A recent investigation by the author revealed the proton-electron mass ratio, a dimensionless number, could be approximates extremely well by a simple closed form equation, namely the fourth root of an integer. The result inspired the reader to account for the fact. This paper details some preliminary theorizing that partly explains the fact. Why the integer has the value that it does remains an open question.

In this paper we enumerate the fine structure constant, the proton-electron mass ratio, the neutron-electron mass ratio and the neutron-proton mass ratio. Instructions are given to the readers so that the readers can pursue this enumeration technique for themselves.

In the context of computational methods, an experiment on the optical Fourier transform with direct phase measurement (Nature 2017) is analyzed, a correct assessment of its actual computational complexity is made, taking into account interference that exceeds the capabilities of computational methods, and an experiment technique for direct measurement of computational complexity is presented.<p>В контексте вычислительных методов разбирается эксперимент по оптическому преобразованию Фурье с прямым измерением фазы (Nature 2017), производится корректная оценка его действительной вычислительной сложности с учётом помех, превосходящей возможности вычислительных методов, приводится методика эксперимента по прямому измерению вычислительной сложности.

On an absolute frame of reference, a Galois connection to a d-brane may be prescribed such that the data of the frame becomes locally presentable. We describe these connections briefly.

This paper conducts a security analysis of the generalized k-out-of-m spacetime-constrained oblivious transfer protocol in the context of relativistic quantum cryptography. The introduction of this paper provides an overview of relativistic quantum cryptography and delves into the details of the spacetime-constrained oblivious transfer protocol. The subsequent sections of the paper focus on determining the successful probability of various cloning and measurement attacks. The majority of the analysis will be based on the simplest case when m = 3 and k=2.

Diophantine treatment of Kepler laws, the Holographic Principle and Arthur Haas's forgotten Principle of Coherence induce a steady-state cosmology down to the billionth precision, which explains the observation of "impossible galaxies", and predicts the isothermicity of the background radiation at temperature 2.725820456 Kelvin. The connections of parameters with those of the solar system impose the Solanthropic Principle: we are alone in the universe.

In this brief paper we relate the universal gravitational constant G and Coulomb’s constant k to the volumes of subatomic particles. We define a new characteristic of subatomic particles, quantum volume, which varies in an inverse proportion to the mass of the subatomic particle. As an immediate corollary, we propose an explanation to the Proton’s radius puzzle that reconciles the various seemingly contradictory results obtained, checking our postulates with a prediction of upper and lower bounds for the electron’s radius which is consistent with the current experimental bounds.

In this paper, we propose a variable modeling for the electric charge of subatomic particles, postulating that the charge of some subatomic particle with charge is dependent on its relativistic speed, with the speed of light as the main inertial reference frame. This variable modeling provides a solid explanation of the quantization of electric charge, and opens a new path of research in quantum physics.

In this paper, we compute an approximate value of vacuum permittivity constant (epsilon naught), with an error of less that 5%, using ether vacuum dipoles concept (Dirac's sea). We start from first principles by defining a field equation that will give bounded states dipoles, described as stationnary waves, and an equation for their polarizability density, very close to the vacuum permittivity value.

This paper presents a novel approach for calculating the solution to n-CongruencyAlgebraist Topologies using intrafunctorial calculus equations. We use a com-bination of the Primal Solution to n-Congruency Algebraist Topologies and theinterpspace calculus equation to calculate the finite integral associated with thealgebraic equations and the corresponding solutions for n. We show how thelogical operator "not" can be used in conjunction with the interpspace calculusequation to both calculate the integral and to negate the algebraic statement.We also provide an example of how this approach can be used to solve a partic-ular form of the equations. The results discussed in this paper can be appliedto a variety of problems in the field of algebraic topology.This paper explored the use of interpspace calculus and logical operations to calculate the finite integral solutions associated with the n-Congruency Algebraic Topologies equation and the associated solutions for n. We then applied this combination of methods to study the dynamics of the sun's gravitational pull on the planets orbiting it. Additionally, we developed a mathematical formulation to calculate the stability of a wormhole solution. Finally, we used the interpspace calculus equation and logical operations to derive an equation for the stability of a wormhole solution. This paper provides a comprehensive approach for studying the mathematics of stable wormholes.

After the clasical approach to acceleration of a charged particle by delta-formimpulsive force, we consider the corresponding quantum theory based on the Volkovsolution of the Dirac equation. We determine the modied Compton formula forfrequency of photons generated by the scattering of the delta-form laser pulse on theelectron in a rest. The article follows the physical ideas involved in the author text -Electron in an Ultrashort Laser Pulse (2003).

Actual Determination of Time-span in Absorption Spectroscopy and variation of absorbance vs.concentration is crucial in chemistry and biology. We investigated molecular absorption spectraof 1,4 -diamino anthraquinone taking concentration 20 − 90μM. We primarily report a violationand quantization of Absorbance in Beer’s Lambert Law and propose an alternative explanationfor the inherent phenomenon, quantum mechanically. Upon laser pulse excitation yielded photontransfer excited state having 17-96 attoseconds lifespan is formed for different concentrations ofsamples. We furnished a general equation for the electrostatic field, the wave function of photonsand its correlation with absorbance. Further, we propose an intricate relationship between theelectromagnetic field generated by particles and its wavefunction.

This article presents a new way of looking at and understanding quantum physics through the lens of a novel realist framework. It addresses core issues of realism, locality, and measurement. It proposes a general quantum ontology consisting of two field-like entities, called W-state and P-state, that respectively account for the wave- and particle-like aspects of quantum systems. Unlike Bohmian mechanics, however, it does not take the conjunction of wave and particle literally.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 enforces entanglement obligations and mediates the global coordination within quantum systems required to bring about wavefunction collapse in causal fashion consistent with special relativity.The framework brings quantum theory much closer to general relativity. The two share common language, concepts, and principles. It offers a sensible alternative to the Copenhagen dispensation, which actively discourages - indeed, oracularly proscribes - inquiry that seeks to explain quantum mechanics more deeply than the fact that the mathematical formalism works.

In one of my previous articles (https://vixra.org/abs/1701.0042) I already demonstrated the deep relationship of this Riemann function (canonical partition function of the imaginary parts of the non-trivial zeros of the Riemann z function) with gravity and electromagnetism. In this work we recover it to show its deep connection with a new very simple function that uses the imaginary part of the first zero of the Riemann zeta function together with another well-known function of the non-trivial zeros of the zeta function.Its extraordinary simplicity, without random terms appearing, and that in both functions (the canonical partition function of the imaginary parts of the non-trivial zeros of the zeta function and the new one, derived from the imaginary part of the first zero of zeta) are present the Planck mass, Newton's gravitation constant and the elementary electric charge, implies that their coincidence is completely impossible. At the same time, and for some time now, both mathematicians and physicists have been trying to demonstrate the Riemann hypothesis from quantum mechanics, but so far this has not been achieved. Our work works in reverse and demonstrates that the Riemann zeta function for non-trivial zeros plays an essential role in quantum mechanics and in a possible unification theory, as will be observed by the equations that we will show. We even dare to conjecture that the Physical baryon density ( value 2018,0.0224±0.0001 ) parameter is obtained with a function involved in this work (non-trivial zeros of the function z)

It is demonstrated that the statistical method of the famous Aspect- Bell experiment requires negative densities and negative probabilities from "the thing" researched, else that thing doesn’t exist. The thing refers here to Einstein hidden variables. This requirement in the experiment is absurd and so the results from such experiment are meaningless.

Entanglement is information distributed over the parts of a system, classical or quantum. It can be modeled as a reduction of the structure group, of horizontal symmetries, extending the Gauge Theory paradigm. Many conflicting interpretations are rooted in considering quantum properties as ``intrinsic'', e.g. in the Point-Form QFT / Gauge Theory, and needing a causal connection for ``changing'' the unknown state of the partner-particle, or confirming that QM is (was) ``incomplete'': EPR. The natural explanation of entanglement starts with Einstein's time synchronization and takes advantage of the advancement in our models of particle physics and quantum computing. The ``external variables'' emerge from the ``intrinsic variables'' and the entanglement relations are in fact generalizations of conservation laws. New aspects will be discussed: beyond Noether Theorem, from gauge fiber to horizontal symmetry groups, Hopf algebras model change of symmetry group, analogous to creation-annihilation of pairs of particle-antiparticle, but for information, corresponding to entanglement. Relations with quantum eraser, 2-slit experiment and retrocausality are discussed.

The traditional understanding of the double-slit experiment, which serves as a classicdemonstration of wave-particle duality, is being reconsidered due to new insights into therole of the central barrier between the slits. Contrary to the expectation of seeing twostripes on the screen when treating light as particles, the pattern can be more complex.This complexity arises from the interaction of light with the central barrier, where it isabsorbed and re-emitted in the form of surface plasma polaritons (SPPs). These SPPs travelalong the barrier's surface and contribute to the observed interference pattern. If theirprogress is interrupted by a Geiger counter, the pattern is altered, suggesting that theparticle nature of light alone can sufficiently explain the phenomena. This challenges thetraditional wave-particle duality interpretation and calls for a more nuanced understandingof quantum behavior.

Quantum mechanics, though empirically validated, confronts numerous interpretative challenges, predominantly centered around the quantum measurement problem. Addressing these challenges, we introduce the "Prescribed Measurement Problem," which serves as an inversion to the traditional wavefunction collapse problem. Rather than axiomatizing the entire framework, our approach emphasizes the axiomatization of a sequence of prescribed measurements, highlighting their complex-phase attributes and inherent linearity. Leveraging entropy maximization techniques specific to these measurements, we recover the core elements of quantum mechanics: the Schrödinger equation, Born rule, complex Hilbert spaces, unitary evolution, and self-adjoint operators. Collectively, this approach offers a comprehensive and equivalent formulation of quantum mechanics that integrates measurement outcomes while sidestepping the traditional measurement problem.

This paper proposes a new picture of spin angular momentum. In the conventional picture of spin, the precession of the axis is based on the assumption that the electron has an acceleration. In this study we first consider the case where the acceleration is expressed as a simple harmonic oscillator and the precession as a sinusoidal function. In this case, a double angle appears in the outer product of the Thomas precession, confirming that an angular velocity of one revolution of space can be obtained with half the circumference of the circle. It also shows the results of operations in which a single electron can take both up and down spin depending on the time transition. Next we consider the case of Lorentz contraction of the circumference in the direction of the axis of rotation. Einstein pointed out that in a rotating coordinate system the ratio of circumference to diameter is not pi. This study propose that the Lorentz contraction is the cause of the anomalous magnetic moment. The anomalous magnetic moment is regarded as a Lorentz contraction of the rotational angular momentum. As a result, the average oscillation velocity of the electron within Compton wavelengths is calculated to be about four percent of the speed of light. Furthermore, the Schwarzschild radius on general relativity included in the scope of the consideration to predict the size of the electron.

By presenting 13 correlations involving Avogadro's number, Jean Perrin definitively imposed the idea of the atom, i.e. the negation of the infinitely small. Here, we're talking about both the negation of the infinitely large and the "infinitely insignificant" advocated by officials. textit{We are therefore alone in the Universe}, which the James Webb telescope should confirm. Already, the observation of old galaxies instead of the baby galaxies predicted by standard cosmology destryesz the latter. This failure of cosmology has brought science to a standstill. In particular, CERN failed to detect the expected super-symmetric particles, forgetting Eddington's prophecy of Proton-Tau hyper-symmetry, here linked to cosmology. What we haven't realized is that understanding the quantum world requires cosmology, which therefore appears to be the essential discipline. In fact, it even provides a limit to science, since there is a PERMANENT CREATION of neutrons. Although too weak to be measured directly, this is manifest in the baby galaxies revealed by Halton Arp. The lack of mastery of quantum phenomena is evident in the turbulent history of the laser, still misunderstood, in the quantum Hall and Josephson effects, and in the lack of understanding of climato-cosmic effects. Unlike Perrin's relations, ours are directly verifiable by everyone, which finally rehumanizes Science

While working on the concept of space volume absorption, as underlying classical Newtonian gravity, I got the idea to connect de Broglie's idea of an inner frequency to the Hubble constant. The space absorption concept brings gravity conceptually in line with Hubble's space expansion and allows balancing Hubble space volume expansion with space volume absorption. This reproduced Friedmann's critical density formula. The introduction of the concept of the rate of space volume absorption, a Lorentz scalar, leads to an expression for a quantized bubble of space absorption of the size of the largest nucleus. The mass independent formula for the volume of this quantized bubble of space absorption combines Friedmann's formula and de Broglie's formula and thus integrates the universal constants of Newton, Hubble, Planck and Einstein. I noticed a conceptual similarity between thus quantized space and the sub-quantum medium of the Bohm-Vigier-de Broglie theory.

Local internal coordinates were achieved with simplified Versions of the localization methods of Boys and Pipek-Mezey. By truncation of the orthogonality tails these internal coordinates can be made even more local. The simplified Versions of the Boys localization and of the Pipek-Mezey localization could be applied to any set of orthonormal vectors, if one can assign a location to each component of these vectors. New intermolecular coordinates for supermolecules were implemented in Turbomole. The generation of internal coordinates becomes more stable and the geometry optimization is much faster in some cases.

The role and importance of EM 4-vector potential extends beyond physics theory. It is conceptually connected with the concept of ether, biofield and qi.Instead of finding an "umbrella theory", we would benefit more from understanding all this knowledge as a Network of Theories, with correspondences and translations, and implications ... This is reminiscent of Topos Theory.At experimental and technological level, the Superconducting Quantum Computing area provides a valuable lesson.At the other level of complex biological systems, the theory of chakras, meridians and acupuncture incites to find a common framework, in the sense of Cybernetics, enriched with Quantum Computing (Hardware and software).An contribution to the EPR debate is included: time-sync needs supplemented by space-alignment.In conclusion matter defines and "follows" the QI flow as a "reference frame", in the spirit of General Relativity, but at a gauge theory connection level.

The notorious ‘measurement problem’ has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of ‘in- terpretations’ of quantum mechanics, which are meant to evade it. We argue that no less than six problems need to be distinguished, and that several of them classify as different types of problems. One of them is what traditionally is called ‘the measurement problem’. Another of them has nothing to do with measurements but is a profound metaphysical problem. We also analyse critically T. Maudlin’s (1995) well-known statement of ‘three measurements problems’, and the clash of the views of H. Brown (1986) and H. Stein (1997) on one of the six meansurement problems. Finally, we summarise a solution to one measurement problem which has been largely ignored but tatictly if not explicitly acknowledged.

In this brief report we point out that the example in the famous paper of D. Bohm and Y.Aharonov in 1957 might not realize the long-distance quantum correlation proposed by Einstein, Rosen and Podolsky in 1935. The reason is presented briefly.

An elemental scheme for an alternative theory to quantum mechanics is proposed. The aim is to reproduce quantum phenomenology avoiding intrinsic randomness and action at a distance, but allowing temporal and spatial non-locality. The hypothesis is that all particle dynamics are driven by a non-local but real optimization principle which determines trajectories by minimizing/maximizing a quantity. This quantity is computed uniformly over an unbounded cluster of events no matter when or where they take place. These events are understood as the points where a possible path forks and eachoption contributes differently to the optimized quantity. In this article the mechanism is sketched using a toy model for the measurement of a particleof spin 1/2 (or two for the entangled case) where the events computed for the particle path are kept discrete and dual. The calculation that follows is aimed to provide a natural yet non-local explanation of the violation of Bell inequalities without the requirement of any intrinsic randomness or express ‘hidden variables’. No method or formalism from current quantum mechanics is intended to be used. Only the experimental outcomes for measurements of spin1/2 particles are considered.

This paper reviews the Organic Semiconductorsand theory behind its development and a brief of the history around developing this technology. A lot of it will discuss the distribution of energy bands in organic semiconductors and the optical properties and luminescence effect when some organic materials such as Phthalocyanine and Polymers such as polypara-phenylene-vinylene. and will discuss OFET and applications of Optical Amplifiers.

There has been a lot of talk about the measurement problem. While the physics of it has been (at least mostly) rigorous, the underlying philosophy has been nothing short of a complete catastrophe. This paper will establish the true philosophical context and integrate the appropriate science into it, as it should have happened from the beginning. Bad philosophy didn’t allow it. I also highlight the false dichotomy underlying the measurement problem so that it can be detected more easily for those who do not engage with philosophy in an extensive manner.

Recently, much progress has been made on understanding transport properties of strongly coupled quantum field theories by employing gauge-gravity duality. However, a theory of transport at finite density and temperature is still lacking for strongly disordered systems. We reduce the computation of direct current electrical conductivity, for a wide variety of strongly disordered holographic systems with no background charge density, to the solution of a linear differential equation dependent only on data on the black hole horizon of the bulk theory. Some strongly coupled theories in two spatial dimensions have a universal conductivity, independent of disorder strength. We realize a disorder-driven holographic metal-insulator transitions through the percolation of poorly-conducting regions across the black hole horizon. We compare results from our exact realizations of holographic disorder with simpler approaches to the problem, such as massive gravity.

