectic invariance with respect to the subgroup of the symplectic group leaving the end points of braid strands invariant. In accordance with the general vision TGD as almost topological QFT would mean symplectic QFT. The identification of braids, partonic 2-surfaces and string world sheets - if correct - would solve quantum TGD explicitly at string world sheet level in other words in finite measurement resolution. <LI> Also a brief summary of generalized Feynman rules in zero energy ontology is proposed. This requires the identification of vertices, propagators, and prescription for integrating over al 3-surfaces. It turns out that the basic building blocks of generalized Feynman diagrams are well-defined. <LI> The notion of generalized Feynman diagram leads to a beautiful duality between the descriptions of hadronic reactions in terms of hadrons and partons analogous to gauge-gravity duality and AdS/CFT duality but requiring no additional assumptions. The model of quark gluon plasma as s strongly interacting phase is proposed. Color magnetic flux tubes are responsible for the long range correlations making the plasma phase more like a very large hadron rather than a gas of partons. One also ends up with a simple estimate for the viscosity/entropy ratio using black-hole analogy. </OL>

A summary about how various ideas about TGD have developed is given. This is a response to a request of Mark McWilliams. I try to represent the development chronologically but I must confess that I have forgotten precise dates so that the chronology is not exact. Very probably I have also forgotten many important ideas and many side tracks which led nowhere. Unavoidably the emphasis is on the latest ideas and there is of course the risk that some of them are not here to stay. Even during writing process some ideas developed into more concrete form. A good example is the vision about what happens in quantum jump and what the unitarity of U-matrix really means, how M-matrices generalize to form Kac-Moody type algebra, and how the notion of quantum jump in zero energy ontology (ZEO) reproduces the basic aspects of quantum measurement theory. Also a slight generalization of quantum arithmetics suggested itself during the preparation of the article.

It seems that- Bohr radius of hydrogen atom, quanta of the angular momentum and the strong interaction range - are connected with the large scale structure of the massive universe. In the accelerating universe, as the space expands, in hydrogen atom, distance between proton and electron increases and is directly proportional to the mass of the universe (which is the product of critical density and the Hubble volume). `Rate of decrease in fine structure ratio' is a measure of cosmic rate of expansion. Considering the integral nature of number of protons (of any nucleus), integral nature of `hbar' can be understood.

Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit, <math>F_C \cong \left(\frac{c^{4} }{G} \right)<\math>. It can be considered as the upper limit of the cosmic string tension. Weak force magnitude <math>F_W<\math> can be considered as the characteristic nuclear weak string tension. In 3+1 dimensions if strong interaction is really <math>10^{39}<\math> times stronger than the strength of gravity, until the measurement of <math>\left(F_C \;\&\; F_W\right)-<\math> it can be assumed that <math>\frac{F_C}{F_W}\cong N^2<\math> where <math>N<\math> is Avogadro like number.

It is very clear that, to unify 2 interactions if 5 dimensions are required, for unifying 4 interactions 10 dimensions are required. For 3+1 dimensions if there exists 4 (observed) interactions, for 10 dimensions there may exist 10 (observable) interactions. To unify 10 interactions 20 dimensions are required. From this idea it can be suggested that- with `n' new dimensions `unification' problem can not be resolved. By implementing the gravitational constant in atomic and nuclear physics, independent of the CGS and SI units, Avogadro number can be obtained very easily and its order of magnitude is $\cong N \cong 6 \times 10^{23}$ but not $6 \times 10^{26}.$ If $M_P$ is the Planck mass and $m_e$ is the rest mass of electron, semi empirically it is observed that, $M_g \cong N^{\frac{2}{3}}\cdot \sqrt{M_Pm_e} \cong 1.0044118 \times 10^{-3} \; Kg.$ If $m_{p} $ is the rest mass of proton it is noticed that $\ln \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} Gm_{P}^{2} } } \cong \sqrt{\frac{m_{p} }{m_{e} } -\ln \left(N^{2} \right)}.$ Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. Assumed relation for strong force and weak force magnitudes is $\sqrt{\frac{F_{S} }{F_{W} } } \cong 2\pi \ln \left(N^{2} \right)$. From SUSY point of view, `integral charge quark fermion' and `integral charge quark boson' mass ratio is $\Psi=2.262218404$ but not unity. With these advanced concepts an ``alternative" to the `standard model' can be developed.

By implementing the gravitational constant in atomic and nuclear physics, independent of the CGS and SI units, Avogadro number can be obtained very easily. It is observed that, either in SI system of units or in CGS system of units, value of the order of magnitude of Avogadro number $\cong N \cong 6 \times 10^{23}$ but not $6 \times 10^{26}.$ Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This may be the beginning of unification of `gravitational and non-gravitational interactions'.

Till today no atomic principle implemented the gravitational constant in nuclear physics. Considering the electromagnetic and gravitational force ratio of electron and proton a simple semi empirical relation is proposed for estimating the strong coupling constant. Obtained value is $\alpha_s \cong 0.117378409.$ It is also noticed that $\alpha_s\cong \ln\left(r_Ur_D\right)$ where $r_U$ and $r_D$ are the geometric ratios of Up and Down quark series respectively. It is noticed that proton rest mass is equal to $\left(\frac{1}{\alpha}+\frac{1}{\alpha_s}\right)\sqrt{UD}.$ With reference to the the electromagnetic and gravitational force ratio of electron, 137 can be fitted at $r_U $ and 128 can be fitted at $r_D.$ Finally semi empirical mass formula energy constants are fitted.

In the atomic or nuclear space, till today no one measured the value of the gravitational constant. To bring down the planck mass scale to the observed elementary particles mass scale a large scale factor is required. Ratio of planck mass and electron mass is close to $\textrm{Avogadro number}/8 \pi\cong N/8 \pi$. The idea of strong gravity originally referred specifically to mathematical approach of Abdus Salam of unification of gravity and quantum chromo-dynamics, but is now often used for any particle level gravity approach. In this connection it is suggested that, key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This is another significance of Avogadro number. If $R_0\cong 1.21$ fermi is the nuclear charge radius, to a very good accuracy it is noticed that in Hydrogen atom, ratio of total energy of electron and nuclear potential is equal to the electromagnetic and gravitational force ratio of electron where the operating gravitational constant is $N^2G_C$ but not $G_C.$ Square root of ratio of strong and weak force magnitudes can be expressed as $2 \pi \ln\left(N^2\right).$ With the defined strong and weak force magnitudes observed elementary particles masses and their magnetic moments can be generated. Interesting application is that: characteristic building block of the cosmological ‘dark matter’ can be quantified in terms of fundamental physical constants. No extra dimensions are required in this new approach.

It is noticed that, when the black hole mass density reaches the nuclear mass density, mass of the black hole approaches to $1.81\times 10^{31} \rm{\;Kg\;} \cong 9.1M_\odot.$ This characteristic mass can be called as the Fermi black hole mass. This proposed mass unit plays an interesting role in grand unification and primordial black holes. Mass ratio of Fermi black hole mass and Chandrasekhar's mass limit is $2\pi.$ Mass ratio of Fermi black hole mass and neutron star mass limit is $\sqrt{2\pi}.$ Considering strong nuclear gravity, Fermi black hole mass can be obtained in a grand unified approach.

Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This can be considered as the beginning of `strong nuclear gravity'. Assumed relation for strong force and weak force magnitudes is $\sqrt{\frac{F_{S} }{F_{W} } } \cong 2\pi \ln \left(N^{2} \right)$. If $m_{p} $ is the rest mass of proton it is noticed that $\ln \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} Gm_{P}^{2} } } \cong \sqrt{\frac{m_{p} }{m_{e} } -\ln \left(N^{2} \right)}.$ From SUSY point of view, `integral charge quark fermion' and `integral charge quark boson' mass ratio is $\Psi=2.262218404$ but not unity. With these advanced concepts starting from nuclear stability to charged leptons, quarks, electroweak bosons and charged Higgs boson's origin can be understood. Finally an ``alternative" to the `standard model' can be developed.

Based on strong nuclear gravity, $N$ being the Avogadro number and $\left(\frac{c^4}{N^2G}\right)$ being the weak force magnitude, electron`s gravitational mass generator $= X_{E} \cong m_{e} c^{2} \div \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} } \left(\frac{c^4}{N^2G}\right) } \cong 295.0606338$. Weak coupling angle is $\sin \theta _{W} \cong \frac{1}{\alpha X_{E} } \cong 0.464433353\cong \frac{{\rm Up}\; {\rm quark}\; {\rm mass}}{{\rm Down}\; {\rm quark}\; {\rm mass}} $. $X_{S} \cong \ln \left(X_{E}^{2} \sqrt{\alpha } \right)\cong 8.91424\cong \frac{1}{\alpha _{s} } $ can be considered as `inverse of the strong coupling constant'.The proton-nucleon stability relation is $A_{S} \cong 2Z+\frac{Z^{2} }{S_{f} }$ where $S_{f} \cong X_{E} -\frac{1}{\alpha } -1\cong 157.0246441$. With reference to proton rest energy, semi empirical mass formula coulombic energy constant is $E_{c} \cong \frac{\alpha }{X_{S} } \cdot m_{p} c^{2} \cong \alpha \cdot \alpha _{s} \cdot m_{p} c^{2} \cong {\rm 0}.7681\; MeV.$ Pairing energy constant is $E_{p} \cong \frac{m_{p} c^{2} +m_{n} c^{2} }{S_{f} } \cong 11.959\; {\rm M}eV$ and asymmetry energy constant is $E_{a} \cong 2E_{p} \cong 23.918\; {\rm M}eV$. It is also noticed that, $\frac{E_{a} }{E_{v} } \cong 1+\sin \theta _{W} $ and $\frac{E_{a} }{E_{s} } \cong 1+\mathop{\sin }\nolimits^{2} \theta _{W} $. Thus $E_{v} \cong 16.332$ MeV and $E_{s} \cong 19.674\; {\rm M}eV.$ Nuclear binding energy can be fitted with 2 terms. In scattering experiments minimum distance between electron and the nucleus is $R_0 \cong \left(\frac{\hbar c}{\left(N.G\right)m_e^2}\right)^2 \frac{2Gm_e}{c^2}.$

This paper presents a unified theory for the universe which encompasses the dominant theories of physics. Our work is strictly based on the philosophy that the work of the universe is extremely simple in the fundamental level. We provide a minimal set of elements as the fundamental constituents of the universe, and demonstrate that all natural phenomena can be explained by a minimum number of laws governing these fundamental elements and their minimal set of properties.

The predominant approaches to understanding how quantum theory and General Relativity are related to each other implicitly assume that both theories use the same concept of mass. Given that despite great efforts such approaches have not yet produced a consistent falsifiable quantum theory of gravity, this paper entertains the possibility that the concepts of mass in the two theories are in fact distinct. It points out that if the concept of mass in quantum mechanics is defined such that it always exists in a superposition and is not a gravitational source, then this sharply segregates the domains of quantum theory and of general relativity. This concept of mass violates the equivalence principle applied to active gravitational mass, but may still produce effects consistent with the equivalence principle when applied to passive gravitational mass (in agreement with observations) by the correspondence principle applied to a weak field in the appropriate limit. An experiment that successfully measures the gravity field of quantum objects in a superposition, and in particular of photons, would not only falsify this distinction but also constitute the first direct empirical test that gravity must in fact be described fundamentally by a quantum theory.