A recent paper submitted to the 79th annual Gravity Research Foundation essay competitionentitled "chatGPT explains Quantum Gravity" [1] was written in collaboration with GPT3.5. Withminimal prompting the bot has generated plausible coherent explanations for what it calls QINs(quantum impedance networks) of the unstable particle spectrum, massless neutrino oscillation,muon collider topological lifetime enhancement, and quantum gravity at the Compton, Planck, andcosmological scales [2]. One goal of that paper was to minimize pretraining, to find out what thebot already ‘understood’ before introducing new ideas.A similar training process on GPT4 has completed the first three dialogs. The first two arepresented here. GPT4 is much deeper, appears much more coherent. And poses its own uniquechallenges to learning and teaching. How to train a generative transformer on QINs? It seems theessential next step is to introduce visualGPT, to train on the images [1, 3].Humility is to be curious and willing to learn. chatGPT appears both humble and very powerful,in some sense an ideal collaborator, when facts matter a model to mirror as best one can.

Photon wave functions collapse into particles only after one discerns their path, as was observed in certain experiments. However, scientists like Wheeler, and Scully contemplated that this causality and the uncertainty principle could be violated through quantum erasure. Complementarity and availability of path information are sufficient to explain quantum mechanics. Scientists widely debate this claim; in the process, they often try to reinterpret the tenets of quantum mechanics. Qureshi employs microscopic-macroscopic entanglement to save causality. Qureshi also posits that the experimenter's active choice of Hilbert space basis determines wave or particle nature. Qureshi insists that when the experimenter measures the photon in the x-basis, it entangles with his novel qubit which-way detector and the two detectors that constitute the screen and show interference. If the basis choice is z, then the interference is destroyed. In this paper, we peruse the shortcomings of Qureshi's analysis.The distinction between evolution and measurement is not acknowledged. The entanglement of a photon with experimental apparatus smears quantum-classical distinction. Qureshi forgets that the screen in quantum experiments can be a single entity. The quantum qubit which-way detector he contemplates will likely function classically. In assigning measurement basis to the photon, Qureshi forgets that the phase change due to path difference in the experimental setup does not influence quantum measurement. Thus, it does not contribute to a distinct quantum state. Scientists have studied wave-particle duality using entangled photons: entanglement alone cannot destroy the interference. The photon can choose its wave-particle option randomly; the experimenter's role is thus inactive. Wave nature formulation is not derived from Hilbert space basis, and the mathematical formulation in quantum mechanics is meant to predict probabilities in the particle nature; it does not say anything about the photon's physical realization. We observe that Complementarity ensures that causality violations are possible.

The current situation of research challenging thedemanding tasks of renormalization implies that the presentframework of quantum scattering theory does not offer goodprospect, and therefore it is necessary to construct a newtheory able to solve the infinity problem fundamentally in ageneral way. Our purpose is to construct an alternative mathematical formulation capable of ensuring the convergenceof the scattering matrix without relying on renormalizationtheory, thus preventing overlapping divergences of the scattering matrix in principle. We demonstrate that the infinityproblem is due mainly to the mathematical representation ofthe scattering operator and present, as a solution to the problem, alternative mathematical representations of the scattering matrix in terms of the local and global time-evolutionoperators which replace the Dyson series and do not need theFeynman diagram. Importantly, the obtained results clarifythat substantially, there does not exist the infinity problemof the scattering matrix. Ultimately, we draw the successfulconclusion that it is possible to conceive of an alternativeto the conventional scattering theory and our formalism as anew proposal can lay the foundation for formulating a consistent theory without infinity and renormalization.

The interpretation that the positive and negative solutions of the Dirac equation are particles and antiparticles is a common and widespread one. In this paper, we would aim to extend the 0-Sphere Electron Model to explore the internal structure of neutrino oscillations. From another point of view, the positive and negative solutions could correspond to a process in which two particles emit and absorb energy. This paper proposes a new model for the internal structure of neutrinos. The model has been created in which the Lissajous curve arises from two energy oscillators obtained from the positive and negative solutions of the Dirac equation. This model, the 0-Sphere Neutrino Model, assumes the existence of oscillators with thermal energy that are converted into kinetic energy, and includes two oscillators with different vibrational frequencies that are described by Lissajous curves.

The one-loop radiative correction to the photon propagator can be graphicallyrepresented by the Feynman diagram of the second order. The physical meaningof this diagram is that photon can existin the intermediate state with electron and positron as virtual particles. The photon propagationfunction based on such process with electron-positron pair is derived. Themodified Lagrangian of electromagnetic field is derived supposing the modifedpropagator of photon. The Schwinger source methods of quantum field theoryis applied. Then, the corresponding Maxwell equations are derived from the newLagrangian.

Previously, an analysis of emergence of 3D-space from quark fields in the context of QCD suggested a similar analysis of the relation between quantum phase and relativistic time.As a follow-up, Einstein's synchronization analysis, in the context of quantum theory of EM leads to emergence of Minkowski Space-Time from quantum phase in the context of Scalar EM.An essential step in this direction was made by Kaluza-Klein approach to unification of gravity and electromagnetism.This research program suggests that GR can be derived from the SM, via gauge theory, with Gravity from quantum origin, emerging macroscopically as geometry. In essence this is a "reverse engineering" of the historical development of modern theories from classical ones, taking the quantum level as primary, in order to derive the classical models we call "reality".

The photonpropagation function with electron-positron pair is determined from the effective emission and absorption sources. The Schwingersource methods of quantum field theory is applied. Then, the Coulomb potentialand Bohr energy with radiative corrections are determined.

This paper shows how an application of zeta function regularisation to a physical model of quantum measurement yields a solution to the problem of wavefunction collapse. A realistic measurement ontology is introduced, which is based on particle distinguishability being imposed by the measurement process entering into the classical regime. Based on this, an outcome function is introduced. It is shown how regularisation of this outcome function leads to apparent collapse of the wavefunction. Some possible experimental approaches are described.

Algebraic mistakes of using a non-relativistic functions betrayed Dirac’s elegant derivation of the relativistic equation of quantum mechanics and exposed a short coming of special relativity. It was a serious mistake because that famous paper became a model for theorist to follow who produced an unending stream of nonsense. The mistake was compounded because it hid the fact that special relativity was still incomplete. Multiple independent spaces are required to generate both dynamics as well as produce particle properties. The concept of statistical independence of spaces that encapsulated quantum objects, fields and particles, was necessary for physics to have a relativistic basis for both massive particles and massless fields. The example that will be developed is the origin of the solar neutrino survival data that requires the electron neutrino to be massless as originally proposed by Pauli. The analysis renders a proof of the original quantum conjecture by Planck and Einstein that radiation is quantized and how inertia for massive particles is generated.

Some theoretical physics models take space-time to be discontinuous. We concur. Further, we suggest that all of space-time consists of real, charged, Planck-scale, particles that move in an imaginary manifold under the influence of a force acting between those particles. We propose such a force, an amalgam of the strong and electro-weak forces. In addition, the gravitational force and the force between charged particles is included. We then drop a large number of the particles into the manifold and observe their motions. The motions can be observed in 3D on a dedicated URL. This lets us explore various quantum mechanical phenomena.

The uncertainty principle is the most important for the foundations of quantum mechanics but it still remains failed to reach a consensus of its interpretation, which gives rise to debates upon its physical nature. In this work, we address the problem of its foundation from a different aspect to present an alternative formulation for proving the uncertainty relations in a general way in terms of commutation relations and action function. The relationship between the de Broglie relation and the uncertainty principle is studied from a new angle. As a result, it is demonstrated that the de Broglie relation is the foundation of the uncertainty principle. Starting with the de Broglie relation as the origin of the problem, we show the logic context that the de Broglie relation provides the form of the wave function and the determined form of the wave function in turn leads to the conception of operators for quantum mechanics, and thus it is possible to provide with the help of the operators and wave function a generalized proof of the uncertainty principle as the law governing ensemble of states. As a decisive solution to the problem, the interpretation of the uncertainty principle in terms of the action function is offered that gives a consistent explanation in agreement with the known physical phenomena. Eventually, we show the necessity and possibility of reassessing and improving the foundation and interpretation of the uncertainty principle as a leading principle of quantum mechanics.

We demonstrate that a Bell experiment asks the impossible of a Kolmogorovian correlation. An Einstein locality explanation in Bell’s format is therefore excluded beforehand by way of the experimental and statistical method followed.

It still remains an important open question of the interpretation of the foundations of quantum mechanics to thoroughly elucidate the essence and significance of the correspondence principle. We focus from a new mathematical aspecton the review of the correspondence principle to gain the correct understanding of the principle. As a result, we show that there does not exist the algebraic isomorphism between the algebra of the observables and that of the quantum operators, and therefore the previous interpretation of the correspondence principle aiming to provide allthe operators corresponding to physical quantities is inconsistent from the mathematical view point. Furthermore, it is demonstrated that the correspondence between physical quantities and quantum operators is possible within canonically conjugate observables constituting the action, while classical and quantum quantities satisfy one and the same dynamical relation. Moreover, it is shown that the classical limit of quantum mechanics can be explained not by the correspondence principle but by the de Broglie relation and the operator equations.

The measurement problem is an important open question for the interpretation of the foundations of quantum mechanics. For the purpose of solving this problem, we focus from a new angle on the interpretation of the superpositionprinciple that is the origin of the measurement problem. As a result, we show that the measurement problem at issuecannot arise, provided the mathematical and physical aspects of the superposition principle are considered correctly.Our work demonstrates that since any mathematical superposition of eigenstates is never a new eigenstate, the superposed state at issue, if any, should be interpreted simply as a statistical ensemble of possible states that occursequentially, instead of a mixed state indicative of simultaneous occurrence. Actually, this view leads to the conclusion that the concept of the currently accepted state vector and the motivation of the measurement problem have noperfect ground from both mathematical and physical aspects. Furthermore, using mainly mathematical method ratherthan thought experiments, we offer a realistic interpretation of the superposition of eigenstates based on ensemble ofquantum states, thereby helping to capture the essence of the measurement problem which actually is not implicatedin Apparatus and Observer.

The hydrodynamical model of quantum mechanics based on the Schroedingerequation is combined with the magnetohydrodynamical term to form so calledquantum magnetohydrodynamic equation. It is shown that the quantum correctionto the Alfven waves follows from this new equation. The possible generalization isconsidered for the so called nonlinear Schroedinger equation and for the situationwhere dissipation is described by the Navier-Stokes equation.

The crises in fundamental physics is by now openly reported and acknowledged. The new paradigm, based on the Network Model, quark field of baryons and mesonic nuclear bonds, proposes a reinterpretation of the Standard Model and fundamental experiments in quantum physics, that claims to resolve major debates, including the Hierarchy Problem. Recall that the Electro-Gravity Magneto-Dynamics is the theory of the long range component of the quark field, which is yet missed by, for instance Yukawa potential, color QCD or chiral Effective Field Theory. The short range component described by the nuclear effective potential of chiral Effective Field Theory is consistent with Yukawa's meson model of nuclear forces, unified by the above approach. The experiments verifying this model of Gravity are recalled: F. Alzofon and D. Sarkadi. Is there a relation between the two? Further confirmations of the new Theory of Gravity come from of Podkletnov and Ning Li's research and experiments. The new paradigm is claimed to be consistent with the already existing Standard Model, with its accurate predictions but containing historical miss-interpretations, proposing a change in our point of view and goals.

With the rising popularity of machine learning in the past decade, a stronger urgency has been placed on drastically improving computational technology. Despite recent advancements in this industry, the speed at which our technologies can complete machine learning tasks continues to be its most significant bottleneck. Modern machine learning algorithms are notorious for requiring a substantial amount of computational power. As the demand for computational power increases, so does the demand for new ways to improve the speed of these algorithms. Machine learning researchers have turned to leverage quantum computation to significantly improve their algorithms' time complexities. This counteracts the physical limitations that come with the chips used in our technology today. This paper questions current classical machine learning practices by comparing them to their quantum alternatives and addressing the applications and limitations of this new approach.

We aim to find a place where hypothetical hidden variables of quantum mechanics might be accommodated. We consider the possibility that hidden variables belong to the Calabi-Yau manifold, the space of six extra dimensions, appearing in the superstring theory.

The 2-slit experiment is explained by using the Network Model, which then transfers to other experiments: entanglement, delayed choice and quantum erasure etc.In essence, De Broglie pilot wave, on a Feynman path are aspects of a fermionic quantum channel transmitting bosonic excitations between tho nodes of the quantum network formed as part of the experiment. This model is called the Network Model.An essential feature of the Network Model is that it evolves in transient-steady state cycles, akin to machine learning: The Living Universe.Other considerations involving Space-Time, antimatter, Heisenberg uncertainty relations, fermion-boson unification etc., are included.

Light propagation is a stone in the construction of A. Einstein SR theory and the comment he made in 1921 is still relevant. The existence of or non existence of a medium for the light propagation has not yet been given a clear answer. It is admited nowadays that light propagates in vaccum", without knowing its nature. Even if we call "vaccum" the medium for the propagation of light, to not say "ether", it is still a mystery how this medium behaves inside transparent matter in motion relative to space. The negation of the term "ether" comes from debates about experiments made in 19th century when stellar aberration was discovered and which gave rise to the Augustin Fresnel proposition of the "entrainment of ether by matter". Hyppolite Fizeau validated this concept with an experiment in which light is propagating through moving water and which was confirmed by Michelson, a few years later, in water and air. To have a clearer idea of the cohabitation of the two entities, matter and ether, Michelson initiated the issue of the behaviour of light in moving matter through ether ("ether wind") which was not treated by Fizeau experiment. The Michelson and Morley experiment was devoted to demonstrate the effect of the earth's motion through space on light propagation. The results obtained are still in controversial. In this paper we shows that the results obtained by Michelson, which were not null, can be explained by a new model of light propagation in transparent matter in motion through space.

According to Maxwell's electromagnetic theory or classical electromagnetic theory, if there is a changing current on the antenna, an electromagnetic wave will be induced around the antenna, which can propagate in space. When the electromagnetic wave propagates to the receiving antenna, the electromagnetic wave transfers the electromagnetic energy and momentum to the receiving antenna. The receiving antenna receives the electromagnetic signal. The above discussion is the standard description of electromagnetic wave in almost all electromagnetic field textbooks. The author found this description wrong. According to Wheeler Feynman's absorber theory, the radiation generated by the transmitting antenna is not only determined by the changing current of the transmitting antenna, but also affected by the current changes of the environmental materials. The material absorbing electromagnetic wave affects the transmitting antenna by radiating the advanced wave. The author supports Wheeler Feynman's view. Maxwell's electromagnetic theory needs to satisfy the Sliver-Muller radiation condition. This condition actually describes that a good absorber material has been arranged at the far field of the transmitting antenna, which can absorb all the radiated electromagnetic waves. Considering these, the author establishes a new electromagnetic theory, in which all transmitting antennas, absorber materials are near the origin. It is assumed that no matter on the sphere with infinite radius can absorb electromagnetic waves, so electromagnetic waves cannot transmit electromagnetic energy to infinity. The author adds this idea to Maxwell's electromagnetic theory. That is to add a boundary condition for Maxwell's electromagnetic theory that radiation does not overflow the universe. This boundary condition must be in conflict with Maxwell's electromagnetic theory. Because the far field of Maxwell's electromagnetic theory can only take the Sliver-Muller radiation condition. However, the author finds that we can relax Maxwell's equation appropriately. In fact, the author relaxes the mutual energy principle equivalent to Maxwell's equation. The relaxed mutual energy principle can add new boundary condition that radiation does not overflow the universe. This constitutes a new electromagnetic theory.

The EPR-phenomenon, usually described with the use of the rather mystical process of quantum entanglement, is consistenly explained here as a consequence of the ambivalence of the time direction in entropy-less physical subsystems of our world.

With the use of local dependency of probability density of local hidden variables on the instrument settings, it is demonstrated that Bell’s correlation formulation is incomplete. This result concurs with a previous computational violation close to quantum correlation with a computer model based on Einstein locality principles.

The Schroedinger equation with the nonlinear term is derived in the frameworkof the Dirac heuristics. The particle behaves classically in case the mass of it is infinite.The nonlinear term involves new physical constant b. The constant b can bemeasured by the same methods that were used in the case of the Casimir effect. Of course, the experimental procedure is based on well educatedexperimenters. The new experiments, different from the Zeilinger ones, are proposed, with theFaraday simplicity. The article isthe extended and perfectionized version of the articles by author (Pardy, 1993; 1994; 2001).

We present an alternative quantum-statistical approach to the electron tunneling through the potential barrier, which is distinguished from the conventional interpretation.In our approach, the tunnel effect is treated in both the statistical aspect and quantum aspect. The conventional interpretation of the tunnel effect based purely on the wave property of a single electron cannot elucidate satisfactorily the dynamics of electron motion in the potential barrier because the interpretation violates the universal law of energy conservation, just as the subtle term `tunnel effect' implies.In this work, we clarify the fact that the tunnel effect has statistical aspects too, and explain it both by applying the electron statistics and by considering the quantum restriction by the potential barrier on electron surmounting the barrier instead of tunneling. Therefore, our interpretation satisfies the law of energy conservation and naturally explains all the characteristics of tunneling including the influence of temperature as the statistical aspect as well. The consideration of the quantum restriction that is determined by potential barrier leads to a satisfactory explanation of the quantum properties of tunneling. Finally, we offer a complete and general explanation of the tunnel effect as a phenomenon of quantum plus statistical origin, thus demonstrating that the tunneling substantially depends on quantum-statistical nature.

We derive a proto-Hamiltonian of quantum electrodynamics (QED) from the coupled Dirac equation by quantizing the electromagnetic field. We then introduce a process of eliminating the gauge symmetry via separation of variables, and argue that this does not break the Lorentz covariance of the theory. From this approach, we obtain a Hamiltonian that is similar to the conventional one of QED. We conclude the paper short of making the Dirac sea reinterpretation, where one would otherwise reinterpret the negative-energy solutions to the Dirac equation as antiparticles.

We outline a proposal for an experimental test of Everett’s many-worlds interpretation of quantum mechanics that could potentially verify the existence of a multiverse. This proposal is based on a quantum field theory formulation of many-worlds through the path integral formalism and a careful choice of the vacuum state.

Torsion field can be used for communicationpurposes because of the Non-Local phenomenarelated to the objects which generate this field. Torsion Field Communication, which is Non-Electromagnetic one, is a very different when compared to normal Electromagnetic communication approach. These new properties bring some advantages. This work introduces a series of TFC experiments between Beijing and New York, accomplished by the authors. SEVA instrument was employed as the receiver in New York, and the scalar wave generator, which is based on tworesonant Tesla coils, was used as the TF transmitter. As the authors believe, such the conceptions like the non-locality, nonlinearity, quantum entanglement, Field Gyroscope and related to them Synchronicity, all having the common root, are the carriers of this NonElectromagneticphenomenon. During these sessions, some accompanying, interesting non-linear phenomenaoccurred.

A magician, seems to be analogous to quantum mechanics, throws the spectators into a bewildering surprise by exhibiting a magic trick similar to the quantum superposition. The trick appears to be strange, weird and counter-intuitive like the quantum superposition, as long as the underlying secret behind its working is unknown. In the present article, the mystery of quantum superposition is demystified at a single-quantum level. Also, the counterfactual reality and the causality in Young's double-slit and Wheeler's delayed-choice experiments are pointed out, respectively.

The equivalent system of equations corresponding to the Duffin-Kemmer-Petiau (DKP)equation is derived and the WKB approximation of this system is found. It is proved thatthe Lorentz equation follows from the new DKP-Pardy system.

Based on the possibility of `indistinguishability' not being a binary property of quantum particles I argue that allowing for fractional quanta to occur can provide a means to `distinguish' so far-indistinguishable quantum particles.

Wilhelm Weber’s electrodynamics is an action-at-a-distance theory which has the property that equal charges inside a critical radius be- come attractive. Weber’s electrodynamics inside the critical radius can be interpreted as a classical Hamiltonian system whose kinetic energy is, however, expressed with respect to a Lorentzian metric. In this article we study the Schroedinger equation associated with this Hamiltonian system, and relate it to Weyl’s theory of singular Sturm-Liouville problems.

The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory, but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted, and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved with a framework for quantum cosmology time arrow eigenstates. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.

Here a correlation to the exact fine-structure constant is found. This derivation suggests that the fine structure constant can be theoretically determined as a Lambert function that utilizes the spectrum range of all the energy modes (radiation modes) that fit inside the observable universe between the particle horizon down to Planck Length. Alternatively, this also could be interpreted as the Lambert function of the particle horizon in natural units. Several methods use hyperbolic geometry to achieve full convergence. A compilation of various convergent equations are found to represent the fine structure constant.

Intuitionistic fuzzy set has been widely applied to decision-making, medical diagnosis, pattern recognition and other fields, because of its powerful ability to represent and address the uncertain of information. In this paper, we propose a novel complex intuitionistic fuzzy set.

Quantum Mechanics and Computation has a major problem called the measurement problem [7] [19]. This has given physicists a very hard time over the years when I first looked into the problem my approach was simple find a new number system that can go with the uncertainty of a Quantum particle the paper deals with the mathematics of uncertainty which has solved 2 millenium prize problems [4], [5] and quantum mea- surement problem very efficiently. We divide chaos into two parts low chaos and high chaos then we find the desired value [19] inside the inter- section of both. This helps us find something in a ℵ3 >>> ∞ this takes the problems around us to the next level if we are able to control a chaos then we can achieve pretty much anything.

Using the quantum formalism, a question - ``Why particle ontology is unavoidable in quantum mechanics?'' - is analyzed. The frequently outspoken inference, ``particle appears to be fuzzy and spread out, i.e., they seem to be at multiple states at once'', is shown to be inconsistent with respect to quantum formalism.

Hydrogen being the most common element in the universe is almost invisible in atomicform though it is common as a as minor contaminating component in most terrestrialcompounds. Atomic hydrogen and its isotopes are the only chemically active atomswhose valence electron is not screened from the nucleus. This unique property leadsto a rich spectroscopic behavior when weakly bonded to other molecules, surfaces, orembedded within solids. The spectra’s origin lie in rotational nuclear degrees of freedomthat become active when the atoms are polarization bonded to other structures. Freeneutral atomic hydrogen is difficult to detect by its 1420.4 MHz emission even in objectsas large as the local Virgo cluster of galaxies. Our surprise was in detecting intensesignals with an inexpensive receiver near 1420.4 MHz in the spectral band reserved forradio astronomy where broadcasting is forbidden. These signals behaved like emissionsfrom slightly perturbed 1S atomic hydrogen possessing rotational states with very smallenergy shifts. These signals are ubiquitous when there is any low level electromagneticnoise present.

The connection between the Schrodinger equation and Einstein diffusion theory on basis of Brownianmotion of independent particles is well known. However, in contrast to diffusion theory, quantummechanics theory has suffered controversial interpretations due to the counterintuitive concept ofwavefunction. Here, while we confirm there is no difference in the mathematical form of these twoequations, we derive the complex version of displacement. Using diffusion theory of particles in amedium, as simple as it is, we describe that quantum mechanics is just an elegant and subtle equationto describe the probability of all the trajectories that a particle can take to propagate in time by apredictive wavefunction. Therefore, information on the position of particles through time in quantumtheory is embedded in the wavefunction which predicts the evolution of an ensemble of individualBrownian particles.

We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field. The electron moving in magnetic field produces so called synchrotron radiation. In other words the photons are emitted from the points of the electron trajectory and it means that the trajectory of electron is visible in the synchrotron radiation spectrum. The extension of the discussion to the cosmical rays moving in the magnetic field of the Saturn magnetosphere and its rings is mentioned. It is related to the probe CASSINI. The solution of the problem in the framework of the hydrodynamical model of quantum mechanics and the nonlinear quantum mechanics is also mentioned.

The Debye length plays a central role in plasma physics and also for semiconductors. We are investigating what the Debye length would be for a hypothetical plasma consisting of Planck mass particles; in other words, what we could coin: Planck plasma. This, we think, could be of interest as the Planck scale is assumed to play a central role in quantum gravity theory and potentially also quantum gravity computers.

Quantum Mechanics is understood by generalizing models for cause-effect from functions, e.g. Differential Equations, to graphs and, via linearization, to linear operators. This also leads from classical logic to quantum logic.

The academic circles over publicize the difficult process of LIGO exploring the signal and extracting the signal according to the predetermined target, which not only exposes the essence that such so-called scientific experiments are more like secret children's play, but also makes readers' attention far deviate from the important theme of how to use scientific methods to test whether LIGO signal is the gravitational wave generated in the process of spiral binary star merger, so as to blindly believe in science fiction news. What exact law should gravitational waves obey? Since LIGO gives the so-called observation data of gw150914 signal, as long as the accurate law obeyed by gw150914 signal is analyzed and compared with the accurate law of gravitational wave, an irrefutable scientific conclusion can be obtained. In fact, the gw150914 signal does not follow the relativistic Blanchet frequency equation of gravitational waves that LIGO likes to talk about (please refer to the paper: relativistic equation failure for LIGO signals). It has a unique law and seems to be a signal on the earth. However, further analysis shows that it has some specific differences from such signals on the earth. The comprehensive conclusion from multiple perspectives shows that the key operators of LIGO secretly extract data of the motion process of the simulation device to confuse the public and thus forge gw150914 gravitational wave, which is very likely. This paper accurately fits the com quantum law obeyed by gw150914 signal frequency. However, almost all famous mainstream academic journals unanimously refuse to publish such papers on the accurate analysis of the precise law of LIGO signal, and continue to publish more science fiction stories without experimental data analysis to further maintain lies. The author now offers a reward of 1 million yuan to reward scholars who strictly deduce the accurate co quantization law of gw150914 signal in theory rather than guessing through hypothesis. People who pursue truth all over the world unite to prevent the further spread of mainstream academic corruption that ignores academic morality, only seeks fame and wealth, cooperates in fraud and stifles truth. This reward is valid before the author publishes the core principles of COM quantum theory and is limited to the author's lifetime.

Quantum mechanics based on Planck hypothesis and statistical interpretation of wave function has achieved great success in describing the discrete law of micro motion. However, the idea of quantum mechanics has not been successfully used to describe the discrete law of macro motion, and the causality implied in the Planck hypothesis and the application scope of the basic principles of quantum mechanics have not been clarified. In this paper, we first introduce the angular motion law and its application, which seems to be of no special significance as a supplement to the perfect classical mechanics, but plays an irreplaceable role in testing whether the core mathematical procedure of quantum mechanics of operator evolution wave equation satisfies the unitary principle. Then, the operator evolution wave equations corresponding to the angular motion law are discussed, and the necessity of generalized optimization of differential equations are illustrated by the form of ordinary differential equations. Finally, the real wave equation which is superior to the Schr\"{o}dinger equation in physical meaning but not necessarily the ultimate answer is briefly introduced. The implicit conclusion is that Hamiltonian can not be the only inevitable choice of constructing wave equation in quantum mechanics, and there is no causal relationship between operator evolution wave equation and quantized energy in bound state system, which indicates that whether the essence of quantum mechanics can be completely revealed is the key to unify macro and micro quantized theory.

The quantum model of valence electron generation orbital penetration of alkali metal elements with unique stable structure is investigated. The electric field outside the atomic kernel is usually expressed by the Coulomb field of the point charge mode, and the composite electric field in atomic kernel can be equivalent to the electric field inside the sphere with uniform charge distribution or other electric fields without divergence point. The exact solutions of two Schrodinger equations for the bound state of the Coulomb field outside the atom and the binding state of the equivalent field inside the atom determine two different quantization energy formulas respectively. Here we show that the atomic kernel surface is the only common zero potential surface that can be selected. When the orbital penetration occurs, the law of conservation of energy requires that the energy level formulas of the two bound states must have corresponding quantum numbers to make them equal. As a result, there is no solution to the quantum number equation, indicating that the two quantum states of the valence electron are incompatible. This irreconcilable contradiction shows that the quantized energy of quantum mechanics cannot absolutely satisfy the law of conservation of energy.

The Planck constant is considered one of the most important universal constants of physics, but its physical nature still has not been fully understood. Further investigation and new perspectives on this quantity should therefore be of interest. We demonstrate that the Planck constant can be directly linked to the Compton frequency of one divided by the Compton frequency of one kg. This further implies that the Planck constant is related to the quantization of matter, not only energy. We will also show that the frequency of one, when expressed in relation to kg, depends on the observation time. This new interpretation of the Planck constant could be an important step towards more in-depth understanding its physical nature, and potentially explaining the origin of the mass-gap and the rest mass of a photon.

Quantum Field Theory, or QFT, is a well-accepted set of theories used in particle physics that involves Lagrangian mechanics. An individual can generate a rich variety of Hamiltonian equation systems from the Lagrangian associated QFT to describe simultaneous or cofounding processes which occur in particle physics. Unfortunately, the equation systems associated with QFT are relatively hard to solve. This paper will show that the generating function technique (GFT) can be used to directly solve these equation systems while also producing renormalization results. The usage of the latter is necessary to display the consistency of the solutions and equation systems. Ultimately, an astute scientist in QFT can claim GFT is a valuable tool to be utilized in the field of particle physics.

In this article give a very simple presentation of Bell's inequality by comparing it to a ``quantum game show'', followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.

Margenau wanted to see reduction of the wave packet in terms of the Schrödinger equation. Here we will look at it in terms of non-locality.

The equivalent system of equations corresponding to the Dirac equation is derived and the WKB approximation of this system is found. Similarly, the WKB approximation for the equivalent system of equation corresponding to the squared Dirac equation is found and it is proved that the Lorentz equation and the Bargmann-Michel-Telegdi iquations follow from the new Dirac-Pardy system. The new tensor equation with sigma matrix is derived for the verification by adequate laboratories.

Newton's Law of Universal Gravitation provides the basis for calculating the attraction force between two bodies, which is called the "gravitational force" \cite{Newton gravitation}. This Law uses the "mass" of bodies. Einstein General Relativity Theory proposes to calculate this gravitational force by using the curvature of space-time. This space-time curvature is supposedly due to the same "mass" \cite{Einstein}. Stephan Hawkings in his book (A Brief History of Time)\cite{Hawkings} supposes that gravitons particles of quantum mechanics are the intermediaries that "give mass" to the bodies. However, there is no explanation about the nature of the gravitons or how their interaction with bodies could "give them mass". This paper presents a new way of explaining how the "mass" can be given to bodies. The starting point is an idea proposed in 1690 by Nicolas Fatio de Duillier and revisited here with new hypotheses, and then further developped with the use of the Bohmian quantum mechanics. It is shown, by means of reasoning and equations reflecting these reasoning, that the gravitational force between two bodies comes from the interaction between the revisited Nicolas Fatio's aether and matter atomic nuclei. It is also shown that the "mass" of a body is not a real entity, but is an emerging phenomenon. This idea has already been suggested by Erick Verlinde in another context \cite{Verlinde}. Here, the emergence of "mass" is given by the interaction of the aether particles with matter atomic nuclei. The interesting point of Nicolas Fatio’s theory is that it is able to solve not only the origin of gravitational force, but also the origin of inertial force. The origin of inertia comes from an induction phenomena between Nicolas Fatio's aether and matter atomic nuclei. This paper uses Nicolas Fatio's medium own word, aether, to describe gravitation and inertia. It has nothing to do with Lorentz or Maxwell luminiferous aether that has been disproved by the scientific community after the Michelson and Morley experiment.

In our terms, this is Bell's 1964 theorem, ‘No local hidden-variable theory can reproduce exactly the quantum mechanical predictions.' Against this, and bound by what Bell takes to be Einstein's definition of locality, we refute Bell's theorem and reveal his error. We show that Einstein was right: the physical world is local; and we advance Einstein's quest to make quantum mechanics intelligible in a classical way. With respect to understanding, and taking mathematics to be the best logic, the author is as close as an email: eprb@me.com

Weak-measurement induced quantum discord or super quantum discord (SQD) is a generalization of the normal quantum discord and is defined as the difference between quantum mutual information and classical correlation obtained by weak measurements in a given quantum system. This correlation is an information-theoretic measure and is, in general, different from entanglement-separability measures such as entanglement. Super quantum discord may be nonzero even for certain separable states. So far, SQD has been calculated explicitly only for a limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for SQD for X states, a seven real-parameter family of two-qubit states and investigate its monogamy properties. The monogamy behaviour of SQD depends on the measurement strength. The formalism can be easily extended to N-qubit X states.

It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an otherwise Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localization are lost.

Recently, we have demonstrated that the Dirac equation can be cast into a form involving higher-order spinors. We have shown that the transformed Dirac equation splits into two equations, describing charged spin $0$ and (massless) spin $\frac{1}{2}$ particles. We apply this result to the problem of spin-charge separation.