<p> The general form of ansatz for preferred extremals implies that the Coulombic term in Kähler action vanishes so that it reduces to 3-dimensional surface terms in accordance with general coordinate invariance and holography. The weak form of electric-magnetic duality in turn reduces this term to Chern-Simons terms. </p><p> The strong form of General Coordinate Invariance implies effective 2-dimensionality (holding true in finite measurement resolution) so that also a strong form of holography emerges. The expectation is that Chern-Simons terms in turn reduces to 2-dimensional surface terms. </p><p> The only physically interesting possibility is that these 2-D surface terms correspond to areas for minimal surfaces defined by string world sheets and partonic 2-surfaces appearing in the solution ansatz for the preferred extremals. String world sheets would give to Kähler action an imaginary contribution having interpretation as Morse function. This contribution would be proportional to their total area and assignable with the Minkowskian regions of the space-time surface. Similar but real string world sheet contribution defining Kähler function comes from the Euclidian space-time regions and should be equal to the contribution of the partonic 2-surfaces. A natural conjecture is that the absolute values of all three areas are identical: this would realize duality between string world sheets and partonic 2-surfaces and duality between Euclidian and Minkowskian space-time regions. </p><p> Zero energy ontology combined with the TGD analog of large N_c expansion inspires an educated guess about the coefficient of the minimal surface terms and a beautiful connection with p-adic physics and with the notion of finite measurement resolution emerges. The t'Thooft coupling λ should be proportional to p-adic prime p characterizing particle. This means extremely fast convergence of the counterpart of large N_c expansion in TGD since it becomes completely analogous to the pinary expansion of the partition function in p-adic thermodynamics. Also the twistor description and its dual have a nice interpretation in terms of zero energy ontology. This duality permutes massive wormhole contacts which can have off mass shell with wormhole throats which are always massive (also for the internal lines of the generalized Feynman graphs). </p>

<p> There are pressing motivations for understanding the preferred extremals of Kähler action. For instance, the conformal invariance of string models naturally generalizes to 4-D invariance defined by quantum Yangian of quantum affine algebra (Kac-Moody type algebra) characterized by two complex coordinates and therefore explaining naturally the effective 2-dimensionality. One problem is how to assign a complex coordinate with the string world sheet having Minkowskian signature of metric. One can hope that the understanding of preferred extremals could allow to identify two preferred complex coordinates whose existence is also suggested by number theoretical vision giving preferred role for the rational points of partonic 2-surfaces in preferred coordinates. The best one could hope is a general solution of field equations in accordance with the hints that TGD is integrable quantum theory. </p><p> A lot is is known about properties of preferred extremals and just by trying to integrate all this understanding, one might gain new visions. The problem is that all these arguments are heuristic and rely heavily on physical intuition. The following considerations relate to the space-time regions having Minkowskian signature of the induced metric. The attempt to generalize the construction also to Euclidian regions could be very rewarding. Only a humble attempt to combine various ideas to a more coherent picture is in question. </p><p> The core observations and visions are following. </p><p> <OL> <LI>Hamilton-Jacobi coordinates for M⁴ > define natural preferred coordinates for Minkowskian space-time sheet and might allow to identify string world sheets for X⁴ as those for M⁴. Hamilton-Jacobi coordinates consist of light-like coordinate m and its dual defining local 2-plane M²⊂ M⁴ and complex transversal complex coordinates (w,w*) for a plane E²_x orthogonal to M²_x at each point of M⁴. Clearly, hyper-complex analyticity and complex analyticity are in question. </p><p> <LI> Space-time sheets allow a slicing by string world sheets (partonic 2-surfaces) labelled by partonic 2-surfaces (string world sheets). </p><p> <LI>The quaternionic planes of octonion space containing preferred hyper-complex plane are labelled by CP₂, which might be called CP₂^mod. The identification CP₂=CP₂^mod motivates the notion of M⁸--M⁴× CP₂. It also inspires a concrete solution ansatz assuming the equivalence of two different identifications of the quaternionic tangent space of the space-time sheet and implying that string world sheets can be regarded as strings in the 6-D coset space G₂/SU(3). The group G₂ of octonion automorphisms has already earlier appeared in TGD framework. </p><p> <LI>The duality between partonic 2-surfaces and string world sheets in turn suggests that the CP₂=CP₂^mod conditions reduce to string model for partonic 2-surfaces in CP₂=SU(3)/U(2). String model in both cases could mean just hypercomplex/complex analyticity for the coordinates of the coset space as functions of hyper-complex/complex coordinate of string world sheet/partonic 2-surface. </OL> </p><p> The considerations of this section lead to a revival of an old very ambitious and very romantic number theoretic idea. <OL> <LI> To begin with express octonions in the form o=q₁+Iq₂, where q_i is quaternion and I is an octonionic imaginary unit in the complement of fixed a quaternionic sub-space of octonions. Map preferred coordinates of H=M⁴× CP₂ to octonionic coordinate, form an arbitrary octonion analytic function having expansion with real Taylor or Laurent coefficients to avoid problems due to non-commutativity and non-associativity. Map the outcome to a point of H to get a map H→ H. This procedure is nothing but a generalization of Wick rotation to get an 8-D generalization of analytic map. </p><p> <LI> Identify the preferred extremals of Kähler action as surfaces obtained by requiring the vanishing of the imaginary part of an octonion analytic function. Partonic 2-surfaces and string world sheets would correspond to commutative sub-manifolds of the space-time surface and of imbedding space and would emerge naturally. The ends of braid strands at partonic 2-surface would naturally correspond to the poles of the octonion analytic functions. This would mean a huge generalization of conformal invariance of string models to octonionic conformal invariance and an exact solution of the field equations of TGD and presumably of quantum TGD itself. </OL> </p>

In zero energy ontology U-matrix replaces S-matrix as the fundamental object characterizing the predictions of the theory. U-matrix is defined between zero energy states and its orthogonal rows define what I call M-matrices, which are analogous to thermal S-matrices of thermal QFTs. M-matrix defines the time-like entanglement coefficients between positive and negative energy parts of the zero energy state. M-matrices identifiable as hermitian square roots of density matrices. In this article it is shown that M-matrices form in a natural manner a generalization of Kac-Moody type algebra acting as symmetries of M-matrices and U-matrix and that the space of zero energy states has therefore Lie algebra structure so that quantum states act as their own symmetries. The generators of this algebra are multilocal with respect to partonic 2-surfaces just as Yangian algebras are multilocal with respect to points of Minkowski space and therefore define generalization of the Yangian algebra appearing in the Grassmannian twistor approach to N=4 SUSY.

In this paper the constructive and consistent formulation of quantum gravity as a quantum field theory for the case of higher dimensional ADM space-times, which is based on the author previous works, is presented. The present model contains a certain new contribution which, however, do not change the general idea which leads to extraordinary simple treatment of quantum gravity in terms of fundamental notions of quantum field theory, like e.g. the Fock space, quantum correlations, etc. We discuss the way to establishing the dimension of space and the relation to string theory of the model.

The recent measurement of speed of muon neutrinos shows that it is possible that speed of neutrinos is faster than speed of light. Here an explanation is suggested, that this is a consequence of Scharnhorst eect. This eect shows that photons propagating through vacuum are modifying in virtual pairs electron-positron for a while and thus the measured speed of light is really lower than one maximal possible speed of light in short moments. Because neutrinos are not modifying so, author supposes that their speed is larger than speed of photons.

Deceleration of massive bodies by the isotropic graviton background is considered here as a possible alternative to dark matter. This deceleration has the same order of magnitude as a small additional acceleration of NASA deep-space probes.

The main features of how to build a Born�s Reciprocal Gravitational theory in curved phase-spaces are developed. The scalar curvature of the 8D cotangent bundle (phase space) is explicitly evaluated and a generalized gravitational action in 8D is constructed that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in momentum space is very large, namely the small size of P is of the order of (1/R_Hubble). More general 8D actions can be developed that involve sums of 5 distinct types of torsion squared terms and 3 distinct curvature scalars R,P, S. Finally we develop a Born�s reciprocal complex gravitational theory as a local gauge theory in 8D of the deformed Quaplectic group that is given by the semi-direct product of U(1, 3) with the deformed (noncommutative) Weyl-Heisenberg group involving four noncommutative coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented.

This adventure started out as a paper, but soon it grew considerably in size and there was no choice left anymore but to present it as a full blown book written in a style which is intermediate between that of an original research paper and that of a book. More precisely, I opted for a style which is somewhat between the historical and axiomatic approach and this manuscript can therefore be read from dierent perspectives depending upon the knowledge and skills of the reader. Since quantum gravity is more than a technical problem, the mandatory sections constitute the introduction as well as the technical and axiomatic framework of sections seven till eleven. However, the reader who is also interested in the philosophical aspects as well as a general overview of the problem is advised to study sections two and three as well. The critical reader who is not willing to take any statement for granted should include also sections four till six, since these are somewhat of a transitional nature closing the gap between the conservative initial point of view and the new theory developed later on. Lecturing about this work made me aware that there is also a more direct way to arrive in Rome and for that very reason, this introduction is also split into two parts. The rst one takes the conservative point of view as it is done by the very large majority of researchers which necessitates a careful and precise way of phrasing the content; the second approach however is more bold and direct but goes, in my humble opinion, much more economic to the heart of the matter. I believe that the variety of presenting the same material in this introduction will allow the reader to choose which way he prefers to follow.

In previous papers we have proposed that the mass of an electromagnetic wave is dependent upon its speed. This relationship is such that when the wave is travelling at the speed of light it has no mass, but its mass monotonically increases as the wave slows down (i.e. the wave has mass when it is passing through a medium). In this paper we propose an experiment that would be able to determine whether electromagnetic waves have mass when they are not travelling at the speed of light. Also the experiment would be able to determine whether the wave�s frequency affects the wave�s mass for a given speed.

In this paper we investigate whether an electromagnetic wave can have mass, whilst also still having a maximum velocity equal to the speed of light. We find that their mass is inversely proportional to their velocity, such that they have no mass when travelling at the speed of light. This proportionality may also help explain the duality of light.

The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their quasinormal modes are natural candidates for an interpretation in terms of quantum levels. The spectrum of black hole's quasinormal modes can be re-analysed by introducing a black hole's effective temperature which takes into account the fact that, as shown by Parikh and Wilczek, the radiation spectrum cannot be strictly thermal. This issue changes in a fundamental way the physical understanding of such a spectrum and enables a re-examination of various results in the literature which realizes important modifies on quantum physics of black holes. In particular, the formula of the horizon's area quantization and the number of quanta of area result modified becoming functions of the quantum "overtone" number n. Consequently, the famous formula of Bekenstein-Hawking entropy, its sub-leading corrections and the number of microstates are also modified. Black hole's entropy results a function of the quantum overtone number too. We emphasize that this is the first time that black hole's entropy is directly connected with a quantum number. Previous results in the literature are re-obtained in the limit n → ∞.

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ₁, δ₂] = δ₃. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative Octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang-Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λ^ab = -Λ^ba. Promoting the latter parameters to spacetime dependent ones Λ^ab(x^μ) allows to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to spacetime-dependent scalings (homothecy) of the gauge fields.

A novel (to our knowledge) nonassociative Octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket structure involving the octonion algebra. The ternary bracket was defined earlier by Yamazaki. The antisymmetric rank-two field strength F_μν is defined in terms of the ternary-bracket (... see paper) involving an auxiliary octonionicvalued coupling (...) . The ternary bracket cannot be rewritten in terms of 2-brackets, [A,B,C] ≠ 1/4[[A,B],C]. It is found that gaugeinvariant matter kinetic terms for an octonionic-valued scalar field can be introduced in the action if one starts instead with an octonionic-valued rank-three antisymmetric field strength (...) permutations, which is defined in terms of an antisymmetric tensor field of rank two (...) and (...) We conclude with some preliminary steps towards the construction of generalized ternary gauge field theories involving both 3-Lie algebras and octonions.