According to the recently proposed ``wave-particle non-dualistic interpretation of quantum mechanics", the physical nature of Schrodinger's wave function is an `instantaneous resonant spatial mode' in which a quantum flies akin to the case of a test particle moving along a geodesic in the curved space-time of general theory of relativity. By making use of this physical nature, a causal explanation is provided for the delayed-choice quantum erasure experiment.

The early twentieth century produced the beginnings of relativity, quantum mechanics, and the big bang, but then went off the rails like much of the world in the early 1930s. The rest of the world recovered but quantum mechanics did not recover. Physics was weighed down with a continuum geometry that did not allow quantum mechanics and relativity to be united. Then came 30 years of cold fusion experiments that could not be explained. To get things back on track we will dispense with the creation myth of this New Age physics that Edwin Hubble’s work produced, the big bang. There is an intimate connection between cold fusion and the improbability of any great bang emanating from a point. The underlying problem was the suppression of the development of both quantum mechanics and relativity.

In this paper, we discuss the phenomenon that in the photons generated after electron-positron annihilation, the sources of thermal potential energy that make up the electrons and positrons are equally divided. As a result, the photon contains one thermal point each for the electron and positron, and a picture of a single system emerges. This annihilation could be predicted to occur at the point where the two domains intersect if the electron and positron phases are properly aligned on the Riemann surface. Taking advantage of the model in which the interior of the electron radiates and radiates thermophores, the electron-positron annihilation could be likened to an inelastic collision observed from opposite directions in time. In addition, we consider that the oscillation caused by thermal radiation inside the electron cancels out that of the positron, causing the electron and positron to lose mass and transform into a photon.

The inner-product, $<\psi|\psi>$, between a state vector, $|\psi>$ and its dual, $<\psi|$, is thoroughly analyzed using the recently developed `wave-particle non-dualistic interpretation of quantum mechanics'; here, $|\psi>$ is a solution of the Schrodinger wave equation. Using this analysis, ``questions about what decides whether a photon is to go through or not and how it changes its direction of polarization when it does go through a polarizing filter" - a statement by Prof. Dirac - is unambiguously explained.

Lorentz transformation plays a key role in Special Relativity by relating the space- time distance between events being observed in a pair of inertial frames of reference. Depending on the relative velocity of the inertial frames, the magnitude of Lorentz transformation varies between the limits 0 and 1. The upper limit 1 represents a case where the pair of inertial frames of reference are stationary relative to each other. The lower limit 0 represents the other extreme case where the relative velocity of the frames is at the speed of light c. Similar numerical limits, on the other hand, appear in Quantum Mechanics but in the context of the summation of the probability density distribution of a particle over a region of space. The upper limit 1 represents a case where the probability of finding a particle in a region of space is certain. The lower limit, represents the opposite case where the probability of finding a particle in a region of space is not likely. The range of the limits being between 0 and 1 in both theories is not a numerical coincidence. In this paper, a combined theory is introduced which relates the Lorentz transformation of Special Relativity to the wavefunction of Quan- tum Mechanics. The combined theory offers a new insight to the physical reality. For instance, it is found that the inherent quantum uncertainties in the spacetime coordinate of a quantum particle in vacuum constitute a timelike four-vector whose length A is invariant. It is also found that local acceleration, like velocity itself, has an upper limit; such that no physical object can undergo a local acceleration higher than c2/A. The latter, in turn, constrains the mass of the smallest possible black hole - called Unit Black Hole (UBH) - to Ac2/4G and its event horizon diameter to the invariant A. The diameter of the event horizon, the mass and the Hawking temperature of more massive black holes are subsequently quantized starting from those of the UBH.

In an earlier paper, a stochastic model had been presented for the Planck-scale nature of space-time. From it, many features of quantum mechanics and relativity were derived. But as mathematical points have no extent, the stochastic manifold cannot be tessellated with points (if the points are independently mobile) and so a granular model is required. As grains have orientations as well as positions, spinors (or quaternians) are required to describe them, resulting in phenomena as described by the Dirac equation. We treat both space and time stochastically and thus require a new interpretation of time to prevent an object being in multiple places at the same time. As the grains do have a definite volume, a mechanism is required to create and annihilate grains (without leaving gaps in space-time) as the universe, or parts thereof, expands or contracts. Making the time coordinate complex provides a mechanism. From geometric considerations alone, both the General Relativity field equations (the master equations of Relativity) and the Schrödinger equation (the master equation of quantum mechanics) are produced. Finally, to preserve the constancy of the volume element even internal to a mass, we propose a rolled-up fifth-dimension which is non-zero only in the presence of mass or energy.

In one-dimensional quantum systems with short-range interactions, a set of leading numerical methods is based on matrix product states, whose bond dimension determines the amount of computational resources required by these methods. We prove that a thermal state at constant inverse temperature $\beta$ has a matrix product representation with bond dimension $e^{\tilde O(\sqrt{\beta\log(1/\epsilon)})}$ such that all local properties are approximated to accuracy $\epsilon$. This justifies the common practice of using a constant bond dimension in the numerical simulation of thermal properties.

The measurement problem in quantum mechanics has been a cause of much puzzlement over the years. The very idea of having two different versions of reality for the same system has been a cause for much debate. Often quantum mechanics textbooks follow the ‘shut up and calculate’ paradigm. This denies the opportunity for the common student to understand the consequence of one of the most elegant and beautiful aspects of science. The state of the art textbooks give a purely algebraic, perfunctory and monotonous approach where the real consequence of the system is not fully appreciated. A good reason for this is the considerable deviation of the quantum mechanical process from the commonsensical idea of truth, reality and reason. We tend to look at the world in a materialistic, deterministic, causal and objectivistic way. We tend not to accept a world of contradictions. A quantum measurement is essentially an amalgamation of contradictions, mystery and duality. It encompasses an implicit dependence on subjectivity and contradicts with causality as we know it. We look at the world as in the present. But a quantum mechanical measurement is a prediction of the future influenced by the observer or the measurer. This offers a philosophical and pedagogical conundrum. It poses a challenge on not just how our perception of the world might change in addition to providing a big challenge on how to make it compatible with the other successful theories of physics. The most common text book interpretation of quantum mechanics has been the Copenhagen Interpretation suggests the ‘collapse of the wave function’ as a mechanism of transition between duality. But a more bizarre yet elegant theory, extending quantum formalism to the classical domain, called the Many Worlds Interpretation has been catching up very quickly; it stands for the split of the universe when we make a quantum mechanical measurement. Consequently, reality as we is redefined as a universal wave function which is a superposition of several outcomes, which is incompatible with many of the successful concepts of physics and has several problems like the correct idea about probability or basis. We adapt the idea of the universal wave function, but instead suggest a continuum interpretation of quantum mechanics where the universal wave function represents the entire singular universe and the concept of atoms or electrons as conceptually a continuous part of it rather than a distinct separate entity. Such an interpretation could be compatible with other continuum theories like the Superfluid vacuum theory or the Higgs Field.

A new definition for quantum-mechanical momentum is proposed which yields novel nonlinear generalisations of Schroedinger and Klein-Gordon equations. It is thence argued that the superposition and uncertainty principles as they stand cannot have general validity.

Extensive experimental tests of the Bell inequality have been conducted over time and the test results are viewed as a testimony to quantum mechanics. In considering the close tie between quantum mechanics and statistical theory, this paper identifies the mistake in previous statistical explanation and uses an elegant statistical approach to derive general formulas for two-particle Bell tests, without invoking any wavefunctions. The results show that, for the special case where the spins/polarizations are in the same, opposite, or perpendicular directions, the general formulas derived in this paper convert to quantum predictions, which are confirmed by numerous experiments. The paper also investigates the linkages between the statistical and quantum predictions and finds that vector decomposition and probability law are at the heart of both approaches. Based on this finding, the paper explains statistically why the local hidden variable theory fails the Bell tests. The paper has important implications for quantum computing, quantum theory in general, and the role of randomism and realism in physics.

Duality in quantum mechanical wave functions is manifest through the famous measurement problem. There have been several interpretations to explain this duality, but none have seen full consensus among physicists. The Copenhagen interpretation, which is at least to some extent the most widely accepted interpretation has the 'collapse' of the wave function (or state vector reduction) during measurement, does not attribute a physical reality to the wave function. Moreover, the idea of measurement having a role in defining reality shakes the very foundation of classical physics. On the other hand, the Many worlds interpretation proposed by Everett is a very brave attempt to attribute physical significance to the wave function. Though mathematically sound and elegant, 'the splitting of the universe' in the Many Worlds Interpretation completely redefines reality as we know it. We test Everett's original thought experiment in the presence of a super observer and for sequential measurements as well. We observe that the no-clone theorem helps the Many Worlds Interpretation, yet it does not provide a consistent picture for sequential measurements, unlike the Copenhagen Interpretation.

We can not think of measurement devices as if they would be a part of nature. Why? Because it violates the definition of nature, becoming the tautology: nature is what (measures) nature.

Relativistic solutions of the bound state problem for the hydrogen atom and one electron ions using the uncorrected Coulomb potential and comparing those results with ones using the correct physical potential reveals that relativity’s gamma in the quantum bound state takes on values less than one. This also explains the physical origin of the Bose-Einstein and Fermi-Dirac statistics for bound state particles.

A rational approach to understanding quantum mechanics is presented in which one is able to account for the observation that two spinning particles, irrespective of their space-time separation, can be correlated in EPR-like experiments.

We define the photoelectric effect with the specific heat term replacing the work function. The photon propagator involving the radiative correction is also considered. We consider the Debye specific head for the 3D crystal medium, the specific heat for the 2D medium and specific heat for the Wigner crystal.

We study spin coherent states, Bell states, entanglement, Husimi distributions, uncertainty relation, Bell inequality. The distance between these states is also derived. The Bell matrix, spin coherent states and Bell states are also investigated.

Promoting the maxim followed in viXra:2101.0094 and viXra:2102.0029 to the Principle of Force-Property Correspondence, we propose that any spinning particle creates a field in spacetime given by the equation $\square\omega=-\frac{4\pi c}{\hbar}\sigma$ where $\omega$ is the frequency of rotation of the particle, and $\sigma$ spin density per unit volume of space.

It is instrumental interpretation of Quantum Mechanics. Why this new interpretation is needed Because all known interpretations only describe how Quantum Mechanics works, so that one can be able to apply equations, but do not answer the question: "why did nature need Quantum Mechanics at all?"

Following the results of our publications, in the first part of this letter, we explain that quantum theory based on finite mathematics (FQT) is more general (fundamental) than standard quantum theory based on Poincare invariance. Standard concept of particle-antiparticle is not universal because it arises as a result of symmetry breaking from FQT to standard quantum theory based on Poincare or standard anti-de Sitter symmetries. In FQT one irreducible representation of the symmetry algebra describes a particle and its antiparticle simultaneously, and there are no conservation laws of electric charge and baryon quantum number. Poincare and standard anti-de Sitter symmetry are good approximations at the present stage of the universe but in the early stages they cannot take place. Therefore, the statement that in such stages the numbers of baryons and antibaryons were the same, does not have a physical meaning, and the problem of baryon asymmetry of the universe does not arise. Analogously, the numbers of positive and negative electric charges at the present stage of the universe should not be the same, i.e., the total electric charge of the universe should not be zero.

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations.

The hermitian polarization matrix is written, using the Pauli matrices and the identity matrix as a basis, with four real coefficients, the four Stokes vector parameters; the interaction of light with matter is described as the modification of these 4 parameters by a 4x4 matrix, the Mueller matrix. Pauli matrices form a Clifford algebra, the projection operators R and L define the two Stokes vectors for right-handed and left-handed circularly polarized light. In four dimensions, the Minkowski metric ηµν = diag(+1, −1, −1, −1) leads to the Clifford algebra C(1,3) Dirac matrices, the 16 Dirac matrices form a basis for the polarization matrix, now with 16 Stokes parameters the interaction of light with matter is described by a 16x16 Mueller matrix, the projection operators R and L in this algebra define the right-handed and left-handed circularly polarized light.

Extending an existing quantum optic model for beamsplitters, a comprehensive model is developed from the first principles of quantum physics to describe photons traversing linear optical devices of arbitrary number of ports and even a circuit of devices, which are essential components of photonic quantum computing gates and circuits. The model derives the quantum operators and states of the photons at the egress ports of a device, gate or circuit from those at the ingress ports. As an application and validation, it is used to model the experiment that discovered the Hong-Ou-Mandel (HOM) effect and to explain the effect without the notion of quantum interference. The experiment is not only a landmark in the research of quantum optics but also important to photonic quantum computing design.

A new `wave-particle non-dualistic interpretation at a single-quantum level' is presented by showing the physical nature of Schrodinger's wave function as an ‘instantaneous resonant spatial mode’ to which a particle's motion is confined. The initial phase associated with a state vector is identified to be related to a particular position eigenstate of the particle and hence, the equality of quantum mechanical time to classical time is obtained; this equality automatically explains the emergence of classical world from the underlying quantum world. Derivation of the Born rule as a limiting case of the relative frequency of detection is provided for the first time, which automatically resolves the measurement problem. Also, the Born rule derivation is supplemented with a geometrical interpretation. `What’s really going on' in Young's double-slit and Wheeler's delayed-choice experiments is explained at a single-quantum level. Also, an interference experiment is proposed to verify the correctness of the non-dualistic interpretation.

Bell's theorem has been described as the most profound discovery of science; one of the few essential discoveries of 20th Century physics; indecipherable to non-mathematicians. However, taking elementary analysis to be an adequate logic here, we refute Bell's theorem, correct his inequality and identify his error. Further, we do this under the principle of true local realism, the union of true locality (or relativistic causality: no influence propagates superluminally) and true realism (or non-naive realism: some existents change interactively). We thus lay the foundation for a more complete physical theory: one in line with Einstein's ideas and Bell's hopes. Let's see.

The Many Worlds Interpretation (MWI) was proposed by H.Everett. It has sounded like most senseless stuff to the scientists of his time, but today it is one of the leading interpretations of Quantum Mechanics (QM). I argue that this interpretation does not conflict with the conventional interpretation. Namely, the observer whose mind does not depart from Our Universe must use the Copenhagen Interpretation (CI).

As R. P. Feynman said: the fine structure constant is the probability that an electron emits or absorbs a photon. In this work several equations are shown; the majority of empirical heuristic character, by which the precise value of the fine-structure constant (its inverse) is obtained. Far from being pure numerology, we think that they are not accidental. We rely to affirm this in that in all there appear repetitively either mathematical constants such as Pi, e, etc, and / or quantum corrections due to the masses of the leptons with electric charge and the masses of the Wand Z bosons (and its entropies). This rules out its casual character. That there are so many possible equations and that they are related to very relevant aspects of mathematics, such as the monster group and others; allows us to demonstrate the extraordinary mathematical properties of this dimensionless constant

I point out some obviously fatal mathematical errors in the recent paper published in Royal Society Open Science and entitled "Quantum correlations are weaved by the spinors of the Euclidean primitives" by Joy Christian, director of the "Einstein Center for Local Realistic Physics" in the city of Oxford, in the UK. Submitted to RSOS on the invitation of the editors. This is my version 3; 29 October, 3020. Minor errors corrected and logos blanked.

The Number Theory comes back as the heart of unified Science, in a Computing Cosmos using the bases 2;3;5;7 whose two symmetric combinaisons explain the main lepton mass ratios. The corresponding Holic Principle induces a symmetry between the Newton and Planck constants which confirms the Permanent Sweeping Holography Bang Cosmology, with invariant baryon density 3/10, the dark baryons being dephased matter-antimatter oscillation. This implies the DNA bi-codon mean isotopic mass, confirming to 0.1 ppm the electron-based Topological Axis, whose terminal boson is the base 2 c-observable Universe in the base 3 Cosmos. The physical parameters involve the Euler ideonal numbers and the special Fermat primes of Wieferich (bases 2) and Mirimanoff (base 3). The prime numbers and crystallographic symmetries are related to the 4-fold structure of the DNA bi-codon. The forgotten Eddington’s proton-tau symmetry is rehabilitated, renewing the supersymmetry quest. This excludes the concepts of Multiverse, Continuum, Infinity, Locality and Zero-mass Particle, leading to stringent predictions in Cosmology, Particle Physics and Biology.

There are solutions of the Klein-Gordon equation for the massless neutrino that produce massless neutrino oscillation of flavor. These solutions serve as a counterexample to Pontecorvo, Maki, Nakagawa, and Sakata theory for neutrino oscillation of flavor, which implies neutrinos must have mass contrary to the standard model. We show that the wave function for the massless antineutrino for an inverse beta decay (IBD) is a superposition of two independent solutions of the Klein-Gordon equation. One solution represents the latent incident wave upon an IBD. The other solution represents the latent reflected wave from the IBD. This superposition renders a compound modulated wave function with regard to amplitude and phase modulations. This compound modulation is shown to facilitate neutrino oscillation that may be massless and, therefore, consistent with the standard model. Extra to a massless counterexample, the weak interaction is shown to transmute the wave function during an IBD by changing the amounts of the latent incident and latent reflected wave functions that are allocated to the superposition.