We consider a system of two free bodies in de Sitter invariant quantum mechanics. De Sitter invariance is understood such that representation operators satisfy commutation relations of the de Sitter algebra. Our approach does not involve quantum field theory, de Sitter space and its geometry (metric and connection). At very large distances the standard relative distance operator describes a well known cosmological acceleration. In particular, the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for solving this problem. At the same time, for systems of macroscopic bodies this operator does not have correct properties at smaller distances and should be modified. We propose a modification which has correct properties, reproduces Newton�s gravity, the gravitational redshift of light and the precession of Mercury�s perihelion if the width of the de Sitter momentum distribution δ for a macroscopic body is inversely proportional to its mass m. We argue that fundamental quantum theory should be based on a Galois field with a large characteristic p which is a fundamental constant characterizing laws of physics in our Universe. Then one can give a natural explanation that δ = constR/(mG) where R is the radius of the Universe (such that λ = 3/R² is the cosmological constant) and G is a quantity defining Newton�s gravity. A very rough estimation gives G ~ R/(m_Nlnp) where mN is the nucleon mass. If R is of order 10²⁶m then lnp is of order 10⁸⁰ and therefore p is of order exp(10⁸⁰). In the formal limit p → ∞ gravity disappears, i.e. in our approach gravity is a consequence of finiteness of nature.

We explore the many novel physical consequences of Born�s reciprocal Relativity theory in flat phase-space and to generalize the theory to the curved phase-space scenario. We provide with six specific novel physical results resulting from Born�s reciprocal Relativity and which are not present in Special Relativity. These are : momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved phase-spaces which requires the introduction of a complex Hermitian metric, torsion and nonmetricity.

The possibility of a 6+1 dimensional spacetime model being the fundamental theory for elementary particle interactions is explored. The dynamical object is an (octonion) spinor defined over a spacetime lattice with S8 permutation symmetry which gets broken to S4 x S4. Electroweak parity violation is argued to arise from the interplay of the two permutation groups S4 or eventually from the definition of the octonion product. It corresponds to a change in sign for odd permutation lattice transformations and is shown to suggest a form for the Hamiltonian.

Nonassociative Octonionic Ternary Gauge Field Theories are revisited paving the path to an analysis of the many physical applications of Exceptional Jordan Strings/Membranes and Octonionic Gravity. The old octonionic gravity constructions based on the split octonion algebra Os (which strictly speaking is not a division algebra) is extended to the full fledged octonion division algebra O. A real-valued analog of the Einstein-Hilbert Lagrangian L = R involving sums of all the possible contractions of the Ricci tensors plus their octonionic-complex conjugates is presented. A discussion follows of how to extract the Standard Model group (the gauge fields) from the internal part of the octonionic gravitational connection. The role of Exceptional Jordan algebras, their automorphism and reduced structure groups which play the roles of the rotation and Lorentz groups is also re-examined. Finally, we construct (to our knowledge) generalized novel octonionic string and p-brane actions and raise the possibility that our generalized 3-brane action (based on a quartic product) in octonionic flat backgrounds of 7, 8 octonionic dimensions may display an underlying E7,E8 symmetry, respectively. We conclude with some final remarks pertaining to the developments related to Jordan exceptional algebras, octonions, black-holes in string theory and quantum information theory.

Formulae for the masses of elementary particles obtained with guessing are presented in the article. A derivation, which tries to physically interpret these formulae, was also made afterward. Said simplied, it is obtained that particle masses are varying quickly that they are mainly zero and sometimes roughly equal to Planckian mass, while we, as measurers, measure a particle mass only as a time average. Then the arguments, why it is possible that those formulae are not contradictory with known physical facts, and why it is necessary that something like should exist to describe the masses of elementary particles, are listed. The formulae and models are realistic according to the known physics. It is shown also an example which can be veried with a statistical analysis. Some ndings are shown, which can survive although maybe formulae will not survive.

<p>A psychological enquiry into the Planck scale in quantum gravity, as guided by the application of Garrett Hardin's three filters against folly: literacy (what are the words?), numeracy (what are the numbers?), and ecolacy (and then, what?).</p> <p>Una indagación psicológica sobre la escala de Planck en la gravedad cuántica según los tres filtros contra la zoncera de Garrett Hardin: alfabetismo (¿cuáles son la palabras?), numerismo (¿cuáles son los números?) y ecolismo (¿y después, qué?).</p>

In a quantum information approach to quantum gravity, one naturally extends the Bilson-Thompson braid particle spectrum by a right handed neutrino sector. This suggests a parity restoring non local form of mirror matter, considered as a novel contributor to the dark matter sector. In the non standard Riofrio cosmology, where the entire dark matter sector is approximated by black hole states, the mirror matter should occupy a space on the other side of our conformal horizons, which are present everywhere in our universe. In particular we note that the Koide matrix antineutrino rest mass prediction of 0.00117 eV corresponds precisely to a black body peak temperature of 2.73 K, the CMB temperature, as a result of its annihilation with mirror antineutrinos. Initial consequences of these ideas for dark matter profiles are discussed.

The starting point of quantum mechanics is the classical algebraic formula connecting energy to momentum: energy is proportional to the squared momentum. As a result, energy and momentum do not be treated equally. The wave equation of quantum mechanics (a differential equation) results from the replacement of the classical energy quantity with the derivative with time and the replacement of the momentum quantity with the derivative with space. Both replacements have a scale factor that is the Planck constant. Similar to the classical formula, the wave equation does not treat time and space equally, and the Planck constant is not canceled out from both sides of the equation. That is, Planck constant remains which describes the microscopic world. My theory of gravity is the local bending of background spacetime based on Mach principle which, as suggested by Einstein, is described by a classical form of second order treating time and space equally. Therefore, the Planck constant is completely canceled out in the wave equation. In other words, the quantization of gravity does not need the Planck constant. This is because gravity obeys Equivalence Principle. But I keep the scale factor which describes the hierarchical structure of local universe as suggested by Laurent Nottale.

A Clifford Cl(5,C) Unified Gauge Field Theory of Conformal Gravity, Maxwell and U(4)xU(4) Yang-Mills in 4D is rigorously presented extending our results in prior work. The Cl(5,C) = Cl(4,C)⊕Cl(4,C) algebraic structure of the Conformal Gravity, Maxwell and U(4)xU(4) Yang-Mills unification program advanced in this work is that the group structure given by the direct products U(2, 2)xU(4)xU(4) = [SU(2, 2)]_spacetimex [U(1) x U(4) x U(4)]_internal is ultimately tied down to four-dimensions and does not violate the Coleman-Mandula theorem because the spacetime symmetries (conformal group SU(2, 2) in the absence of a mass gap, Poincare group when there is mass gap) do not mix with the internal symmetries. Similar considerations apply to the supersymmetric case when the symmetry group structure is given by the direct product of the superconformal group (in the absence of a mass gap) with an internal symmetry group so that the Haag-Lopuszanski-Sohnius theorem is not violated. A generalization of the de Sitter and Anti de Sitter gravitational theories based on the gauging of the Cl(4, 1,R),Cl(3, 2,R) algebras follows. We conclude with a few remarks about the complex extensions of the Metric Affine theories of Gravity (MAG) based on GL(4,C) x_s C⁴, the realizations of twistors and the N = 1 superconformal su(2, 2|1) algebra purely in terms of Clifford algebras and their plausible role in Witten�s formulation of perturbative N = 4 super Yang-Mills theory in terms of twistor-string variables.

The interplay between continuous and discrete structures results in a duality between the moduli space for black hole types and AdS₇ spacetime. The 3 and 4 Q-bit structures of quantum black holes is equivalent to the conformal completion of AdS.

The holographic principle of black holes tells us the field theoretic information of strings on the event horizon is completely equivalent to field theoretic information in the spacetime one dimension larger outside. This physics is observed on a frame stationary with respect to the black hole. The question naturally arises; what physics is accessed by the observer falling through the event horizon on an inertial frame? This paper examines this and demonstrates a duality between the two perspectives. This question is important for the black hole small enough to exhibit fluctuations comparable to its scale. A sufficiently small quantum black hole will be composed of strings in a superposition of interior and exterior configurations or states

A novel (to our knowledge) nonassociative and noncommutative octonionic ternary gauge field theory is explicitly constructed that it is based on a ternary-bracket structure involving the octonion algebra. The ternary bracket was defined earlier by Yamazaki. The field strengths F_μ_ν are given in terms of the 3-bracket [B_μ,B_ν, Φ] involving an auxiliary octonionic-valued scalar field Φ = Φ^ae_a which plays the role of a "coupling" function. In the concluding remarks a list of relevant future investigations are briefly outlined.

There are various physics phenomenon which can find a simple explanation in linking gravity and electromagnetism. Einstein's Relativity can simply explain only the mass because he considered time as a scalar rather than a vector. The intension of this paper is to propose a new point of view, treating time as a three-dimensional vector, finding three vector value formula by three-dimensional space-time formula (curvature formula), finding a new symmetry on the plane for a wave equation substitute for Maxwell's symmetrical wave, only E and only B, not E and B linked. This linking is in error; in fact they are a two sum effect. The electromagnetic wave in space has, as well known, three energy components: B field E field and wave length (frequency). This energy is acknowledged, but we must see the wave like an elastic chain of single wavelets (a string of individual wavelets).

In this theory I measure the "light speed" per duration of "X particle motions". This basic definition of C exclude the term time (the fourth dimension). Instead it include the term "motion inside a particle" ("a particle's spin" may be a better term). Then, in chapter B1 to B9, I first show the 9 consequenses of this new expression in a philosophical description. In chapter C, I show how these consequenses can be used to explain "The quantum theory of wave / particle duality and the phenomenon of wave collapse". In chapter D the consequenses is described in depth in the mathematical form. I will espesially draw your attention to chapter D 3 wich shows two clear-cut predictions. 1. The gravity-ratio between two particle-positions, relative to a reference object/particle (for instance a sun), will sharply drop for the particles farthest away from us, from 12 billion lightyears and farther away. 2. C, the speed limit, is slightly higher inside dense matter than the observed light speed in vacuum out in the universe. This theory shows that not only is mass and "time" relative, in reference to the "constant" C, but also gravity and electromagnetism is relative, here in reference to the constant edge of our universe.

Some years ago, Bilson-Thompson [1] characterised the fundamental leptons and quarks using simple three strand ribbon diagrams. These diagrams are interpreted in an abstract categorical language, which underlies an information theoretic quantum gravity. More recently, Graham Dungworth [2] has discussed the astrophysical consequences of this non local quantum gravity, under a symmetry restoring extension of the braid set that doubles the matter sector to include mirror matter. The resulting low energy particle set is reinterpreted in the categorical framework for localization, which considers neutral particle oscillations to be responsible for gravity. A few quantitative observational consequences, such as CPT violation in the neutrino sector, are discussed.