The necessity of Lorentz transforming the Dirac matrices is an ongoing issue with contradicting opinions. The Lorentz transformation of Dirac spinors is clear but for the Dirac adjoint, the combination of a spinor and the `time-like' zeroth gamma-matrix, the situation is fussy again. In the Feynman slash objects, the gamma matrix four vector connects to the dynamic four vectors without really becoming one itself. The Feynman slash objects exist in 4-D Minkowsky space-time on the one hand, the gamma matrices are often taken as inert objects like the Minkowski metric itself on the other hand. To be short, a slumbering confusion exists in RQM's roots. In this paper, first a Pauli-level biquaternion environment equivalent to Minkowski space-time is presented. Then the Weyl-Dirac environment is produced as a PT doubling of the biquaternion Pauli-environment. It is the production process from basic elements that produces some clarification regarding the mentioned RQM foundational fussiness.

According to non-dualistic interpretation of quantum mechanics, the initial/ global/overall phase associated with a quantum state vector is related to a particular eigenstate of an observable. This phase gives raise to a ``tube" like geometrical structure, associated with the state vector and the tube branches into several smaller tubes. The total number of smaller tubes is equal to the total number of eigenstates of the observable; each branch is associated with a particular eigenstate. The cross-sectional area of the initial tube is equal to the sum of cross-sectional areas of all tubes, resulting in the Born rule and also in the conservation of probability in quantum mechanics.

In this paper, we propose an alternate interpretation of the quantum theory using objective physical reality that does not depend on the conventional probability interpretation.As typical physical phenomena for the probability interpretation, we consider the single-photon interference, single-electron interference, and EPR correlation experimentsusing photon polarization. For the calculation using the alternate interpretation, the minus sign derived from the covariant quantization of Maxwell’s equations,which is associated with the scalar potential of time axis component of four-vector, is taken as it is as an inevitable request from the theory. In addition, geometrical phaseis incorporated, which can be recognized as a kind of scalar potential. We show that both conventional and alternate interpretation derive the identical calculation resultsfor these single photon, single electron interference, and EPR correlation.These alternate calculation processes describe that there is a kind of scalar potential in whole space-time and when there is some geometrical arrangement in thespace, the scalar potential forms the oscillatory field of the potential according to the arrangement. It reveals the objective physical reality that the single-photon,single-electron interference, and EPR correlation are generated by the movement of the photons and electrons in the oscillatory field with interference.In addition, we show that the oscillatory field formation of the scalar potential depending on the geometrical arrangement causes energy fluctuation in the space,which enables removal of infinite zero-point energy and causes spontaneous symmetry breaking and Casimir effect. By recognizing the electromagnetic field as anunitary U(1) gauge field and generalizing it to a special unitary SU(2), we also show the uncharged particle, e.g. neutron, interferences are generated by the geometricalarrangement of the SU(2) gauge field or geometrical phase. Furthermore, we discuss the origin of the scalar potential by distinguishing the space where the substanceexists and the vacuum.Finally, by introducing the extended Lorentz gauge, we propose the alternate solution without physical state and subsidiary condition for the contradiction between Lorentz gauge as an operator equation and the commutation relation in the covariant canonical quantization of Maxwell’s equations with the conventional Lorentz gauge.This paper contains the compilation of published author’s papers cite{Morimoto1,Morimoto2} in addition to featured discussions such as the physical reality, uncharged particle interference,geometrical phase and alternate proposal for the contradiction between Lorentz gauge as an operator equation and commutation relation.

Hasegawa Yuji of the Vienna University of Technology and Masaaki Ozawa of Nagoya University and other scholars published empirical results against Heisenberg’s uncertainty principle on January 15, 2012.They got a measurement result with a smaller error than the Heisenberg uncertainty principle, which proved the measurement advocated by the Heisenberg uncertainty principle.This article follows the method I used to study superradiation and connects the uncertainty principle with the superradiation effect. I found that under the superradiation effect, the measurement limit of the uncertainty principle can be smaller.

In this short note we will show the Haug-1 quantum wave equation in relation to where we incorporate spin following the Pauli route. This lead to a similar equation to the Schrodinger-Pauli equation, but our equation is relativistic while the Schrodinger-Pauli equation is non-relativistic, our equation is also simpler in terms of for example the time and space are on the same order (first derivatives), while in the Schrodinger-Pauli equation time is on first order and spatial-spin dimensions on second order. Comments are welcome.

Against Bell (1964c), and via classical analysis (including the principle of relativity): we make quantum correlations intelligible by completing the quantum mechanical account in a classical way. We find that Bell neglects a logical correlation that refutes his theorem, while a commutation relation and some easy algebra refute his inequality. So: for Einstein -- and against Bell's naive local realism; with certainty -- relativistic causality prevails. In this way we arrive at wholistic mechanics (WM): ie, classical mechanics extended from light-speed c to Planck's constant h. Importantly, for STEM students and teachers, and against popular opinion-pieces about quantum nonlocality, our results require no knowledge of quantum theory: for the quantum is here, to be found. Let's see.

In this paper, we look further into one of the relativistic wave equations we have introduced recently. Our relativistic wave equation is a PDE that is rooted in the relativistic energy Compton momentum relation, rather than the standard energy momentum relation. They are two sides of the same coin, but the standard momentum is just a derivative of the Compton momentum, so this simplifies things considerably. Here the main focus is to rewrite our relativistic PDE wave equation in spherical polar coordinates, then by some separation of variables we end up with three ordinary differential equations (ODEs) for which we present possible solutions, and we also provide a table where we compare our ODEs with the ODEs one gets from the Schro ̈dinger equation [1]. This approach is used to describe hydrogen-like atoms. We encourage other researchers to check our calculations and the predictions from our solutions and see how they fit compared to observations from hydrogen-like atoms.

In this note, we present a table with a summary of recent developments in quantum mechanics. If you not have studied our papers carefully already [1–4], then this paper will not make much sense and the equations could easily be misunderstood, so we strongly encourage the reader to become familiar with this material first. We will possibly write a long paper on this topic later, but it may be helpful to present the essence of both old and new QM, as we understand it today. This is useful for both tracing the history of ideas related to QM in mathematical form and for creating an opportunity to compare equations and analyze their similarities and differences.

In this paper, we discuss in brief the most common wave equations in quantum mechanics and some recent development in wave mechanics. We also present two new quantum wave mechanics equations based on the Compton momentum. We also question the idea that energy and mass are scalars, and we claim they are vectors instead. We have good reasons to think that the standard momentum is a mathematical derivative of the more fundamental Compton momentum. This will hopefully simplify interpretations of quantum mechanics significantly; our new relativistic wave equations look promising, but need further investigation into what they predict. This way of looking at quantum mechanics in new light is not in conflict with existing equations, but they are supplemental to the collection of existing wave equations. We prove mathematically that if one satisfies our new relativistic energy Compton momentum relation, one also satisfies the standard relativistic energy momentum relation automatically. They are two sides of the same coin, where the relations to the Compton wavelength likely represent the deeper reality, so we have reasons to think our new wave mechanics addresses a deeper level of understanding than the existing conception. We also look at our new wave equation in relation to hydrogen-like atoms; we follow the “standard approach” used for the Schro ̈dinger equation of putting it in polar coordinate form and, by change of variables, finding three ODEs and their solutions. We give a table summary of our new ODEs and their solutions compared to the well-known solutions of the Schro ̈dinger equation.

‘Experiments violating a Bell inequality [BI] thus leave [‘realists'] no option: the principle of relativity is false [sic]. The world is nonlocal [sic],' Wiseman & Cavalcanti (2015). But we show that even high-school math violates a BI; in fact, all BIs—being inadequate for experiments with highly correlated outcomes—are false. Moreover: under the principle of relativity, elementary math shows that wholistic mechanics (WM)—classical mechanics extended to include Planck's constant—also violates BIs. So, with 3 ways to violate a BI—experiment, high-school math, WM—true-realists find: Bellians are being rather silly, as Bell (1990) half-expected; quantum correlations are wholly explicable via WM in our relativistically local world; the principle of relativity is true, nonlocality false. Importantly: for STEM teachers, and against popular opinion-pieces about quantum nonlocality, our results require no knowledge of QM. Let's see.

My previous work [arXiv:1902.00977] studied the dynamics of R\'enyi entanglement entropy $R_\alpha$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_\alpha$ with R\'enyi index $\alpha>1$ grows no faster than ``diffusively'' (up to a sublogarithmic correction) if charge transport is not faster than diffusive. The proof was given only for qubit or spin-$1/2$ systems. In this note, I extend the proof to qudit systems, i.e., spin systems with local dimension $d\ge2$.

We consider a frame of reference moving along a line with respect to an inertial frame of reference. We expect the rate of total energy expectation value not to depend on the order of transformations of a transformation that is a composition of a translation and a transformation that has a frame of reference accelerating with a time dependent acceleration with respect to an inertial frame of reference.

In modern physics, the de Broglie wavelength is considered to be the matter wave. However, the de Broglie wave has a series of strange properties. It is not mathematically defined for a rest-mass particle, when v=0. However, one can claim a particle never stands still and that the de Broglie wavelength only converges towards infinite when v converges to zero. An infinite matter wavelength would also be strange. We have good reasons to think that the de Broglie wavelength only is a mathematical derivative of the true matter wavelength, which we believe is the Compton wavelength. Although noted briefly here, this has already been described by Haug \cite{Hau20UnifiedA} and is a topic for another article. What we will focus on here is that the length of the de Broglie wavelength, if we use an observational window of one second and the minimum observable velocity, is the Planck length per second. Then the de Broglie wavelength for a proton actually has a length very close to the assumed radius of the observable universe. We think most likely this is a coincidence, particularly since one second is an arbitrarily chosen time unit, and not a fundamental time unit such as the Compton time, or the Planck time, for example. Still, we think this finding is worth mentioning and could be the basis for further discussion.

An anomaly of the Earth gravitational field could increase the second-order gravity-gradient tensor more than an order of magnitude and third-order gravity-gradient tensor more than 4 orders of magnitudes. As a result estimates of the systematic errors in the atomic gravimetry considered in the articles [1, 2] should be proportionally enlarged.

We obtain formulas (bot. p. 12)--including $\frac{2}{121}$ and $\frac{4 \left(242 \sqrt{3} \pi -1311\right)}{9801}$--for the eight atoms (Fig.~\ref{fig:Venn}), summing to 1, which span a 256-dimensional three-set (P, S, PPT) entanglement-probability boolean algebra for the two-qutrit Hiesmayr-L{\"o}ffler states. PPT denotes positive partial transpose, while P and S provide the Li-Qiao necessary {\it and} sufficient conditions for entanglement. The constraints ensuring entanglement are $s> \frac{16}{9} \approx 1.7777$ and $p> \frac{2^{27}}{3^{18} \cdot 7^{15} \cdot13} \approx 5.61324 \cdot 10^{-15}$. Here, $s$ is the square of the sum (Ky Fan norm) of the eight singular values of the $8 \times 8$ correlation matrix in the Bloch representation, and $p$, the square of the product of the singular values. In the two-{\it ququart} Hiesmayr-L{\"o}ffler case, one constraint is $s>\frac{9}{4} \approx 2.25$, while $\frac{3^{24}}{2^{134}} \approx 1.2968528306 \cdot 10^{-29}$ is an upper bound on the appropriate $p$ value, with an entanglement probability $\approx 0.607698$. The $S$ constraints, in both cases, prove equivalent to the well-known CCNR/realignment criteria. Further, we detect and verify--using software of A. Mandilara--pseudo-one-copy undistillable (POCU) negative partial transposed two-qutrit states distributed over the surface of the separable states. Additionally, we study the {\it best separable approximation} problem within this two-qutrit setting, and obtain explicit decompositions of separable states into the sum of eleven product states. Numerous quantities of interest--including the eight atoms--were, first, estimated using a quasirandom procedure.

This paper is about a proposed "New Mathematics" (NM) and its potential in science. The NM is proposed as an amalgamation of mathematics with the "SP System" -- meaning the "SP Theory of Intelligence" and its realisation in the "SP Computer Model" -- both now and as they may be developed in the future. A key part of the structure and workings of the SP System and the proposed NM is the compression of information via the matching and unification of patterns. A preamble includes: brief notes about solipsism in science; an introduction to the SP System with pointers to where fuller information may be found; an outline of how the NM may be developed; and a discussion of several aspects of information compression; In sections that follow: 1) A summary of some of the potential benefits of the NM in science, including: adding an AI dimension to mathematics; facilitating the integration of mathematics, logic, and computing; development of the NM as a "universal framework for the representation and processing of diverse kinds of knowledge" (UFK); a new perspective on statistics; and new concepts of proof, theorem, and so on. 2) A discussion of mathematical and non-mathematical means of representing and processing scientific knowledge. 3) A discussion of how the NM may help overcome the known problems with infinity in physics. 4) how the NM may help in modelling of the quantum mechanics concepts of 'superposition' and 'qubits' via analogies with concepts in stochastic computational linguistics and ordinary mathematics. 5) Likewise, how the NM may prove useful in modelling the quantum mechanics concept of 'nonlocality' and 'entanglement' via an analogy with the phenomenon of discontinuous dependencies in natural languages. 6) How the NM, with the SP System, provides alternative, and arguably more plausible, interpretations of such concepts as the 'Mathematical Universe Hypothesis' and the 'Many Worlds' interpretation of quantum mechanics, as described in Max Tegmark's book "Our Mathematical Universe". Two appendices including: A) a tentative 'tsunami' interpretation of the concept of 'wave-particle duality' in quantum mechanics; and B) A discussion of the possibility of interference fringes with real tsunamis.

Having solved the Dirac equation, we obtained the concept of a spinor. There are two solutions to the Dirac equation, one with positive-energy states and one with negative-energy states. Conventionally, these two positive and negative states have been interpreted and corresponded to electrons and positrons. This paper aims to represent that we interpret the positive and negative states of the Dirac equation as two spinor particles contained in one electron, and examine their validity. As a result, adapting the previous study (i.e., The 0-sphere Electron Model) to the Dirac equation's positive and negative solutions gave a new interpretation of the negative-energy status. The positive and negative states of mass correspond to a thermal potential energy's radiation and absorption, respectively. The positive and negative momentum states could be described based on the simple harmonics oscillation of the virtual photon's kinetic energy.

In this paper the quantised version of Newton Second Law is derived assuming merely the existence of de Broglie matter-waves and their basic properties. At the same time we keep an eye towards interpretations of quantum mechanics and will realise that the two most different interpretations (Copenhagen interpretation and the de Broglie-Bohm theory) owe their difference to two fundamentally different approaches to `Harmonisation'. In this regard we shall see that the guiding equation of the de Broglie-Bohm theory currently found in literature is not the most complete equation possible; as a result we answer one of the important questions in interpreting quantum mechanics, namely that `when does the concept of classical path (trajectory) makes sense in quantum mechanics?' Moreover, in light of special-relativistic considerations we shall easily see that in the Number-Division approach, i.e. that of de Broglie-Bohm, the wave operator no longer appears, making it in turn impossible the application of Clifford algebras (Dirac's `square root' of the wave operator).

The quaternion is an effective tool to evaluate uncertainty, and it has been studied widely. However, what is the quaternion probability still an open question. This paper has proposed the quaternion probability, which is the extent of classical probability and plural probability with the aid of quaternion. The quaternion probability can apply classical probability theory to the four-dimensional space. Based on the quaternion probability, the quaternion probability multiplication has been proposed, which is a method of multiplication conforming to the law of quaternion multiplication. Under the bayesian environment, the quaternion full joint probability and the quaternion conditional probability is proposed, which can apply the quaternion probability to address the issues of quantum decision making. Numerical examples are applied to prove the efficiency of the proposed model. The experimental results show that the proposed model can apply the quaternion theory to the bayesian updating effectively and successfully.

In this paper, we show how one can find the Compton scattering formula and thereby also the Compton wavelength based on new concepts from collision-space time. This gives us the standard Compton wavelength, but we go one step forward and show how to find the relativistic Compton wavelength from Compton scattering as well. (That is, when the electron is also moving initially.) The original Compton formula only gives the electron’s rest-mass Compton wavelength, or we could call it the standing electron’s Compton wave.

K. Suto has recently pointed out an interesting relativistic extension of Rydberg's formula. Here we also discuss Rydberg's formula, and offer additional evidence on how one can easily see that it is nonrelativistic and therefore a good approximation, at best, when v<<c. We also extend the Suto formula to hold for any atom and examine the formula in detail.

In 1923, Arthur Holly Compton introduced what today is known as the Compton wave. Even if the Compton scattering derivation by Compton is relativistic in the sense that it takes into account the momentum of photons traveling at the speed of light, the original Compton derivation indirectly assumes that the electron is stationary at the moment it is scattered by electrons, but not after it has been hit by photons. Here, we extend this to derive Compton scattering for the case when the electron is initially moving at a velocity v. This gives us a relativistic Compton wave, something we remarkably have not seen published before.

Quantum computing, a fancy word resting on equally fancy fundamentals in quantum mechanics, has become a media hype, a mainstream topic in popular culture and an eye candy for high-tech company researchers and investors alike. Quantum computing has the power to provide faster, more efficient, secure and accurate computing solutions for emerging future innovations. Governments the world over, in collaboration with high-tech companies, pour in billions of dollars for the advancement of computing solutions quantum-based and for the development of fully functioning quantum computers that may one day aid in or even replace classical computers. Despite much hype and publicity, most people do not understand what quantum computing is, nor do they comprehend the significance of the developments required in this field, and the impact it may have on the future. Through this lecture notes, we embark on a pedagogic journey of understanding quantum computing, gradually revealing the concepts that form its basis, later diving in a vast pool of future possibilities that lie ahead, concluding with understanding and acknowledging some major hindrance and speed breaking bumpers in their path.

Perturbative solution to Schr¨odinger equation for N charged particles is studied. We use an expansion that is equivalent to Fock’s one. In the case that the zeroth-order approximation is a harmonic homogeneous polynomial a first-order approximation is found.

Neutrons are the particles that move on circular orbits inside the nuclei (with the remaining half of their kinetic energy) around immobilized protons which have spin only. If protons were rotating they would cause orbital magnetism, which has never been observed, beyond magnetic dipole moment of nucleons spin. In addition, no regression of proton has occurred, because it would cause alternating magnetism, which has also never been observed. The first nuclear units are the deuterium, the tritium, the helium-3 and the helium-4, which is the basic structure unit of the large nuclei. The spin, the magnetic moment and the mass deficit of the above units and of the bonding neutrons are the three experimental constants upon which the nuclei structure is based.

We employ the maximum entropy principle, in the context of statistical inference by impersonal physical interactions, together with the experimental position-momentum uncertainty phenomenon to construct the general wave mechanical static state of a single, interacting mass particle with no internal degrees of freedom. Subsequently, this first principle approach allows to derive via Newtonian mechanics the dynamical equation of motion in the realm of non-relativistic wave mechanics, i.e., the Schrödinger equation.

Electric charges may have mass in part or in full because they are charged. The explanation here avoids charge distribution models by associating the charge's mass with intrinsic quantum mechanical quantities, similar to the way spin angular momentum dispenses with mechanical models. Inhomogeneous Lorentz, i.e. `Poincare, dual fermion, 8-spinor fields are needed. Poincare fields have a probability current that acts as an intrinsic vector potential. The potential obeys a Maxwell-like equation which identifies the charged source. Intrinsic gauge freedom allows the chosen intrinsic gauge to provide the charged source with mass, which is, therefore, `electromagnetic mass'. One of the two fermions obeys the Dirac equation for a massless, chargeless particle while the other is charged and massive. These conventional equations describe neutrinos and electrons and similar lepton pairs with well-known accuracy.

In the paper zero-point energy density of free photons is estimated for an empty space surrounded by — and observed by — a bath of thermal background photons. Interpreting the results, the outline of the cosmological arrow of time is suggested.

In this paper, we will point out an important inconsistency in modern physics. When relativistic momentum and relativistic energy are combined with key concepts around Planck momentum and Planck energy, we find an inconsistency that has not been shown before. The inconsistency seems to be rooted in the fact that momentum, as defined today, is linked to the de Broglie wavelength. By rewriting the momentum equation in the form of the Compton wavelength instead, we get a consistent theory. This has a series of implications for physics and cosmology.

If a clear no-go for Einsteinian hidden parameters is real, it must be in no way possible to violate the CHSH with local hidden variable computer simulation. In the paper we show that with the use of a modified Glauber-Sudarshan method it is possible to violate the CHSH. The criterion value comes close to the quantum value and is $> 2$. The proof is presented with the use of an R computer program. The important snippets of the code are discussed and the complete code is presented in an appendix.

This paper presents a theoretical estimate for the vacuum energy density which turns out to be near zero and thus much more palatable than an infinite or a very large theoretical value obtained by imposing an ultraviolet frequency cut-off. This result helps address the "vacuum catastrophe" and the "cosmological constant problem".

Quantum mechanics has the quantization. The quantization offer us a method from the mechanic equation to build the quantum wave equation. For example the Canonical quantization offers a method to build the Schrödinger equation from Hamilton in classical mechanics. This is also referred as first quantization. In general, Maxwell equation itself is wave equation, hence, it doesn't need the first quantization. There is second quantization, for electromagnetic field. The second quantization discuss how many photons can be created when the energy of electromagnetic field is known. This is not interesting to this author. This author is interested how to build a particle from the wave equations (Maxwell equations or Schrödinger equation). Here the particle should confined in space locally. It should has the properties of wave. Our traditional quantization is to find the wave equation. This author try to build a particle from this wave equation, this process can be called as particleization. This author has introduced the mutual energy principle, the mutual energy principle successfully solved the problem of conflict between the Maxwell equations and the law of the energy conservation. The mutual energy flow theorem is derived from the mutual energy principle. The mutual energy flow is consist of the retarded wave and the advanced wave. The mutual energy flow theorem tell us the total energy of the energy flow passes through any surfaces between the emitter to the absorber are all exactly same. This property is required by the photon and any particle in quantum mechanics. Hence, this author has linked the mutual energy flow to the photon and also other particle. The mutual energy flow has the property of waves and also confined in space locally. However there is still a problem, the field of an emitter or the field of an absorber decreases according to the distance from the field point to the source point. If the current (or charge) of a source or sink for a photon is constant. The energy of the photon which equals the inner product of the current and the field will depended on the distance between the the source and the sink of the photon. If the distance increases, the amount of photon energy will decrease to infinite small. This is not correct. The energy of a photon should be a constant E=hv. The energy of the photon cannot decrease with the distance between the emitter and the absorber. In order overcome this difficulty, this author suggests a normalization for the mutual energy flow. It is assume that the retarded wave sent from the emitter has collapse back in all direction. But the mutual energy flow build a energy channel between the source and sink. Since the energy can only go through this channel, the total energy of one photon must go through this channel. Hence, the total energy of the mutual energy flow has to be normalized to the energy of one photon. The mutual energy flow will increase to the energy of one photon. This leads that the amplitude of the wave does not decrease on the direction along the energy channel. The amplitude of the advanced wave also does not decrease on the direction of the energy channel. The electromagnetic wave in the space between an emitter (source) and an absorber (sink) looks like a wave inside a wave guide. The wave in a wave guide, the amplitude does not decrease alone the wave guide if the loss of energy can be omitted. This wave guide can be referred as the “nature wave guide”. In the nature wave guide the advanced wave leads the the retarded wave, hence, the retarded wave can only goes at the direction where has advanced wave. The retarded wave also leads the advanced wave. The advanced wave can only goes in the direction of the retarded wave. This normalization process successfully particularized the the mutual energy flow. This author believe this theory about the normalization/particleization of the mutual energy flow is also correct for other particle for example electron.

We report several witness-parameterized families of bound-entangled probabilities. Two pertain to the $d=3$ (two-qutrit) and a third to the $d=4$ (two-ququart) subsets analyzed by Hiesmayr and L{\"o}ffler of ``magic" simplices of Bell states that were introduced by Baumgartner, Hiesmayr and Narnhofer. The Hilbert-Schmidt probabilities of positive-partial-transpose (PPT) states--within which we search for bound-entangled states--are $\frac{8 \pi }{27 \sqrt{3}} \approx 0.537422$ ($d=3$) and $\frac{1}{2}+\frac{\log \left(2-\sqrt{3}\right)}{8 \sqrt{3}} \approx 0.404957$ ($d=4$). We obtain bound-entangled probabilities of $-\frac{4}{9}+\frac{4 \pi }{27 \sqrt{3}}+\frac{\log (3)}{6} \approx 0.00736862$ and $\frac{-204+7 \log (7)+168 \sqrt{3} \cos ^{-1}\left(\frac{11}{14}\right)}{1134} \approx 0.00325613$ ($d=3$) and $\frac{8 \log (2)}{27}-\frac{59}{288} \approx 0.00051583$ and $\frac{24 \text{csch}^{-1}\left(\frac{8}{\sqrt{17}}\right)}{17 \sqrt{17}}-\frac{91}{544} \approx 0.00218722$ ($d=4$). (For $d=3$, we also obtain $\frac{2}{81} \left(4 \sqrt{3} \pi -21\right) \approx 0.0189035$ based on the realignment criterion.) The families, encompassing these results, are parameterized using generalized Choi and Jafarizadeh-Behzadi-Akbari witnesses. In the $d=3$, analyses, we utilized the mutually unbiased bases (MUB) test of Hiesmayr and L{\"o}ffler, and also the Choi $W^{(+)}$ test. The same bound-entangled probability was achieved with both--the sets (``jagged islands") detected having void intersection. The entanglement (bound and ``non-bound"/``free") probability for each was $\frac{1}{6} \approx 0.16667$, while their union and intersection gave $\frac{2}{9} \approx 0.22222$ and $\frac{1}{9} \approx 0.11111$. Further, we examine generalized Horodecki states, as well as estimating PPT-probabilities of approximately 0.39339 (very well-fitted by $\frac{7 \pi}{25 \sqrt{5}} \approx 0.39338962$) and 0.115732 (conjecturally, $\frac{1}{8}+\frac{\log \left(3-\sqrt{5}\right)}{13 \sqrt{5}} \approx 0.115737$) for the original (8- [two-qutrit] and 15 [two-ququart]-dimensional) magic simplices themselves.

One of Einstein’s most famous quotes is; ‘I am at all events convinced that God does not play dice’. This study attempted to be a conversion of “uncertainty principle” to a “certainty principle.” With the previous electron model, bare electrons moved discretely, and the photons surrounding them moved continuously. In this study, we shall notice the traveling of free electrons with thermal conductance, and how to determine the unique discrete traveling point by using thermal potential energy gradient.

Schrodinger's cat and Wigner's friend paradoxes are analyzed using the `wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' and are shown to be non-paradoxes within the quantum formalism. Then, the extended version of Wigner's friend thought experiment, proposed in a recent article titled, ``Quantum theory cannot consistently describe the use of itself '', Nature Communications {\bf 9}, 3711 (2018), by Frauchiger and Renner (FR) is considered. In quantum mechanics, it's well-known that, statistically observing a large number of identical quantum systems at some particular quantum state, which results in Born's probability, and merely inferring its presence in the same quantum state with the same probability yield distinct physical phenomena. If this fact is not taken care while interpreting any experimental outcomes, then FR type paradoxes pop up. ``What an astonishingly self-consistent the Quantum Theory is!' - is explicitly worked out in the case of FR gedankenexperiment. The present work shows the importance of single-quantum phenomenon for the non-paradoxical interpretation of statistically observed experimental outcomes.

Bell's inequality is widely regarded as a profound proof that nature is nonlocal, not Einstein-local. Against this, and supporting Einstein, we refute Bell's inequality and correct his error. We thus advance the principle of true-local-realism (TLR); the union of true-locality (no beables move superluminally, after Einstein) and true-realism (some beables change interactively, after Bohr). Importantly, for STEM teachers: we believe our commonsense results require no knowledge of quantum mechanics. Let us see.

The main ideas of the wave-particle non-dualistic interpretation of quantum mechanics are elucidated using two well-known examples, viz., (i) a spin-1/2 system in the Stern-Gerlach experiment and (ii) Young's double-slit experiment, representing the cases of observables with discrete and continuous eigenvalues, respectively. It's proved that only Born's rule can arise from quantum formalism as a limiting case of the relative frequency of detection. Finally, non-duality is used to unambiguously explain Hanbury Brown-Twiss effect, at the level of individual quanta, for the two-particle coincidence detection.

The solutions of Maxwell equations includes the restarted and the advanced waves. There are a few famous scientists supported the concept of advanced wave. Wheeler and Feynman have introduced the absorber theory in1945 which told us the absorbers can send the advanced wave. The absorber theory is based on the action-at-a-distance of Schwarzschild, Tetrode and Fokker, which told us the electric current sends a half retarded wave and a half advanced wave. John Cramer has introduced transactional interpretation in quantum mechanics, which said the retarded wave and the advanced wave have a handshake. What is the advanced wave in electromagnetic field theory? In 1960, Welch introduced the reciprocity theorem in arbitrary time domain which involved the advanced wave. In 1963 V.H. Rumsey mentioned a method to transform the Lorentz reciprocity theorem to a new formula. In early of 1987 Shuang-ren Zhao (this author) introduced the mutual energy theorem in frequency domain. In the end of 1987 de Hoop introduced the time-domain cross-correlation reciprocity theorem. All these theories can be seen a same theorem in different domain: Fourier domain or in time domain. This theorem can be applied to prove the directivity diagram of a receiving antenna are equal to the directivity diagram when the receiving antenna are used as a transmitting antenna. According to this theory, the receiving antenna sends the advanced wave. As a reciprocity theorem the two fields in it do not need to be real for all. Hence, for the reciprocity theorem of Welch, Rumsey and Hoop do not need to claim that the advanced wave is a physical wave. However, when Shuang-ren Zhao said it is a energy theorem that means the two waves the retarded wave and the advanced wave in the theorem must be all real physical waves. After the mutual energy theorems has been published 30 years, Shuang-ren Zhao re-enter this field. First, the mutual energy flow theorem is derived. The mutual energy flow produced by the superposition of the retarded wave and the advanced wave. The mutual energy flow can carry the energy from the transmitting antenna to the receiving antenna. Our textbook of electromagnetic field tell us the energy is carried by the energy flow of the Poynting vector which is the self-energy flow. Hence, there is a question that the energy of electromagnetic field is transferred by the mutual energy or self-energy or by both? This author found that only the former can offer a self-consistency theory. This author also proved that the energy is transferred by the self-energy or both all conflict with the energy conservation law and hence cannot be accept. If the energy is transferred by the mutual energy, the axioms of the electromagnetic field needs to be modified. Hence, the mutual energy principle is introduced to replace the Maxwell equations as axioms. The mutual energy principle can be derived from the Maxwell equations. The Maxwell equations can also be derived from the mutual energy principle. However, the mutual energy principle does not equivalent to the Maxwell's equations. Starting from the mutual energy principle, the solution needs to be two groups of Maxwell equations existing together. One group of the Maxwell equation is corresponding to the retarded wave, another is corresponding to the advanced wave. The two waves must be synchronized to produce the mutual energy flow. The conflict of Maxwell equations with the energy conservation law further suggest that there exist a time-reversal wave and self-energy principle. Self energy principle tells us that self-energy flow or the energy flow corresponding to Poynting vector does not carry or transfer the energy, because there exist 2 time-reversal waves corresponding to the retarded wave and the advanced wave. The energy flow of the time-reversal waves cancels the energy flows of the self-energy flows of the retarded wave and the advanced wave. This also tell us there are 4 waves for electromagnetic fields, the retarded wave, the advanced wave, the 2 time-reversal waves corresponding to the retarded wave and the advanced wave. The self-energy flow of these 4 waves are all canceled. However the mutual energy flow of the retarded wave and the advanced wave does not disappear. The energy of electromagnetic field is transferred by the mutual energy flow. Photons can be explained by the mutual energy flows. There is also the time-reversal mutual energy flow which can wipe out the half-photon or partial photon. Anti-particle can also be explained by the time-reversal mutual energy flow. This theory has been widen to the quantum mechanics. That means all particles for example electron is also consist of 4 waves and 6 energy flows. There is the mutual energy principle and self-energy principle corresponding to the Schrödinger equation. In this article 3 modes of radiation are introduced which are photon, anti-photon, ant unsuccessful radiation. Photon is consist of one mutual energy flow, self-energy flow for the retarded wave and advanced wave, self-energy flow of the time-reversal waves. All self-energy flows are canceled. Hence only the mutual energy flow survive. Anti-photon is consist of the time-reversal mutual energy flow; Time-reversal self-energy flow and self-energy flows. All the self-energy flow canceled. Only the time-reversal mutual energy survived. The last mode is the unsuccessful radiation. The retarded wave is sent out but it did not meat any advanced wave to handshake/synchronized. Hence, the energy is returned, the radiation is unsuccessful. Photon is transfer the radiation energy. Anti-photon is responsible to eliminate the half-photon or partial photon. The unsuccessful radiation is the necessary result that the source and sink both send the waves, one is the retarded wave and the other is the advanced wave.