The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the Principle of Relativity. It is bonafide knowledge, known even to Einstein the founder, that the GTR violates the very principle upon which it is founded i.e., it violates the Principle of Relativity; because a central equation i.e., the geodesic law which emerges from the GTR, is well known to be in conflict with the Principle of Relativity because the geodesic law, must in complete violation of the Principle of Relativity, be formulated in special (or privileged) coordinate systems i.e., Gaussian coordinate systems. The Principle of Relativity clearly and strictly forbids the existence/use of special (or privileged) coordinate systems in the same way the Special Theory of Relativity forbids the existence of privileged and or special reference systems. In the pursuit of a more Generalized Theory of Relativity i.e., an all-encampusing unified field theory to include the Electromagnetic, Weak & the Strong force, Einstein and many other researchers, have successfully failed to resolve this problem. In this reading, we propose a solution to this dilemma faced by Einstein and many other researchers i.e., the dilemma of obtaining a more Generalized Theory of Relativity. Our solution brings together the Gravitational, Electromagnetic, Weak & the Strong force under a single roof via an extension of Riemann geometry to a new hybrid geometry that we have coined the Riemann-Hilbert Space (RHS). This geometry is a fusion of Riemann geometry and the Hilbert space. Unlike Riemann geometry, the RHS preserves both the length and the angle of a vector under parallel transport because the affine connection of this new geometry, is a tensor. This tensorial affine leads us to a geodesic law that truly upholds the Principle of Relativity. It is seen that the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the non-Abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac equation.

Since early 1980 there is no new discoveries for the basic laws of physics[1], the main problem behind that is the missing of a complete physical description for our universe physics. The concepts of space time, particles (mass), fields, and energy have a big ambiguity in our deep understanding of physics. One of reasons for that is the limitation of our experimental technology in high energy accelerators, and in cosmological observations. In this research the author follows the creative thinking rules which discovered in the field of human psychology studies[2{4] for solving difficult problems through human specie history. The main idea in creative thinking is to borrow ideas and concepts from fields away from the problems own field, those new ideas and concepts are brought to the field of the problems to help human to go inside the problems and get the solution[5]

Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl(3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancellation of the contributions of a very large cosmological constant term and the extra terms present in the modified field equations. Generalized gravitational actions in Clifford-spaces are provided and some of their physical implications are discussed. It is shown how the 16 fermions and their masses in each family can be accommodated within a Cl(4) gauge field theory. In particular, the Higgs fields admit a natural Clifford-space interpretation that differs from the one in the Chamseddine-Connes spectral action model of Noncommutative geometry. We finalize with a discussion on the relationship with the Pati-Salam color-flavor model group SU(4)_C x SU(4)_F and its symmetry breaking patterns. An Appendix is included with useful Clifford algebraic relations.

Quantum information theory motivates certain choices for parameterizations of the CKM and MNS mixing matrices. In particular, we consider the rephasing invariant parameterization of Kuo and Lee, which is given by a sum of real circulants. Noting the relation of this parameterization to complex rotation matrices we find a potential reduction in the degrees of freedom required for the CKM matrix.

The possibility of Universe-scale black holes living in closed 3D space of constant positive curvature was briefly considered in previous work. Further consideration of this possibility is given here. A possible link between gravitation and electromagnetism is discussed.

In earlier work, it was found that the edges of a complete graph can very nearly form a radially symmetric field at long distance in at 2D and 3D space if the number of graph vertices is great enough. In this work, it is confirmed that the edges of a complete graph can also very nearly form a radially symmetric field in closed 2D and 3D space of constant positive curvature if the graph is small compared to the entirety of the space in which it lives and if the number of graph vertices is great enough.

It is shown explicitly how to construct a novel (to our knowledge) realization of the Poincare superalgebra in 2D. These results can be extended to other dimensions and to (extended) superconformal and (anti) de Sitter superalgebras. There is a fundamental difference between the findings of this work with the other approaches to Supersymmetry (over the past four decades) using Grassmannian calculus and which is based on anti-commuting numbers. We provide an algebraic realization of the anticommutators and commutators of the 2D super-Poincare algebra in terms of the generators of the tensor product Cl1,1(R) x A of a two-dim Clifford algebra and an internal algebra A whose generators can be represented in terms of powers of a 3 x 3 matrix Q, such that Q3 = 0. Our realization differs from the standard realization of superalgebras in terms of differential operators in Superspace involving Grassmannian (anticommuting) coordinates θ^α and bosonic coordinates x^μ. We conclude in the final section with an analysis of how to construct Polyvector-valued extensions of supersymmetry in Clifford Spaces involving spinor-tensorial supercharge generators Qμ1μ2.....μn and momentum polyvectors Pμ1μ2....μn. Clifford-Superspace is an extension of Clifford-space and whose symmetry transformations are generalized polyvector-valued supersymmetries.

Earlier it was shown that in the model of low-energy quantum gravity by the author, observations of Supernovae 1a and GRBs, which are corrected by observers for characteristic for the standard cosmological model time dilation, may be fitted with the theoretical luminosity distance curve only up to z ~ 0:5; for higher redshifts the predicted luminosity distance is essentially bigger. The model itself has not time dilation due to another redshift mechanism. It is shown here that a correction of observations for no time dilation leads to a good accordance of observations and theoretical predictions for all achieved redshifts.

A unique matrix is easily assigned to each Bilson-Thompson braid diagram. The quark and lepton matrices are then related to bosons via a twisted quantum Fourier transform, for which fermion and boson multiplets fit the dimension structure of heterotic strings.

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson's fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of Quantum Gravity.

A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented. This solution is based on a Wheeler-DeWitt equation obtained by Krechet, Fil'chenkov, and Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.

The Newtonian attraction turns out to be the main statistical effect in the sea of super-strong interacting gravitons, with bodies themselves being not sources of gravitons - only correlational properties of in and out fluxes of gravitons in their neighbourhood are changed due to an interaction with bodies. Other quantum effects of low-energy quantum gravity are the following ones: redshifts, their analog - a deceleration of massive bodies, and an additional relaxation of any light flux.

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative binary star products are associative and require the use of the Baker-Campbell-Hausdorff formula. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X¹,X², ......,Xⁿ] and the poly-vector valued coordinates X^123...n in noncommutative Clifford spaces is explicitly derived and is given by [X¹,X², ......,Xⁿ] = n! X^123...n. It is argued how the large N limit of n-ary commutators of n hyper-matrices X_i₁_i₂...._{i_n} leads to Eguchi-Schild p-brane actions when p+1 = n. A noncomutative n-ary generalized star product of functions is provided which is associated with the deformation quantization of n-ary structures. Finally, brief comments are made about the mapping of the Nambu-Heisenberg n-ary commutation relations of linear operators into the deformed Nambu-Poisson brackets of their corresponding symbols.

A brief review of a Conformal Gravity and U(4) x U(4) Yang-Mills Unification model in four dimensions from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) is presented. It based on the (complex) Clifford Cl(4,C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). The 16 fermions of each generation can be arranged into the 16 entries of a 4 x 4 matrix associated with the A = 1, 2, 3, ....., 16 indices corresponding to the dimensions of the Cl(4) gauge algebra. The Higgs sector is also part of the Cl(4)-algebra polyvector valued gauge field in C-space. The Yukawa couplings which furnish masses to the fermions (after symmetry breaking) admit a C-space geometric interpretation as well.

Two somewhat long overdue arguments presented here may help in further clarifying the so called "Black Whole War" and beyond that, may be useful in Physics at large.

The objective of this paper is to identify a way to relate entropy with the synchronization of the input/output power of a system of oscillators. This view is ultimately reconciled through an examination of the geometric differences that exist between 2D shell and 3D lattice oscillator arrangements.

A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cl_0,6 is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action. The feebleness of gravity as well as the smallness of the cosmological constant and theta terms are discussed at the classical level. The invariance groups, including the de Sitter and the Pati-Salam SU(4) subgroups, consist of gauge transformations from either side of an algebraic spinor. Upon symmetry breaking via the Higgs fields, the remaining symmetries are the Lorentz SO(1,3), color SU(3), electromagnetic U(1)_EM, and an additional U(1). The first generation leptons and quarks are identified with even and odd parts of spinor idempotent projections. There are still several shortcomings with the current model. Further research is needed to fully recover the standard model results.

Based on a possible solution to the tetron spin problem, a modification of the standard Big Bang scenario is suggested, where the advent of a spacetime manifold is connected to the appearance of tetronic bound states. The metric tensor is constructed from tetron constituents and the reason for cosmic inflation is elucidated. Furthermore, there are natural dark matter candidates in the tetron model. The ratio of ordinary to dark matter in the universe is calculated to be 1:5.

A Moyal deformation quantization approach to a spherical membrane (moving in flat target backgrounds) in the light cone gauge is presented. The physical picture behind this construction relies in viewing the two spatial membrane coordinates σ₁, σ₂ as the two phase space variables q, p, and the temporal membrane coordinate τ as time. Solutions to the Moyal-deformed equations of motion are explicitly constructed in terms of elliptic functions. A knowledge of the Moyal-deformed light-cone membrane's Hamiltonian density H(q, p, τ ) allows to construct a timedependent Wigner function ρ(q, p, τ ) as solutions of the Moyal-Liouville equation, and from which one can obtain the expectation values of the operator < H > = Trace (ρH) that define the quantum average values of the energy density configurations of the membrane at any instant of time. It is shown how a time-dependent quartic oscillator with q⁴, p⁴, q²p² terms plays a fundamental role in the quantum treatment of membranes and displays an important p ↔ q duality symmetry.

The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry - the Reimann-Hilbert Space, is a tensor and this leads us to a geodesic law that truly upholds the Principle of Relativity. The geodesic law emerging from the General Theory of Relativity (GTR) is well known to be in contempt of the Principle of Relativity which is a principle upon which the GTR is founded. The geodesic law for particles in the GTR must be formulated in special (or privileged) coordinate systems i.e. gaussian coordinate systems whereas the Principle of Relativity clearly forbids the existence of special (or privileged) coordinate systems in manner redolent of the way the Special Theory of Relativity forbids the existence of an absolute (or privileged) frame of reference. In the low energy regime and low spacetime curvature the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the none-abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac Equation. Further, to the already existing four known forces, the theory predicts the existence of yet another force. We have coined this the super-force and this force obeys SU(4, 4) gauge invariance. Furthermore, unlike in the GTR, gravitation is here represented by a single scaler potential, and electromagnetic field and the nuclear forces are described by the electromagnetic vector potential (A_μ) which describes the metric tensor i.e. g_μν = A_μA_ν. From this (g_μν = A_μA_ν), it is seen that gravity waves may not exist in the sense envisaged by the GTR.

We study black-hole-like solutions ( spacetimes with singularities ) of Einstein field equations in 3+1 and 2+2-dimensions. In the 3+1-dim case, it is shown how the horizon of the standard black hole solution at r = 2G_NM can be displaced to the location r = 0 of the point mass M source, when the radial gauge function is chosen to have an ultra-violet cutoff R(r = 0) = 2G_NM if, and only if, one embeds the problem in the Finsler geometry of the spacetime tangent bundle (or in phase space) that is the proper arena where to incorporate the role of the physical point mass M source at r = 0. We find three different cases associated with hyperbolic homogeneous spaces. In particular, the hyperbolic version of Schwarzschild's solution contains a conical singularity at r = 0 resulting from pinching to zero size r = 0 the throat of the hyperboloid H² and which is quite different from the static spherically symmetric 3+1-dim solution. Static circular symmetric solutions for metrics in 2+2 are found that are singular at ρ = 0 and whose asymptotic ρ → ∞ limit leads to a flat 1+2-dim boundary of topology S¹ x R². Finally we discuss the 1+1-dim Bars-Witten stringy black-hole solution and show how it can be embedded into our 3 + 1-dimensional solutions with a displaced horizon at r = 0 and discuss the plausible stringy nature of a point-mass, along with the maximal acceleration principle in the spacetime tangent bundle (maximal force in phase spaces). Black holes in a 2 + 2-dimensional "spacetime" from the perspective of complex gravity in 1 + 1 complex dimensions and their quaternionic and octonionic gravity extensions deserve furher investigation. An appendix is included with the most general Schwarzschild-like solutions in D ≥ 4.

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X¹,X², ......,Xⁿ] with the poly-vector valued coordinates X^123...n in noncommutative Clifford spaces is explicitly derived [X¹,X², ......,Xⁿ] = n! X^123...n. The large N limit of n-ary commutators of n hyper-matrices X_i₁i₂....in leads to Eguchi-Schild p-brane actions for p + 1 = n. Noncommutative Clifford-space gravity as a poly-vector-valued gauge theory of twisted diffeomorphisms in Clifford spaces would require quantum Hopf algebraic deformations of Clifford algebras.

A proposal outlining an approach to a unified field theory is presented. A general solution to the time-dependent Schrödinger Equation using an alternative boundary condition is found to derive the Heisenberg uncertainty formulae. A general relativity/quantum mechanical interaction between a photon and a gravitational field is examined to determine the degree of red shifting of light passing through a gravitational field. The Einstein field equations, complete with an arrangement of Faraday tensors, are presented with suggestions to determine the energy of a photon from Einstein's and Maxwell's equations. Schrödingers Equation is coupled with both the Einstein field equations and Maxwells equations to derive a possible foundation for string theory.

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The star products are noncommutative and associative and require the use of the Baker-Campbell-Hausdorff formula. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Clifford-spaces would require quantum Hopf algebraic deformations of Clifford algebras.

Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic Supersymmetric pointparticle action in Clifford-space backgrounds. The relativistic Supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector Super-Poincare and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our final analysis of the novel Clifford-Superspace realizations of generalized Supersymmetries in Clifford spaces.

We explore Yang's Noncommutative space-time algebra (involving two length scales) within the context of QM defined in Noncommutative spacetimes; the Holographic principle and the area-coordinates algebra in Clifford spaces. Casimir invariant wave equations corresponding to Noncommutative coordinates and momenta in d-dimensions can be recast in terms of ordinary QM wave equations in d+2-dimensions. It is conjectured that QM over Noncommutative spacetimes (Noncommutative QM) may be described by ordinary QM in higher dimensions. Novel Moyal-Yang-Fedosov-Kontsevich star products deformations of the Noncommutative Poisson Brackets (NCPB) are employed to construct star product deformations of scalar field theories. Finally, generalizations of the Dirac-Konstant and Klein-Gordon-like equations relevant to the physics of D-branes and Matrix Models are presented.

A novel Weyl-Heisenberg algebra in Clifford-spaces is constructed that is based on a matrix-valued H^AB extension of Planck's constant. As a result of this modifiedWeyl-Heisenberg algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, p_x); (x, p_y); (x, p_z); (y, p_x), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford-spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative space-time algebra and the area-coordinates algebra associated with Clifford spaces. The former Yang's algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = ℏ/R (maximal length R, infrared cutoff ). The double-scaling limit of Yang's algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L² = nλ² ( in Planck area units ) given in terms of the discrete angular-momentum eigenvalues n. It is shown how Modified Newtonian dynamics is also a consequence of Yang's algebra resulting from the modified Poisson brackets. Finally, another noncommutative algebra ( which differs from the Yang's algebra ) and related to the minimal length uncertainty relations is presented . We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford-spaces.

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6,R) and complexified Clifford Cl_C(4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale (ℏλ/R). Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant ) is given by a geometric mean relationship ρ ~ L^-2_PlanckR^-2 = L^-4_P(L_Planck/R)² ~ 10^-122M⁴_Planck, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl(1,7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, and Brandt's action related to the 8D spacetime tangentbundle involving coordinates and velocities ( Finsler geometries ). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.

It is shown how w_∞,w_1+∞ Gauge Field Theory actions in 2D emerge directly from 4D Gravity. Strings and Membranes actions in 2D and 3D originate as well from 4D Einstein Gravity after recurring to the nonlinear connection formalism of Lagrange-Finsler and Hamilton-Cartan spaces. Quantum Gravity in 3D can be described by aW1 Matrix Model in D = 1 that can be solved exactly via the Collective Field Theory method. We describe why a quantization of 4D Gravity could be attained via a 2D Quantum W_∞ gauge theory coupled to an infinite-component scalar-multiplet. A proof that non-critical W_∞ (super) strings are devoid of BRST anomalies in dimensions D = 27 (D = 11), respectively, follows and which coincide with the critical (super) membrane dimensions D = 27 (D = 11). We establish the correspondence between the states associated with the quasi finite highest weights irreducible representations of W_∞,<span style="text-decoration: overline;">W</span>_∞ algebras and the quantum states of the continuous Toda molecule. Schroedinger-like QM wave functional equations are derived and solutions are found in the zeroth order approximation. Since higher-conformal spin W_∞ symmetries are very relevant in the study of 2D W_∞ Gravity, the Quantum Hall effect, large N QCD, strings, membranes, ...... it is warranted to explore further the interplay among all these theories.

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D₄ - D₅ - E₆ - E₇ - E₈ model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith's model to the full Clifford-space is presented when we write explictly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E₈ X E₈ Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford ( 16 ) group.

Noncommutative p-brane actions, for even p+1 = 2n-dimensional world-volumes, are written explicitly in terms of the novel Moyal-Yang ( Fedosov-Kontsevich ) star product deformations of the Noncommutative Nambu Poisson Brackets (NCNPB) that are associated with the noncommuting world-volume coordinates q^A, p^A for A = 1, 2, 3, ...n. The latter noncommuting coordinates obey the noncommutative Yang algebra with an ultraviolet L_P (Planck) scale and infrared (R ) scale cutoff. It is shown why our p-brane actions in the "classical" limit ℏ_eff = ℏL_P/R → 0 still acquire nontrivial noncommutative corrections that differ from ordinary p-brane actions. Super p-branes actions in the light-cone gauge are also amenable to Moyal-Yang star product deformations as well due to the fact that p-branes moving in flat spacetime backgrounds, in the light-cone gauge, can be recast as gauge theories of volume-preserving diffeomorphisms. The most general construction of noncommutative super p-branes actions based on non ( anti ) commuting superspaces and quantum group methods remains an open problem.

A candidate action for an Exceptional E₈ gauge theory of gravity in 8D is constructed. It is obtained by recasting the E₈ group as the semi-direct product of GL(8,R) with a deformed Weyl-Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quartic E₈ group-invariant action in 8D associated with the Chern-Simons E₈ gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize, it is shown how the E₈ gauge theory of gravity can be embedded into a more general extended gravitational theory in Clifford spaces associated with the Cl(16) algebra and providing a solid geometrical program of a grand-unification of gravity with Yang-Mills theories. The key question remains if this novel gravitational model based on gauging the E8 group may still be renormalizable without spoiling unitarity at the quantum level.

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Z_a,Z_b] ≠ 0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R_μν, S_μν. The deformed Born's reciprocal gravitational action linear in the Ricci scalars R, S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z_μ = E_μ^a Z_a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E_μ^a is the complex vielbein associated with the Hermitian metric G_μν = g_(μν) + ig_[μν] = E_μ^a Ē_ν^b This could be one of the underlying reasons why string-theory involves gravity.

The Octonionic Geometry (Gravity) developed long ago by Oliveira and Marques is extended to Noncommutative and Nonassociative Spacetime coordinates associated with octonionic-valued coordinates and momenta. The octonionic metric G_μν already encompasses the ordinary spacetime metric g_μν, in addition to the Maxwell U(1) and SU(2) Yang-Mills fields such that implements the Kaluza-Klein Grand Unification program without introducing extra spacetime dimensions. The color group SU(3) is a subgroup of the exceptional G₂ group which is the automorphism group of the octonion algebra. It is shown that the flux of the SU(2) Yang-Mills field strength F_μν through the area momentum Σ^μν in the internal isospin space yields corrections O(1/M²_Planck) to the energy-momentum dispersion relations without violating Lorentz invariance as it occurs with Hopf algebraic deformations of the Poincare algebra. The known Octonionic realizations of the Clifford Cl(8),Cl(4) algebras should permit the construction of octonionic string actions that should have a correspondence with ordinary string actions for strings moving in a curved Clifford-space target background associated with a Cl(3, 1) algebra.

The large N → ∞ limit of the Exceptional F₄,E₆ Jordan Matrix Models of Smolin-Ohwashi leads to novel Chern-Simons Membrane Lagrangians which are suitable candidates for a nonperturbative bosonic formulation of M Theory in D = 27 real, complex dimensions, respectively. Freudenthal algebras and triple Freudenthal products permits the construction of a novel E₇ X SU(N) invariant Matrix model whose large N limit yields generalized nonlinear sigma models actions on 28 complex dimensional backgrounds associated with a 56 real-dim phase space realization of the Freudenthal algebra. We argue why the latter Matrix Model, in the large N limit, might be the proper arena for a bosonic formulation of F theory. To finalize we display generalized Dirac-Nambu-Goto membrane actions in terms of 3 X 3 X 3 cubic matrix entries that match the number of degrees of freedom of the 27-dim exceptional Jordan algebra J₃[0].

An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces) is presented whose "point" coordinates are non-commuting Clifford-valued quantities which incorporate lines, areas, volumes, hyper-volumes.... degrees of freedom associated with the collective particle, string, membrane, p-brane,... dynamics of p-loops (closed p-branes) in target Ddimensional spacetime backgrounds. C-space Relativity naturally incorporates the ideas of an invariant length (Planck scale), maximal acceleration, non-commuting coordinates, supersymmetry, holography, higher derivative gravity with torsion and variable dimensions/signatures. It permits to study the dynamics of all (closed) p-branes, for all values of p, on a unified footing. It resolves the ordering ambiguities in QFT, the problem of time in Cosmology and admits superluminal propagation ( tachyons ) without violations of causality. A discussion of the maximalacceleration Relativity principle in phase-spaces follows and the study of the invariance group of symmetry transformations in phase-space allows to show why Planck areas are invariant under acceleration-boosts transformations . This invariance feature suggests that a maximal-string tension principle may be operating in Nature. We continue by pointing out how the relativity of signatures of the underlying n-dimensional spacetime results from taking different n-dimensional slices through C-space. The conformal group in spacetime emerges as a natural subgroup of the Clifford group and Relativity in C-spaces involves natural scale changes in the sizes of physical objects without the introduction of forces nor Weyl's gauge field of dilations. We finalize by constructing the generalization of Maxwell theory of Electrodynamics of point charges to a theory in C-spaces that involves extended charges coupled to antisymmetric tensor fields of arbitrary rank. In the concluding remarks we outline briefly the current promising research programs and their plausible connections with C-space Relativity.

It is shown how a Conformal Gravity and U(4) X U(4) Yang-Mills Grand Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl(4,C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary Gravity and the Standard Model in four real dimensions. A brief conclusion about the Noncommutative star product deformations of this Grand Unified Theory of Gravity with the other forces of Nature is presented.