Absorber theory published in 1945 and 1949 by Wheeler and Feynman. In the electromagnetic field theory, W. J. Welch introduced the reciprocity theorem in 1960. V.H. Rumsey mentioned a method to transform the Lorentz reciprocity theorem to a new formula in 1963. In early of 1987 Shuang-ren Zhao (this author) introduced the mutual energy theorem in frequency domain. In the end of 1987. Adrianus T. de Hoop introduced the time-domain cross-correlation reciprocity theorem. All these theories can be seen as a same theorem in different domain: Fourier domain or in time domain. After 30 years silence on this topic, finally, this author has introduced the mutual energy principle and self-energy principle which updated the Maxwell's electromagnetic field theory and Schrödinger's quantum mechanics. According to the theory of mutual energy principle, the energy of all particles are transferred through the mutual energy flows. The mutual energy flow are inner product of the retarded wave and the advanced wave. The mutual energy flow satisfies the mutual energy flow theorem. The retarded wave is the action the emitter gives to the absorber. The advanced wave is the reaction the absorber gives to the emitter. In this article this author will derive the Huygens principle from the mutual energy flow theorem. The bra, ket and the unit operator of the quantum mechanics will be applied to the inner space defined on 2D surface instead of the 3D volume.

This author has replaced the Maxwell equations with the corresponding mutual energy principle, self-energy principle as the axioms in electromagnetic field theory. The advantage of doing this is that it can overcome the difficulty of the Maxwell equations, which conflicts to the energy conservation law. The same conflict also exists in the Schrödinger equation in the quantum mechanics. This author would like to intruded the mutual energy principle to quantum mechanics, but has met the difficulty that there is no advanced solution for the Schrödinger equation. This difficulty is overcome by introducing a negative radius. After this, all the theory about the mutual energy can be extend from the field satisfying Maxwell equations to the field satisfying Schrödinger equation. The Schrödinger equation can also be derived from the corresponding mutual energy principle. However, this doesn't mean both sides are equivalent. The mutual energy principle cannot derive a single solution of Schrödinger equation. The mutual energy principle can only derive a pair solutions of the Schrödinger equations. One is for retarded waves and another is for advanced waves. The retarded wave and the advanced wave must be synchronized. The solutions of the mutual energy principle is in accordance with the theory of the action-at-a-distance and the absorber theory. A action is done always between two objects, for example a source (emitter) and a sink (absorber). The mutual energy principle tell us that a particle is an action and a reaction between the source and the sink. In other hand the wave satisfying Schrödinger equation only need one source or one sink. From the mutual energy principle, it is easy to derive the mutual energy theorem, the mutual energy flow theorem, corresponding Huygens–Fresnel principle. All these will solve the wave-particle duality paradox.

This paper proposes mass interaction principle (MIP) as: the particles will be subjected to the random frictionless quantum Brownian motion by the collision of space time particle (STP) ubiquitous in spacetime. The change in the amount of action of the particles during each collision is an integer multiple of the Planck constant $h$. The motion of particles under the action of STP is a quantum Markov process. Under this principle, we infer that the statistical inertial mass of a particle is a statistical property that characterizes the difficulty of particle diffusion in spacetime. Within the framework of MIP, all the essences of quantum mechanics are derived, which proves that MIP is the origin of quantum mechanics. Due to the random collisions between STP and the matter particles, matter particles are able to behave exactly as required by the supervisor and shepherd for all microscopic behaviors of matter particles. More importantly, we solve a world class puzzle about the anomalous magnetic moment of muon in the latest experiment, and give a self-consistent explanation to the lifetime discrepance of muon between standard model prediction and experiments at the same time.

In their celebrated paper titled "Can quantum mechanical description of physical reality be considered complete?", Einstein, Podolsky and Rosen (EPR) showed for the first time the existence of `Spooky action-at-a-distance'. Though the result of their paper is unquestionable, but the conclusion of the same became sensational because of its challenge to quantum mechanical formalism whether it's complete or not in describing the physical reality of Nature. Bohr's physical and philosophical reply to that conclusion justified the completeness of quantum mechanics. Here, a simple algebraic way is presented for the results of these two classic papers in such a way that the actual reason behind why quantum world necessarily exhibits the action-at-a-distance and how Bohr defended against the incompleteness of the quantum formalism will become clear.This approach naturally reveals what physical assumption of EPR went wrong while considering the entangled quantum system and also provides the missing mathematical argument in Bohr's reply.

An Urdu translation of the landmark article by Einstein, Podolsky and Rosen from the year 1935 is presented with the hope that it will be of academic and research interest to the readers in that language.

In this paper it is demonstrated that a hidden spin component may exist that in local hidden variables, but quantum manner, invalidates the nonlocality analysis with e.g. inequalities such as CHSH.

Using a newly proposed `wave-particle non-dualistic interpretation' of the quantum formalism, Bohr's principle of complementarity is analyzed in the context of the single-slit diffraction and the Afshar's experiments - at the single-quantum level. The fundamental flaw in the Afshar's argument is explicitly pointed out.

The delayed-choice entanglement swapping experiments, both in space and time, are casually explained at a single quantum level by using the `wave-particle non-dualistic interpretation of quantum mechanics'. In order to achieve this, the actual mechanisms involved in the Wheeler's delayed-choice experiment and Einstein's spooky-action-at-a-distance are uncovered from the quantum formalism. The continuity in the motion of any individual quantum particle, due to the constants of motion, is responsible for the outcomes of Wheeler's delayed-choice experiment. The purpose for the existence of spooky action in Nature is to strictly maintain the conservation laws in absence of exchange-interactions. The presence of a casual structure in the entanglement swapping is shown by detailed analysis of the experimental results presented in the papers, ``X-S. Ma et al., Nature. Phys. 8, 480, (2012)'' and ``E. Megidish et al., Phys. Rev. Lett. 110, 210403 (2013)'', at the level of individual quantum events. These experiments are directly confirming the wave-particle non-duality.

The Schroedinger equation with the logarithmic nonlinear term is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the infinite mass limit of the wave function. The article is the modified version of the articles by author (Pardy, 1993; 2001).

Conventionally, the wave of particles which through the double-slit is assumed plane waves. In this research, we considered that the interference fringes built up through the double-slit have a difference amplitudes between the case of electrons and the case of photons. The difference between the two fringes is in the troughs of the waves. In this research, it is hypothesized that the amplitudes of waves passing through the left and right slits are not even in the double-slit experiment of electrons. Computer simulations performed to obtain the results supporting this hypothesis. The concept that waves of different amplitudes pass through a double-slit is reasonably to have the notion that two spinor particles pass through each slit.

The commutator of the Dirac free-particle's velocity operator with its Hamiltonian operator is nonzero and independent of Planck's constant, which starkly violates the quantum correspondence-principle requirement that commutators of observables must vanish when Planck's constant vanishes, as well as violating the extended Newton's First Law principle that relativistic free particles do not accelerate. The consequent nonphysical particle "zitterbewegung" is of course absent altogether when the natural relativistic free-particle square-root Hamiltonian operator, which is the transparent consequence of the free particle's Lorentz-covariant energy-momentum, replaces the free-particle Dirac Hamiltonian. The energy spectrum of the pathology-free relativistic square-root free-particle Hamiltonian is, however, matched perfectly by the positive-energy sector of the Dirac free-particle Hamiltonian's energy spectrum. But when a hydrogen type of potential energy is added to the free particle Dirac Hamiltonian, Foldy-Wouthuysen unitary transformation of the result reveals a "Darwin term" in its positive-energy sector which stems from nonphysical "zitterbewegung"-smearing of that potential energy. This physically nonexistent smearing of the potential energy can alternatively be viewed as having been produced by physically nonexistent smearing of its proton charge density source, which using the Dirac theory for data analysis erroneously compensates, resulting in a misleadingly contracted impression of the proton's charge radius.

A simple model known as the V4 wave function is studied for a simple (non-equivalent) wave function, which describes the in-medium oscillations of the space-time. The new model is employed for the detailed study of the spectral properties of the V4 wave function, and one of the upcoming projects is to use it to study the spectral properties of the strongly interacting quark-gluon interaction.

The Feynman integral is generalised so as to involve the random fluctuations of vacuum, from this integral the generalized Schroedinger equation is derived and the energy spectrum for the Coulomb potential determined.

A stochastic model is presented for the Planck-scale nature of space-time. From it, many features of quantum mechanics and relativity are derived. As mathematical points have no extent, the stochastic manifold cannot be tessellated with points and so a granular model is required. A constant grain size is not Lorentz invariant but, since volume is a Lorentz invariant, we posit grains with constant volumes. We treat both space and time stochastically and thus require a new interpretation of time to prevent an object being in multiple places at the same time. As the grains do have a definite volume, a mechanism is required to create and annihilate grains (without leaving gaps in space-time) as the universe, or parts thereof, expands or contracts. Making the time coordinate complex provides a mechanism. As this is a 'root' model, it attempts to explicate phenomena usually taken for granted, such as gravity and the nature of time. Both the General Relativity field equations (the master equations of Relativity) and the Schrödinger equation (the master equation of quantum mechanics) are produced.

From the existence of a line element field $(A^{\beta},-A^{\beta}) $ on a four-dimensional time oriented Lorentzian manifold with metric, the Klein-Gordon equation in curved spacetime, $ \nabla_{\mu}\nabla^{\mu}\Psi=k^{2}\Psi $, can be constructed from one of the pair of regular vectors in the line element field, its covariant derivative and associated spinor-tensor; and scalar product for spins 1,1/2 and 0, respectively. The left side of the asymmetric wave equation can then be symmetrized. The symmetric part, $ \tilde{\varPsi}_{\alpha\beta}$, is the Lie derivative of the metric, which links the Klein-Gordon equation to modified general relativity for spins 1,1/2 and 0. Modified general relativity is intrinsically hidden in the Klein-Gordon equation for spins 2 and 3/2. Massless gravitons do not exist as force mediators of gravity in a four-dimensional time oriented Lorentzian spacetime. The diffeomorphism group Diff(M) is not restricted to the Lorentz group. $ \tilde{\varPsi}_{\alpha\beta}$ can instantaneously transmit information to, and quantum properties from, its antisymmetric partner $ K_{\alpha\beta} $ along $ A^{\beta} $. This establishes the concept of entanglement.

According to the Cosmic Microwave Background (CMB) temperature and Wien's displacement law, the CMB's energy value is equivalent to that of the measured and determined neutrino energy. The resulting CMB/neutrino mass is used to determine a ratio by correlating the accelerative work of two forces which corresponds to the cosmic particle horizon and Planck length. Planck's constant is shown to be proportional to the cosmic particle horizon and the CMB mass/energy and the speed of light in vacuum. Planck's constant, the cosmic horizon, the CMB energy and speed of light all appear to be interconnected and their correlations provide an amending perspective on the concepts of the fundamental laws and theories of the cosmos. Specifically, the squared energy of a CMB/neutrino is equal to the product of the energy of the maximum cosmic Rindler horizon, cosmic diameter, and the Schwarzschild radius for a Planck mass.

The commutator of the Dirac free-particle's velocity operator with its Hamiltonian operator is nonzero and independent of Planck's constant, which violates the quantum correspondence-principle requirement that commutators of observables must vanish when Planck's constant vanishes, as well as violating the absence of spontaneous acceleration of relativistic free particles. The consequent physically pathological "zitterbewegung" is of course completely absent when the natural relativistic square-root free-particle Hamiltonian operator is used; nevertheless the energy spectrum of that pathology-free natural relativistic square-root free-particle Hamiltonian is exactly matched by the positive-energy sector of the Dirac free-particle Hamiltonian's energy spectrum. Contrariwise, however, Foldy-Wouthuysen unitary transformation of the positive-energy sector of any hydrogen-type Dirac 4 x 4 Hamiltonian to 2 x 2 form reveals a "zitterbewegung"-induced "Darwin-term" smearing of the proton charge density which is completely absent in the straightforward relativistic extension of the corresponding hydrogen-type nonrelativistic Pauli 2 x 2 Hamiltonian. Compensating for an atomic proton's physically absent "electron zitterbewegung"-induced charge smearing would result in a misleadingly contracted impression of its charge radius.

In this study, we will describe how one electron could consist of a two-state spin system on the basis of a previous study, wherein we obtained a model in which two spinor particles could exist in one electron. The previously reported electronic model used equations to show the energy conservation law of an electron system, which included two spinors. Herein, we will consider these two oscillators as two bases and will start the discussion from the viewpoint that one electron can be considered two-bitwise. For this purpose, we apply the two-bitwise system with a Riemann surface via an analytic continuation. This trial could explain the mixed state of up and down spin states. Furthermore, the two states in which the electron can be of either state can be selected as the disconnection of the analytic continuation of the complex analysis. To consider the magnetic gradient field which would have a force to disconnect the analytic continuation to separate the two domains, it is possible to explain how the spin is fixed in the abovementioned states.

This article is a concise statement of the machinery of quantum indeterminacy — in response to the question: What is indeterminacy; is it something that can be written down?<br>br>Keywords<br>foundations of quantum theory, quantum randomness, quantum indeterminacy, logical independence, self-reference, logical circularity, mathematical undecidability, Kurt Gödel.

In the paper it is demonstrated that integration of products of sign functions and probability density functions such as in Bell’s formula for ±1 measurement functions, leads to inconsistencies. Keywords Inconsistency, Bell’s theorem.

The following paper derives the fine-structure constant. This derivation suggests that the fine-structure constant can be theoretically determined as the spectrum range of all the energy modes fitting inside the observable universe. This corresponds to the number of allowed radiation modes of a particle from the cosmic horizon down to Planck length. Additionally, an association between Newton's Law of Gravity and Coulomb's Law suggests there is a connection between mass and charge via the fine-structure constant.

With Bell's inequality refuted and his error identified [see References], we now explain Aspect's experiment and refute Bell's theorem via what we call Einstein-classicality: the union of true locality (no influence propagates superluminally) and true realism (some beables change interactively). We also remedy many of Aspect's pro-Bell comments; eg, inability to picture in 3-space, hopeless searching, vindicated nonlocality.

Physicists usually understand that physics cannot (and should not) derive that $c\approx 3\cdot 10^8m/s$ and $\hbar \approx 1.054\cdot 10^{-34}kg\cdot m^2/s$. At the same time they usually believe that physics should derive the value of the cosmological constant $\Lambda$ and that the solution of the dark energy problem depends on this value. However, background space in General Relativity (GR) is only a classical notion while on quantum level symmetry is defined by a Lie algebra of basic operators. We prove that the theory based on Poincare Lie algebra is a special degenerate case of the theories based on de Sitter (dS) or anti-de Sitter (AdS) Lie algebras in the formal limit $R\to\infty$ where R is the parameter of contraction from the latter algebras to the former one, and $R$ has nothing to do with the radius of background space. As a consequence, $R$ is necessarily finite, is fundamental to the same extent as $c$ and $\hbar$, and a question why $R$ is as is does not arise. Following our previous publications, we consider a system of two free bodies in dS quantum mechanics and show that in semiclassical approximation the cosmological dS acceleration is necessarily nonzero and is the same as in GR if the radius of dS space equals $R$ and $\Lambda=3/R^2$. This result follows from basic principles of quantum theory. It has nothing to do with existence or nonexistence of dark energy and therefore for explaining cosmological acceleration dark energy is not needed. The result is obtained without using the notion of dS background space (in particular, its metric and connection) but simply as a consequence of quantum mechanics based on the dS Lie algebra. Therefore, $\Lambda$ has a physical meaning only on classical level and the cosmological constant problem and the dark energy problem do not arise. In the case of dS and AdS symmetries all physical quantities are dimensionless and no system of units is needed. In particular, the quantities $(c,\hbar,s)$, which are the basic quantities in the modern system of units, are not so fundamental as in relativistic quantum theory. "Continuous time" is a part of classical notion of space-time continuum and makes no sense beyond this notion. In particular, description of the inflationary stage of the Universe by times $(10^{-36}s,10^{-32}s)$ has no physical meaning.