Long ago, Bergshoeff, Sezgin, Tanni and Townsend have shown that the light-cone gauge-fixed action of a super p-brane belongs to a new kind of supersymmetric gauge theory of p-volume preserving diffeomorphisms (diffs) associated with the p-spatial dimensions of the extended object. These authors conjectured that this new kind of supersymmetric gauge theory must be related to an infinite-dim nonabelian antisymmetric gauge theory. It is shown in this work how this new theory should be part of an underlying antisymmetric nonabelian tensorial gauge field theory of p+1-dimensional diffs (upon supersymmetrization) associated with the world volume evolution of the p-brane. We conclude by embedding the latter theory into a more fundamental one based on the Clifford-space geometry of the p-brane configuration space.

The first part of book discusses the new physics relevant to biology and the vision about Universe as topological quantum computer (tqc). </p><p Second part describes concrete physical models. </p><p> <OL> <LI> The notion of many-sheeted DNA and a model of genetic code inspired by the notion of Combinatorial Hierarchy predicting what I call memetic code are introduced. The almost exact symmetries of the code table with respect to the third letter inspire the proposal that genetic code could have evolved as fusion of two-letter code and single-letter code. <LI> A model for how genome and cell membrane could act as tqc is developed. Magnetic flux tubes containing dark matter characterized by large value of Planck constant would make living matter a macroscopic quantum system. DNA nucleotides and lipids of the cell membrane would be connected by magnetic flux tubes and the flow of the 2-D liquid formed by lipids would induce dynamical braiding defining the computation. <LI> The net of magnetic flux tubes could explain the properties of gel phase. Phase transitions reducing Planck constant would induce a contraction of the flux tubes explaining why bio-molecules manage to find each other in a dense soup of bio-molecules. The topology of the net would be dynamical and ADP &harr; ATP transformation could affect it. The anomalies related to ionic currents, nerve pulse activity, and interaction of ELF radiation with vertebrate brain find an explanation in this framework. The number theoretic entanglement entropy able to have negative values could be seen as the real quintenssence associated with the metabolic energy transfer, and the poorly understood high energy phosphate bond could be interpreted in terms of negentropic entanglement rather than ordinary bound state entanglement. <LI> The discoveries of Peter Gariaev about interaction of ordinary and laser light with genome combined with ideas about dark matter and water memory lead to a model for the interaction of photons with DNA. Dark &harr; ordinary transformation for photons could allow to "see" dark matter by allowing ordinary light to interact with DNA. <LI> A physical model for genetic code emerged from an attempt to understand the mechanism behind water memory. Dark nuclei which sizes zoomed up to atomic size scale could represent genes. The model for dark nucleon consisting of three quarks predicts counterparts of 64 DNAs, 64 RNAs, and 20 aminoacids and allows to identify genetic code as a natural mapping of DNA type states to amino-acid type states and consistent with vertebrate genetic code. </OL> </p><p> The third part of the book discusses number theoretical models of the genetic code based on p-adic thermodynamics and maximization of entropy or negentropy. These models reproduce the genetic code but fail to make killer predictions.

This book is devoted to a detailed representation of the recent state of quantum TGD. </p><p> The first part of the book summarizes quantum TGD in its recent form. </p><p> <OL> <LI> General coordinate invariance and generalized super-conformal symmetries are the basic symmetries of TGD and Equivalence Principle can be generalized using generalized coset construction. <LI> In zero energy ontology the basis of classical WCW spinors fields forms unitary U-matrix having M-matrices as its orthogonal rows. M-matrix defines time-like entanglement coefficients between positive and negative energy parts of the zero energy states. M-matrix is a product of a hermitian density matrix and unitary S-matrix commuting with it. The hermitian density matrices define infinite-dimensional Lie-algebra extending to a generalization of Kac-Moody type algebra with generators defined as products of hermitian density matrices and powers of S-matrix. Yangian type algebra is obtained if only non-negative powers of S are allowed. The interpretation is in terms of the hierarchy of causal diamonds with size scales coming as integer multiples of CP₂ size scale. Zero energy states define their own symmetry algebra. For generalized Feynman diagrams lines correspond to light-like 3-surfaces and vertices to 2-D surfaces. <LI> Finite measurement resolution realized using fractal hierarchy of causal diamonds (CDs) inside CDs implies a stringy formulation of quantum TGD involving replacement of 3-D light-like surfaces with braids representing the ends of strings. Category theoretical formulation leads to a hierarchy of algebras forming an operad. <LI> Twistors emerge naturally in TGD framework and several proposal for twistorialization of TGD is discussed in two chapters devoted to the topic. Twistorial approach combined with zero energy ontology, bosonic emergence, and the properties of the Chern-Simons Dirac operator leads to the conjecture that all particles -also string like objects- can be regarded as bound states of massless particles identifiable as wormhole throats. Also virtual particles would consist of massles wormhole throats but bound state property is not assumed anymore and the energies of wormhole throats can have opposite signs so that space-like momentum exchanges become possible. This implies extremely strong constraints on loop momenta and manifest finiteness of loop integrals. </p><p> An essential element of the formulation is exact Yangian symmetry obtained by replacing the loci of multilocal symmetry generators of Yangian algebra with partonic 2-surfaces so that conformal algebra of Minkowski space is extened to infinite-dimensional algebra bringing in also the conformal algebra assigned to the partonic 2-surfaces. Yangian symmetry requires the vanishing of both UV and IR divergences achieved if the physical particles are bound states of massless wormhole throats. </p><p> Rather general arguments suggest the formulation of TGD in terms of holomorphic 6-surfaces in the product CP₃&times; CP₃ of twistor spaces leading to a unique partial differential equations determining these surfaces in terms of homogenous polynomials of the projective complex coordinates of the two twistor spaces. </OL> </p><p> Second part of the book is devoted to hyper-finite factors and hierarchy of Planck constants. </p><p> <OL> <LI> The Clifford algebra of WCW is hyper-finite factor of type II₁. The inclusions provide a mathematical description of finite measurement resolution. The included factor is analogous to gauge symmetry group since the action of the included factor creates states not distinguishable from the original one. TGD Universe would be analogous to Turing machine able to emulate any internally consistent gauge theory (or more general theory) so that finite measurement resolution would provide TGD Universe with huge simulational powers. <LI> In TGD framework dark matter corresponds to ordinary particles with non-standard value of Planck constant. The simplest view about the hierarchy of Planck constants is as an effective hierarchy describable in terms of local, singular coverings of the imbedding space. The basic observation is that for K&auml;hler action the time derivatives of the imbedding space coordinates are many-valued functions of canonical momentum densities. If all branches for given values of canonical momentum densities are allowed, one obtains the analogs of many-sheeted Riemann surfaces with each sheet giving same contribution to the K&auml;hler action so that Planck constant is effectively a multiple of the ordinary Planck constant. Dark matter could be in quantum Hall like phase localized at light-like 3-surfaces with macroscopic size and analogous to black-hole horizons. </OL>

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts. </p><p> <OL><LI> The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis. <LI> Second part of the vision involves hyper counterparts of the classical number fields defined as subspaces of their complexificationsnwith Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be callednhyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M⁴&times; CP₂ in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the induced or modified gamma matrices defined by the canonical momentum currents of K&auml;hler action. Induced gamma matrices seem to be preferred mathematically: they correspond to modified gamma matrices assignable to 4-volume action, and one can develop arguments for why K&auml;hler action defines the dynamics. </p><p> Also a general vision about preferred extremals of K&auml;hler action emerges. The basic idea is that imbedding space allows octonionic structure and that field equations in a given space-time region reduce to the associativity of the tangent space or normal space: space-time regions should be quaternionic or co-quaternionic. The first formulation is in terms of the octonionic representation of the imbedding space Clifford algebra and states that the octonionic gamma "matrices" span a complexified quaternionic sub-algebra. Another formulation is in terms of octonion real-analyticity. Octonion real-analytic function f is expressible as f=q₁+Iq₂, where q_i are quaternions and I is an octonionic imaginary unit analogous to the ordinary imaginary unit. q₂ (q₁) would vanish for quaternionic (co-quaternionic) space-time regions. The local number field structure of the octonion real-analytic functions with composition of functions as additional operation would be realized as geometric operations for space-time surfaces. The conjecture is that these two formulations are equivalent. <LI> The third part of the vision involves infinite primes identifiable in terms of an infinite hierarchy of second quantized arithmetic quantum fields theories on one hand, and as having representations as space-time surfaces analogous to zero loci of polynomials on the other hand. Single space-time point would have an infinitely complex structure since real unity can be represented as a ratio of infinite numbers in infinitely many manners each having its own number theoretic anatomy. Single space-time point would be in principle able to represent in its structure the quantum state of the entire universe. This number theoretic variant of Brahman=Atman identity would make Universe an algebraic hologram. </p><p> Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes. </OL> </p><p> Besides this holy trinity I will discuss in the first part of the book loosely related topics such as the relationship between infinite primes and non-standard numbers. </p><p> Second part of the book is devoted to the mathematical formulation of the p-adic TGD. The p-adic counterpart of integration is certainly the basic mathematical challenge. Number theoretical universality and the notion of algebraic continuation from rationals to various continuous number fields is the basic idea behind the attempts to solve the problems. p-Adic integration is also a central problem of modern mathematics and the relationship of TGD approach to motivic integration and cohomology theories in p-adic numberfields is discussed. </p><p> The correspondence between real and p-adic numbers is second fundamental problem. The key problem is to understand whether and how this correspondence could be at the same time continuous and respect symmetries at least in discrete sense. The proposed explanation of Shnoll effect suggests that the notion of quantum rational number could tie together p-adic physics and quantum groups and could allow to define real-p-adic correspondence satisfying the basic conditions. </p><p> The third part is develoted to possible applications. Included are category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.

This book is devoted to what might be called classical TGD. </p><p> <OL> <LI> Classical TGD identifies space-time surfaces as kind of generalized Bohr orbits. It is an exact part of quantum TGD. <LI> The notions of many-sheeted space-time, topological field quantization and the notion of field/magnetic body, follow from simple topological considerations. Space-time sheets can have arbitrarily large sizes and their interpretation as quantum coherence regions implies that in TGD Universe macroscopic quantum coherence is possible in arbitrarily long scales. Also long ranged classical color and electro-weak fields are predicted. <LI> TGD Universe is fractal containing fractal copies of standard model physics at various space-time sheets and labeled by p-adic primes assignable to elementary particles and by the level of dark matter hierarchy characterized partially by the value of Planck constant labeling the pages of the book like structure formed by singular covering spaces of the imbedding space M⁴&times; CP₂ glued together along four-dimensional back. Particles at different pages are dark relative to each other since local interactions defined in terms of the vertices of Feynman diagram involve only particles at the same page. </p><p> The simplest view about the hierarchy of Planck constants is as an effective hierarchy describable in terms of local, singular coverings of the imbedding space. The basic observation is that for K&auml;hler action the time derivatives of the imbedding space coordinates are many-valued functions of canonical momentum densities. If all branches for given values of canonical momentum densities are allowed, one obtains the analogs of many-sheeted Riemann surfaces with each sheet giving same contribution to the K&auml;hler action so that Planck constant is effectively a multiple of the ordinary Planck constant. <LI> Zero energy ontology brings in additional powerful interpretational principle. </OL> </p><p> The topics of the book are organized as follows. <OL> <LI> In Part I extremals of K&auml;hler action are discussed and the notions of many-sheeted space-time, topological field quantization, and topological condensation and evaporation are introduced. <LI> In Part II many-sheeted-cosmology and astrophysics are summarized. p-Adic and dark matter hierarchies imply that TGD inspired cosmology is fractal. Cosmic strings and their deformations giving rise to magnetic flux tubes are basic objects of TGD inspired cosmology. Magnetic flux tubes can in fact be interpreted as carriers of dark energy giving rise to accelerated expansion via negative magnetic "pressure". The study of imbeddings of Robertson-Walker cosmology shows that critical and over-critical cosmology are unique apart from their duration. The idea about dark matter hierarchy was originally motivated by the observation that planetary orbits could be interpreted as Bohr orbits with enormous value of Planck constant, and this picture leads to a rather detailed view about macroscopically quantum coherent dark matter in astrophysics and cosmology. </p><p> <LI> Part III includes old chapters about implications of TGD for condensed matter physics. The phases of CP₂ complex coordinates could define phases of order parameters of macroscopic quantum phases manifesting themselves in the properties of living matter and even in hydrodynamics. For instance, Z⁰ magnetic gauge field could make itself visible in hydrodynamics and Z⁰ magnetic vortices could be involved with super-fluidity. </OL>

The topics of this book is a vision about physics as infinite-dimensional K&auml;hler geometry of the "world of classical worlds" (WCW), with "classical world" identified either as light-like 3-D surface X³ of a unique Bohr orbit like 4-surface X⁴(X³) or X⁴(X³) itself. The non-determinism of K&auml;hler action defining K&auml;hler function forces to generalize the notion of 3-surface. Zero energy ontology allows to formulate this generalization elegantly using a hierarchy of causal diamonds (CDs) defined as intersections of future and past directed light-cones, and a geometric realization of coupling constant evolution and finite measurement resolution emerges. </p><p> The general vision about quantum dynamics is that the basis for WCW spinor fields defines in zero energy ontology unitary U-matrix having as orthogonal rows M-matrices. Given M-matrix is expressible as a product of hermitian square root of density matrix and S-matrix. M-matrices define time-like entanglement coefficients between positive and negative energy parts of zero energy states represented by the modes of WCW spinor fields. </p><p> One encounters two challenges. <OL><LI> Provide WCW with K&auml;hler geometry consistent with 4-dimensional general coordinate invariance. Clearly, the definition of metric must assign to given light-like 3-surface X³ a 4-surface X⁴(X³) as kind of Bohr orbit. <LI> Provide WCW with spinor structure. The idea is to express configuration space gamma matrices using super algebra generators expressible using second quantized fermionic oscillator operators for induced free spinor fields at X⁴(X³). Isometry generators and contractions of Killing vectors with gamma matrices would generalize Super Kac-Moody algebra. </OL> </p><p> The condition of mathematical existence poses stringent conditions on the construction. </p><p> <OL> <LI> The experience with loop spaces suggests that a well-defined Riemann connection exists only if this space is union of infinite-dimensional symmetric spaces. Finiteness requires that vacuum Einstein equations are satisfied. The coordinates labeling these symmetric spaces do not contribute to the line element and have interpretation as non-quantum fluctuating classical variables. <LI> The construction of the K&auml;hler structure requires the identification of complex structure. Direct construction of K&auml;hler function as action associated with a preferred extremal for K&auml;hler action leads to a unique result. The group theoretical approach relies on direct guess of isometries of the symmetric spaces involved. Isometry group generalizes Kac-Moody group by replacing finite-dimensional Lie group with the group of symplectic transformations of &delta; M⁴₊&times; CP₂, where &delta; M⁴₊ is the boundary of 4-dimensional future light-cone. The generalized conformal symmetries assignable to light-like 3-surfaces and boundaries of causal diamonds bring in stringy aspect and Equivalence Principle can be generalized in terms of generalized coset construction. <LI> Configuration space spinor structure geometrizes fermionic statistics and quantization of spinor fields. Quantum criticality can be formulated in terms of the modified Dirac equation for induced spinor fields allowing a realization of super-conformal symmetries and quantum gravitational holography. <LI> Zero energy ontology combined with the weak form of electric-magnetic duality led to a breakthrough in the understanding of the theory. The boundary conditions at light-like wormhole throats and at space-like 3-surfaces defined by the intersection of the space-time surface with the light-like boundaries of causal diamonds reduce the classical quantization of K&auml;hler electric charge to that for K&auml;hler magnetic charge. The integrability of field equations for the preferred extremals reduces to the condition that the flow lines of various isometry currents define Beltrami fields for which the flow parameter by definition defines a global coordinate. The assumption that isometry currents are proportional to the instanton current for K&auml;hler action reduces K&auml;hler function to a boundary term which by the weak form of electric-magnetic duality reduces to Chern-Simons term. This realizes TGD as almost topological QFT. <LI> There are also number theoretical conjectures about the character of the preferred extremals. The basic idea is that imbedding space allows octonionic structure and that field equations in a given space-time region should reduce to the associativity of the tangent space or normal space so that space-time regions should be quaternionic or co-quaternionic. The first formulation is in terms of the octonionic representation of the imbedding space Clifford algebra and states that the octonionic gamma "matrices" span a quaternionic sub-algebra. Another formulation is in terms of octonion real-analyticity. Octonion real-analytic function f is expressible as f=q₁+Iq₂, where q_i are quaternions and I is an octonionic imaginary unit analogous to the ordinary imaginary unit. q₂ (q₁) would vanish for quaternionic (co-quaternionic) space-time regions. The local number field structure of octonion real-analytic functions with composition of functions as additional operation would be realized as geometric operations for space-time surfaces. The conjecture is that these two formulations are equivalent. <LI> An important new interpretational element is the identification of the K&auml;hler action from Minkowskian space-time regions as a purely imaginary contribution identified as Morse function making possible quantal interference effects. The contribution from the Euclidian regions interpreted in terms of generalized Feynman graphs is real and identified as K&auml;hler function. These contributions give apart from coefficient identical Chern-Simons terms at wormhole throats and at the space-like ends of space-time surface: it is not clear whether only the contributions these 3-surfaces are present. <LI> Effective 2-dimensionality suggests a reduction of Chern-Simons terms to a sum of real and imaginary terms corresponding to the total areas of of string world sheets from Euclidian and Minkowskian string world sheets and partonic 2-surfaces, which are an essential element of the proposal for what preferred extremals should be. The duality between partonic 2-surfaces and string world sheets suggests that the total area of partonic 2-surfaces is same as that for string world sheets. <LI> The approach leads also to a highly detailed understanding of the Chern-Simons Dirac equation at the wormhole throats and space-like 3-surfaces and K&auml;hler Dirac equation in the interior of the space-time surface. The effective metric defined by the anticommutators of the modified gamma matrices has an attractive interpretation as a geometrization for parameters like sound velocity assigned with condensed matter systems in accordance with effective 2-dimensionality and strong form of holography. </OL>

The topics of this book could be called fringe physics involving claimed phenomena which do not have explanation in terms of standard physics. </p><p> Many-sheeted space-time with p-adic length scale hierarchy, the predicted dark matter hierarchy with levels partially characterized by quantized dynamical Planck constant, and the prediction of long ranged color and weak forces alone predict a vast variety of new physics effects. Zero energy ontology predicts that energy can have both signs and that classical signals can propagate in reversed time direction at negative energy space-time sheets and an attractive identification for negative energy signals would be as generalizations of phase conjugate laser beams. This vision leads to a coherent view about metabolism, memory, and bio-control and it is natural to ask whether the reported anomalies might be explained in terms of the mechanisms giving hopes about understanding the behavior of living matter. </p><p> <OL> <LI> The effects involving coin words like antigravity, strong gravity, and electro-gravity motivate the discussion of possible anomalous effects related to long range electro-weak fields and many-sheeted gravitation. For instance, TGD leads to a model for the strange effects reported in rotating magnetic systems. <LI> Tesla did not believe that Maxwell's theory was an exhaustive description of electromagnetism. He claimed that experimental findings related to pulsed systems require the assumption of what he called scalar waves not allowed by Maxwell's electrodynamics. TGD indeed allows scalar wave pulses propagating with light velocity. The dropping of particles to larger space-time sheets liberating metabolic energy, transformation of ordinary charged matter to dark matter and vice versa, dark photons, etc... might be needed to explain Tesla's findings. Also phase conjugate, possibly dark, photons making possible communications with geometric past might be involved. <br> These speculative ideas receive unexpected support from the TGD inspired view about particle physics. The recent TGD inspired view about Higgs mechanism suggests strongly that photon eats the remaining component of Higgs boson and in this manner gets longitudinal polarization and small mass allowing to avoid infrared divergences of scattering amplitudes. <LI> The reports about ufos represent a further application for TGD based view about Universe. Taking seriously the predicted presence of infinite self hierarchy represented by dark matter hierarchy makes it almost obvious that higher civilizations are here, there, and everywhere, and that their relationship to us is like that of our brain to its neurons, so that Fermi paradox (Where are they all?) would disappear. Although the space travel might be quite too primitive idea for the civilizations at higher levels of hierarchy, ufos might be real objects representing more advanced technology rather than plasmoid like life forms serving as mediums in telepathic communications. </OL>

This book tries to give an overall view about quantum TGD as it stands now. The topics of this book are following. <OL><LI> Part I: An overall view about the evolution of TGD and about quantum TGD in its recent form. Two visions about physics are discussed at general level. According to first vision physical states of the Universe correspond to classical spinor fields in the world of the classical worlds (WCW) identified as 3-surfaces or equivalently as corresponding 4-surfaces analogous to Bohr orbits and identified as special extrema of K&auml;hler action. TGD as a generalized number theory vision leading naturally also to the emergence of p-adic physics as physics of cognitive representations is the second vision. <LI> Part II: The vision about physics as infinite-dimensional configuration space geometry. The basic idea is that classical spinor fields in WCW describe the quantum states of the Universe. Quantum jump remains the only purely quantal aspect of quantum theory in this approach since there is no quantization at the level of the configuration space. Space-time surfaces correspond to special extremals of the K&auml;hler action analogous to Bohr orbits and define what might be called classical TGD discussed in the first chapter. The construction of the configuration space geometry and spinor structure are discussed in remaining chapters. <LI> Part III: Physics as generalized number theory. Number theoretical vision involves three loosely related approaches: fusion of real and various p-adic physics to a larger whole as algebraic continuations of what might be called rational physics; space-time as a hyper-quaternionic surface of hyper-octonion space, and space-time surfaces as a representations of infinite primes. <LI> Part IV: The first chapter summarizes the basic ideas related to von Neumann algebras known as hyper-finite factors of type II₁ about which configuration space Clifford algebra represents canonical example. Second chapter is devoted to the basic ideas related to the hierarchy of Planck constants and related generalization of the notion of imbedding space to a book like structure. <LI> Part V: Physical applications of TGD. Cosmological and astrophysical applications are summarized and applications to elementary particle physics are discussed at the general level. TGD explains particle families in terms of generation-genus correspondence (particle families correspond to 2-dimensional topologies labeled by genus). The general theory for particle massivation based on p-adic thermodynamics is discussed at the general level. </OL>

In the model of low-energy quantum gravity by the author, cosmological redshifts are caused by interactions of photons with gravitons. Non-forehead collisions with gravitons will lead to an additional relaxation of any photonic flux. It gives a possibility of another interpretation of supernovae 1a data. Every massive body would be decelerated due to collisions with gravitons that may be connected with the Pioneer 10 anomaly. This mechanism needs graviton pairing and "an atomic structure" of matter for working it. Also an existence of black holes contradicts to the equivalence principle: any black hole should have a gravitational mass to be much bigger - about three orders - than an inertial one.

The property of asymptotic freedom of the model of low-energy quantum gravity by the author leads to the unexpected consequence: if a black hole arises due to a collapse of a matter with some characteristic mass of particles, its full mass should be restricted from the bottom. For usual baryonic matter, this limit of mass is of the order 107M_☉

A model of Emergent Gravity with the observed Cosmological Constant from a BF-Chern-Simons-Higgs Model is revisited which allows to show how a Conformal Gravity, Maxwell and SU(2) x SU(2) x U(1) x U(1) Yang-Mills Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in a very natural and geometric fashion.

This article represents a speculative model in which a connection between homeopathy and water memory with phantom DNA eect is proposed and on basis of this connection a vision about how the hardware of topological quantum computation (tqc) represented by the genome is actively developed by subjecting it to evolutionary pressures represented by a virtual world representation of the physical environment and internal mileau including basic bio-molecules. The most important result is the discovery that the analogs of DNA, RNA and aminoacid are realized as dark nuclei realized as neutral dark nuclear strings. Vertebrate nuclear genetic code is predicted correctly. The result suggests deep and totally unexpected connection between elementary particle physics and biology.

The identication of the experienced time te and geometric time tg involves well-known problems. Physicist is troubled by the reversibility of tg contra irreversibility of te, by the con ict between determinism of Schrödinger equation and the non-determinism of state function reduction, and by the poorly understood the origin of the arrow of tg. In biology the second law of thermodynamics might be violated in its standard form for short time intervals. Neuroscientist knows that the moment of sensory experience has a nite duration, does not understand what memories really are, and is bothered by the Libet's puzzling nding that neural activity seems to precede conscious decision. These problems are discussed in the framework of Topological Geometrodynamics (TGD) and TGD inspired theory of consciousness constructed as a generalization of quantum measurement theory. In TGD space-times are regarded as 4-dimensional surfaces of 8-dimensional space-time H = M4xCP2 and obey classical eld equations. The basic notions of consciousness theory are quantum jump and self. Subjective time is identied as a sequence of quantum jumps. Self has as a geometric correlate a xed volume of H- "causal diamond"-dening the perceptive eld of self. Quantum states are regarded as quantum superpositions of space-time surfaces of H and by quantum classical correspondence assumed to shift towards the geometric past of H quantum jump by quantum jump. This creates the illusion that perceiver moves to the direction of the geometric future. Self is curious about the geometric future and induces the shift bringing it to its perceptive eld. Macroscopic quantum coherence and the identication of space-times as surfaces in H play a crucial role in this picture allowing to understand also other problematic aspects in the relationship between experienced and geometric time.

Peter Gariaev and collaborators have reported several strange eects of laser light and also ordinary light on DNA. These ndings include the rotation of polarization plane of laser light by DNA, phantom DNA eect, the transformation of laser light to radio-wave photons having biological eects, the coding of DNA sequences to the modulated polarization plane of laser light and the ability of this kind of light to induce gene expression in another organisms provided the modulated polarization pattern corresponds to an "address" characterizing the organism, and the formation of images of what is believed to be DNA sample itself and of the objects of environment by DNA sample in a cell irradiated by ordinary light in UV-IR range. In this chapter a TGD based model for these eects is discussed. A speculative picture proposing a connection between homeopathy, water memory, and phantom DNA eect is discussed and on basis of this connection a vision about how the tqc hardware represented by the genome is actively developed by subjecting it to evolutionary pressures represented by a virtual world representation of the physical environment. The speculation inspired by this vision is that genetic code as well as DNA-, RNA- and amino-acid sequences should have representation in terms of nuclear strings. The model for dark baryons indeed leads to an identication of these analogs and the basic numbers of genetic code including also the numbers of aminoacids coded by a given number of codons are predicted correctly. Hence it seems that genetic code is universal rather than being an accidental outcome of the biological evolution.

The model for the evolution of genetic code leads to the idea that the folding of proteins obeys a folding code inherited from the genetic code. After some trials one ends up with a general conceptualization of the situation with the identication of wormhole magnetic ux tubes as correlates of attention at molecular level so that a direct connection with TGD inspired theory of consciousness emerges at quantitative level. This allows a far reaching generalization of the DNA as topological quantum computer paradigm and makes it much more detailed. By their asymmetric character hydrogen bonds are excellent candidates for magnetic ux tubes serving as correlates of attention at molecular level.

The topics of the chapter has been restricted to those, which seem to represent the most well-established ideas. There are many other, more speculative, ideas such as the strong form of the hypothesis that plasmoid like life forms molecular life forms has evolved in "Mother Gaia's womb", maybe even in the hot environment dened by the boundary of mantle and core.

This article represents a vision about how DNA might act as a topological quantum computer (tqc). Tqc means that the braidings of braid strands dene tqc programs and M-matrix (generalization of S-matrix in zero energy ontology) dening the entanglement between states assignable to the end points of strands dene the tqc usually coded as unitary time evolution for Schrödinger equation. One can ends up to the model in the following manner.

Basic ideas of TGD inspired view about quantum biology are discussed. TGD inspired theory of consciousness provides the basic conceptual framework besides new view about spacetime and quantum theory, in particular dark matter hierarchy whose levels are labelled by the increasing value of Planck constant so that macroscopic quantum systems are predicted to be present in all length scales. This gives a justication for the notion of eld body having onionlike fractal structure with astrophysical size and using biological body as a sensory receptor and motor instrument. Great evolutionary leaps correspond naturally to the increases of Planck constant for the highest level in "personal" hierarchy of Planck constants implying a scaling up of time scales of long term memory and planned action. The notion of magnetic body leads to a generalization of the notion genome: one can assign coherently expressed super genome to single organ and hyper genome to an entire population. Important experimental input comes from high Tc superconductivity, from the strange ndings related to cell membrane, and from the eects of ELF em elds on vertebrate brain. The model for EEG based on "dark" photons predicts correctly its band structure and also narrow resonances in theta and beta bands in terms of cyclotron resonance frequencies of biologically important ions.

A brief summary of various competing visions about the basic principles of quantum Topological Geometrodynamics (TGD) and about tensions between them is given with emphasis on the recent developments. These visions are following. Quantum physics as as classical spinor field geometry of the "world of classical worlds" consisting or light-like 3-surfaces of the 8-D imbedding space H = M4xCP2; zero energy ontology in which physical states correspond to physical events; TGD as almost topological quantum field theory for light-like 3-surfaces; physics as a generalized number theory with associativity defining the fundamental dynamical principle and involving a generalization of the number concept based on the fusion of real and p-adic number fields to a larger book like structure, the identification of real and various p-adic physics as algebraic completions of rational physics, and the notion of infinite prime; the identification of configuration space Clifford algebra elements as hyper-octonionic conformal fields with associativity condition implying what might be called number theoretic compacticitation; a generalization of quantum theory based on the introduction of hierarchy of Planck constants realized geometrically via a generalization of the notion of imbedding space H to a book like structure with pages which are coverings and orbifolds of H; the notion of finite measurement resolution realized in terms of inclusions of hyperfinite factors as the fundamental dynamical principle implying a generalization of S-matrix to M-matrix identified as Connes tensor product for positive and negative energy parts of zero energy states; two different kinds of extended super-conformal symmetries assignable to the light-cone of H and to the light-like 3-surfaces leading to a concrete construction recipe of M-matrix in terms of generalized Feynman diagrams having light-like 3-surfaces as lines and allowing to formulate generalized Einstein's equations in terms of coset construction.

The new dynamical theory of space is further confirmed by showing that the effective �black hole� masses M_BH in 19 spherical star systems, from globular clusters to galaxies, with masses M, satisfy the prediction that M_BH = α/2 M, where α is the fine structure constant. As well the necessary and unique generalisations of the Schrödinger and Dirac equations permit the first derivation of gravity from a deeper theory, showing that gravity is a quantum effect of quantum matter interacting with the dynamical space. As well the necessary generalisation of Maxwell�s equations displays the observed light bending effects. Finally it is shown from the generalised Dirac equation where the spacetime mathematical formalism, and the accompanying geodesic prescription for matter trajectories, comes from. The new theory of space is non-local and we see many parallels between this and quantum theory, in addition to the fine structure constant manifesting in both, so supporting the argument that space is a quantum foam system, as implied by the deeper information-theoretic theory known as Process Physics. The spatial dynamics also provides an explanation for the �dark matter� effect and as well the non-locality of the dynamics provides a mechanism for generating the uniformity of the universe, so explaining the cosmological horizon problem.

A theory of 3-space explains the phenomenon of gravity as arising from the timedependence and inhomogeneity of the differential flow of this 3-space. The emergent theory of gravity has two gravitational constants: G_N - Newton�s constant, and a dimensionless constant α. Various experiments and astronomical observations have shown that α is the fine structure constant =~ 1/137. Here we analyse the Greenland Ice Shelf and Nevada Test Site borehole g anomalies, and confirm with increased precision this value of a. This and other successful tests of this theory of gravity, including the supermassive black holes in globular clusters and galaxies, and the �dark-matter� effect in spiral galaxies, shows the validity of this theory of gravity. This success implies that the non-relativistic Newtonian gravity was fundamentally flawed from the beginning, and that this flaw was inherited by the relativistic General Relativity theory of gravity.

For some 100 years physics has modelled space and time via the spacetime concept, with space being merely an observer dependent perspective effect of that spacetime - space itself had no observer independent existence - it had no ontological status, and it certainly had no dynamical description. In recent years this has all changed. In 2002 it was discovered that a dynamical 3-space had been detected many times, including the Michelson-Morley 1887 light-speed anisotropy experiment. Here we review the dynamics of this 3-space, tracing its evolution from that of an emergent phenomena in the information-theoretic Process Physics to the phenomenological description in terms of a velocity field describing the relative internal motion of the structured 3-space. The new physics of the dynamical 3-space is extensively tested against experimental and astronomical observations, including the necessary generalisation of the Maxwell, Schrödinger and Dirac equations, leading to a derivation and explanation of gravity as a refraction effect of the quantum matter waves. Phenomena now explainable include the bore hole anomaly, the systematics of black hole masses, the flat rotation curves of spiral galaxies, gravitational light bending and lensing, and the supernova and Gamma-Ray Bursts magnitude-redshift data, for the dynamical 3-space possesses a Hubble expanding 3-space solution. Most importantly none of these phenomena now require dark matter nor dark energy. The flat and curved spacetime formalism is derived from the new physics, so explaining the apparent many successes of those formalisms, but which have now proven to be ontologically and experimentally flawed.

It is shown how Quantum Gravity in D = 3 can be described by a W_inifnity Matrix Model in D = 1 that can be solved exactly via the Collective Field Theory method. A quantization of 4D Gravity can be attained via a 2D Quantum W_inifnity gauge theory coupled to an infinite-component scalar-multiplet ; i.e. the quantization of Einstein Gravity in 4D admits a reformulation in terms of a 2D Quantum W_inifnity gauge theory coupled to an infinite family of scalar fields. Since higher-spin W_inifnity symmetries are very relevant in the study of 2D W_inifnity Gravity, the Quantum Hall effect, large N QCD, strings, membranes, topological QFT, gravitational instantons, Noncommutative 4D Gravity, Modular Matrix Models and the Monster group, it is warranted to explore further the interplay among all these theories.

The vision that the quantum dynamics for dark matter is behind the formation of the visible structures suggests that the formation of the astrophysical structures could be understood as a consequence of Bohr rules.