Given the inverse of the Golden Mean $ \tau^{ -1} = \phi = { 1\over 2} (\sqrt 5 - 1)$, it is known that the continuous fraction expansion of $ \phi^{ -1} = 1 + \phi = \tau$ is $ ( 1, 1, 1, \cdots )$. Integer solutions for the pairs of numbers $ ( d_i, n_i ), i = 1, 2, 3, \cdots $ are found obeying the equation $ ( 1 + \phi)^n = d + \phi^n$. The latter equation was inspired from El Naschie's formulation of fractal Cantorian space time $ {\cal E}_\infty$, and such that it furnishes the continuous fraction expansion of $ ( 1 + \phi )^n ~= ~ (d, d, d, d, \cdots )$, generalizing the original expression for the Golden mean. Hardy showed that is possible to demonstrate nonlocality without using Bell inequalities for two particles prepared in $nonmaximally$ entangled states. The maximal probability of obtaining his nonlocality proof was found to be precisely $\phi^5$. Zheng showed that three-particle nonmaximally entangled states revealed quantum nonlocality without using inequalities, and the maximal probability of obtaining the nonlocality proof was found to be $ 0.25 \sim \phi^3 = 0.236$. Given that the two-parameter $ p, q$ quantum-calculus deformations of the integers $ [ n ]_{ p, q} = F_n $ $coincide$ precisely with the Fibonacci numbers, as a result of Binet's formula when $ p = ( 1 + \phi) = \tau, q = - \phi = - \tau^{ -1} $, we explore further the implications of these results in the quantum entanglement of two-particle spin-$s$ states. We finalize with some remarks on the generalized Binet's formula corresponding to generalized Fibonacci sequences.

Dirac sought a relativistic quantum free-particle Hamiltonian that imposes space-time symmetry on the Schroedinger equation in configuration representation; he ignored the Lorentz covariance of energy-momentum. Dirac free-particle velocity therefore is momentum-independent, breaching relativity basics. Dirac also made solutions of his equation satisfy the Klein-Gordon equation via requirements imposed on its operators. Dirac particle speed is thereby fixed to the unphysical value of c times the square root of three, and anticommutation requirements prevent four observables, including the components of velocity, from commuting when Planck's constant vanishes, a correspondence-principle breach responsible for Dirac free-particle spontaneous acceleration (zitterbewegung) that diverges in the classical limit. Nonrelativistic Pauli theory contrariwise is physically sensible, and its particle rest-frame action can be extended to become Lorentz invariant. The consequent Lagrangian yields the corresponding closed-form relativistic Hamiltonian when magnetic field is absent, otherwise a successive-approximation regime applies.

The Feynman diagrams of Quantum Electrodynamics are assembled from vertices where three edges meet: an incoming fermion, an outgoing fermion and an interaction line. If all vertices are of degree 3, the graphs are 3-regular (cubic), defining the vacuum polarization diagrams. Cutting an edge -- a fermion line or an interaction line -- generates fairly cubic graphs where two vertices have degree 1. These emerge in the perturbation theory for the Green's function (self energy) and for the effective interaction (polarization). The manuscript plots these graphs for up to 8 internal vertices.

A universe based on a fully deterministic, Euclidean, 4-torus cellular automaton is presented using a constructive approach. Each cell contains one integer number forming bubble-like patterns propagating at the speed of light, interacting and being reissued constantly. The collective behavior of these integers is conjectured to form patterns similar to classical and quantum physics, including the mass spectrum, quantum correlations and relativistic effects. Although essentially non-local, it preserves the non-signaling principle. This flexible model predicts that gravity is not quantized as well as the appearence of an arrow of time. Being a causal theory, it can potentially explain the emergence of the classical world and acroscopic observers.

Elementary instance-tracking identifies a contagious error in Bell (1964). To wit, and against his own advice: in failing to match instances, Bell voids his own conclusions. The contagion extends to Aspect, Griffiths, Levanto, Motl, Peres and each of CHSH.

This paper aims to present intuitive imagery of the angular momentum of electrons, which has not been attempted yet. As electrons move similarly to a slinky spring, we first discuss the motions of a slinky progressing down an uneven stairway. The spin angular momentum under a magnetic field gradient is analogous to a slinky traveling down the uneven stairway inclined perpendicular to the advancing direction (i.e., every step inclined a bit to the left or right side to the advancing direction). The study extends our previous work from a single virtual oscillating photon to a particle moving linearly in one direction. The entire mass energy of the electrons is assumed as thermal potential energy. Particles (spinors) possessing this energy emit all their energy by radiation, which is then absorbed by a paired spinor particle. This transfer of radiative energy is accomplished by a virtual photon enveloping the spinor particles. Although the spinor particle contains both the absorber and emitter depending on its phase, a spinor particle cannot exhibit both the functions simultaneously; therefore, the spinor particle moves similar to a slinky spring.

Bell’s inequality is widely regarded as a profound impediment to any intuitive understanding of physical reality. We disagree. So here, via elementary algebra - backed by experiments; and thus with certainty - we refute his famous inequality, correct his key error, resolve his locality-dilemma: all in accord with the antiBellian true-local-realism that we’ve advanced since 1989. We thus restore commonsense/intuitive ideas to physics - thereby making physical reality more intelligible - by completing the quantum mechanical account of EPR-Bohm correlations via a wholistic/Einsteinian approach in spacetime.

A new formula for the energy density of electrostatic field is derived. Based on the conservation of energy and momentum, the classical equations of motion of an electron, which is considered as a point particle, are then obtained by establishing a delay coordinate system. The resulting equations are exact but not covariant. Finally we calculate the self-energy of a free electron in quantum electrodynamics using a new cut-off procedure.

We present a novel formulation of particle physics that dispenses with space-time derivative operators in favour of null cone integrations. It is shown that the loss of locality incurred is compensated by gains in con- ceptual and mathematical simplicity, the absence of non-physical gauge degrees of freedom and the concomittant complications of ghosts etc.. Central to the formulation is a dimensionless homologue of the Lagrangian density, formed from integrals of scalar product terms over null cones. In- stead of covariant derivatives, the gauge fields are represented by rotations over the simple product of the internal and Lorentz symmetry groups. We demonstrate that application of a variational principle to this quasi-action functional yields essentially the same equations of motion as the SM. As a consequence of the enlarged symmetry group, the primordial electroweak Higgs field is shown to be the origin of all bosonic degrees of freedom, not just the Goldstone modes, prior to the symmetry breaking that reduces it to an isospin carrying scalar. Although this paper is restricted to considerations of leptons and the elec- troweak SU (2) L × U (1) Y symmetry group, the extension of the method to quarks and SU (3) C ⊂ SO(10) would appear to be straightforward and will be the subject of a subsequent paper.

A previous publication in Phys. Rev. D, (Part A of this paper) pointed out that vacuum energy fluctuations implied mass fluctuations which implied curvature fluctuations which then implied fluctuations of the metric tensor. The metric fluctuations were then taken as fundamental and a stochastic space-time was theorized. A number of results from quantum mechanics were derived. This paper (Part B), in addressing some of the difficulties of Part A, required an extension of the model: In so far as the fluctuations are not in space-time but of space-time, a granular model was deemed necessary. For Lorentz invariance, the grains have constant 4-volume. Further, as we wish to treat time and space similarly, we propose fluctuations in time. In order that a particle not appear at different points in space at the same time, we find it necessary to introduce a new model for time where time as we know it is emergent from an analogous coordinate, tau-time, τ, where ' τ -Time Leaves No Tracks' (that is to say, in the sub-quantum domain, there is no 'history'). The model provides a 'meaning' of curvature as well as a (loose) derivation of the Schwartzschild metric without need for the General Relativity field equations. The purpose is to fold the seemingly incomprehensible behaviors of quantum mechanics into the (one hopes) less incomprehensible properties of space-time.

Abstract Much of quantum mechanics may be derived if one adopts a very strong form of Mach's Principle, requiring that in the absence of mass, space-time becomes not flat but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can derive the uncertainty principle. Finally, the superposition of stochastic metrics and the identification of the square root of minus the determinant of the metric tensor as the indicator of relative probability yields the phenomenon of interference, as will be described for the two-slit experiment.

This is a continuation of Parts A and B which describe a stochastic, granular space-time model. In this, Part C, in order to tessellate the space-time manifold, it was necessary to introduce a fifth dimension which is 'rolled up' at the Planck scale. The dimension is associated with mass and energy (in a non-trivial way). Further, it addresses other problems in the granular space-time model.

In electromagnetic theory and quantum theory, there are superposition principle. Traditionally there are only one kind superposition principle. However, in this author's theory the retarded wave and advanced wave are all involved, the superposition become multiple. For example this author need to deal the problem how to superpose the retarded wave and the advanced wave. This author found that there are 5 different kinds of superpositions. The superposition principles have some differences. The research about these differences is a key to open the door of many physical difficulties. For example the particle and wave duality problem, and to judge which interpretation of the quantum mechanics is a correct one. The first two superposition principles are the superpositions with and without the test charges. The slight different superposition principles are the superposition with a retarded wave alone and the superposition with the advanced wave alone. According to theory of this author, the emitter sends the retarded wave, the absorber sends the advance wave. Hence, normal electromagnetic field actually is consist of retarded wave and advanced wave. This two waves together become the traditional electromagnetic fields. This kind of electromagnetic fields can be seen approximately as retarded wave only, this kind wave also has its own superposition. This kind of superposition is also different with the superposition when we consider the retarded waves alone and also the advanced waves alone. In this article this author will discuss the differences of these different superpositions. This author will also discuss the different physical result with a few different superposition principles. In this article this author will prove the superposition with test charge and the superposition with retarded waves alone or advance wave alone can be see one kind of superposition. This superposition is correct and can be derived from the mutual energy principle. This will be referred as first kind of superposition. The superposition without test charge and the superposition with the retarded waves and advanced waves can be seen as one kind of superposition. For this kind of superpositions are not correct naturally. This kind of super position are applied to N-charge's Poynting theorem. In order to make this superposition work, the self-energy principle have to be applied. Without self-energy principle this kind of superpositions will violate the energy conservation law. Considering the self-energy conservation this kind of superposition become the superposition of first kind. This is referred as second kind of superposition. The third kind of superposition is for the traditional electromagnetic field. Here the traditional electromagnetic field means the electromagnetic field where the advanced waves are omit. When the advanced waves are omit doesn't mean the advanced waves do not exist, that is only means the retarded wave and the advanced wave are with nearly same intensity and can be treated together in some situation, for example, in wave guide, or in the free space where the absorber are uniformly distributed at infinite big sphere. Abstract Only when the self-energy principle is accept, all kinds of superposition can be accept. However different superposition has different physical meanings. Otherwise only the superposition with test charge or the superposition with only one kind wave either retarded waves or advanced waves can be accepted. Hence, the discussion about the superposition also support the concept of the self-energy principle which means there must exist the time reversal waves. That also means the waves do not collapse but collapse back. Wave collapse means collapse to its target, for example, the retarded wave will collapse to an absorber and the advanced wave will collapse to an emitter. Wave collapse back means the retarded wave sent from emitter will collapse back to an emitter; The advanced wave sent from the absorber will collapse back to an absorber. Hence, one purpose of this article is to clarify the superposition principles, and another purpose is to support this author's electromagnetic field theory which is started from two new axioms the self-energy principle and the mutual energy principle.

We derive the index of refraction of light from quantum theory of atoms and from the Dirac equation with the plane wave. The result is the integral a part of the mainstream of the quantum optics. The article involves also discussion on the possibility to create the electron-positron pairs during the Cherenkov process with the adequate intex of refraction.

This paper modifies two significant points of existing quantum electrodynamics. First, the image of a virtual photon is replaced with a real one, i.e., till date, we consider virtual photon as being capable of exchanging its energy between two particles along with self interaction, and that it is a transient fluctuation. We shall change this definition such that what we call “an electron” would include two bare electrons and these two would interact within a real photon. The virtual photon in this study is the same as the real photon which is not to observe, but difference from traditional virtual photon because the re-imaged virtual photon would exist continuously not temporally. Second, it is assumed that the bare electron is a perfect black body. To meet the constraints of charge conservation, a virtual photon must include two bare electrons. There is a temperature gradient between the two because the two particles alternate between behaving as emitters and absorbers. The proposed study extends this model by considering that an electron comprises two blinking bare electrons and at least one real photon by exchanging the energies within the three. Consequently, we attempt to create an electron model that exhibits spinor behavior by setting and modifying a trigonometric function which could periodically achieve the value of zero-point energy.

In the paper it is demonstrated that integration of products of sign functions and probability density functions such as in Bell's formula for +/-1 measurement functions, leads to inconsistencies.

With the use of tropical algebra operators and a d=2 parameter vectors space, Bell's theorem does not forbid a, physics vvalid, reproduction of the quantum correlation.

According to the generally accepted physical theory, the synthesis of the elements may happen at a very high temperature in supernova explosions. In consequence of nuclear fusion, the supernova stars emit a very strong electromagnetic (EM) radiation, predominantly in form of X-rays and gamma rays. The intensive EM radiation drastically decreases the masses of the exploding stars, directly causing mass defects of the resulting atoms. The description of black body EM radiation is based on the famous Planck's radiation theory, which supposes the existence of independent quantum oscillators inside the black body. In this paper, it is supposed that in exploding supernova stars, the EM radiating oscillators can be identied with the nascent elements losing their specic yields of their own rest masses in consequence of the radiation process. The nal binding energy of the atoms (nuclei) is additionally determined by the strong neutrino radiation what also follows the Maxwell- Boltzmann distribution in the extremly high temperature. Extending Planck's radiation law for discrete radiation energies, a very simple formula is obtained for the theoretical determination of the atomic masses. In addition, the newly introduced theoretical model gives the fusion temperature what is necessary for the generation of the atoms of the Periodic Table. Keywords: nuclear binding energy, Planck radiation law, generation of atoms, the origin of the elements, new theoretical model of the nuclear synthesis, fusion temperature.

We discuss a specific way in which the conclusions of the Kochen-Specker theorem may be avoided while, at the same time, closing the gap in a practical but usually neglected matter regarding scientific methodology in general. Implications of the possibilities of hidden variables thus defined are discussed, and a tentative connexion with cosmology is delineated.

Based on the quantum modification of general relativity (Qmoger), gravitational angel (gravitangel) is introduced as a cloud of the background gravitons hovering over the ordinary matter (OM). According to Qmoger, the background gravitons are ultralight and they form the quantum condensate even for high temperature. The quantum entanglement of OM particles is explained in terms of splitting gravitangels. A hierarchy of gravitangels of different scale is considered. One of the simplest gravitangel is hovering over neutrino, which explains the neutrino oscillations. A more large-scale gravitangels are hovering over the neuron clusters in the brain, which explains the subjective experiences (qualia). The global gravitangel (GG) is connected to all processes happening with OM in the universe. GG can be considered as a gigantic quantum supercomputer.

This is a short note on a new way to describe Haug’s newly introduced maximum velocity for matter in relation to the Schwarzschild radius. This leads to a probabilistic Schwarzschild radius for elementary particles with mass smaller than the Planck mass. In addition, our maximum velocity, when linked to the Schwarzschild radius, seems to predict that particles just at that radius cannot move. This implies that radiation from the Schwarzschild radius not can undergo velocity time dilation. Our maximum velocity of matter, therefore, seems to predict no time dilation, even in high Z quasars, as has surprisingly been observed recently.

By taking spin away from particles and putting it in the metric, thus following Dirac's vision, I start my attempt to formulate an alternative math-phys language, biquaternion based and incorporating Clifford algebra. At the Pauli level of two by two matrix representation of biquaternion space, a dual base is applied, a space-time and a spin-norm base. The chosen space-time base comprises what Synge called the minquats and in the same spirit I call their spin-norm dual the pauliquats. Relativistic mechanics, electrodynamics and quantum mechanics are analyzed using this approach, with a generalized Poynting theorem as the most interesting result. Then moving onward to the Dirac level, the M{\"o}bius doubling of the minquat/pauliquat basis allows me to formulate a generalization of the Dirac current into a Dirac probability/field tensor with connected closed system condition. This closed system condition includes the Dirac current continuity equation as its time-like part. A generalized Klein Gordon equation that includes this Dirac current probability tensor is formulated and analyzed. The usual Dirac current based Lagrangians of relativistic quantum mechanics are generalized using this Dirac probability/field tensor. The Lorentz transformation properties the generalized equation and Lagrangian is analyzed.

I begin with a short historical analysis of the problem of the electron from Lorentz to Dirac. It is my opinion that this problem has been quasi frozen in time because it has always been formulated within the paradigm of the Minkowski-Laue consensus, the relativistic version of the Maxwell-Lorentz theory. By taking spin away from particles and putting it in the metric, thus following Dirac's vision, I start my attempt to formulate an alternative math-phys language. In the created non-commutative math-phys environment, biquaternion and Clifford algebra related, I formulate an alternative for the Minkowski-Laue consensus. This math-phys environment allows me to formulate a generalization of the Dirac current into a Dirac probability/field tensor with connected closed system condition. This closed system condition includes the Dirac current continuity equation as its time-like part. A generalized Klein Gordon equation that includes this Dirac current probability tensor is formulated and analyzed. The Standard Model's Dirac current based Lagrangians are generalized using this Dirac probability/field tensor. The Lorentz invariance or covariance of the generalized equations and Lagrangians is proven. It is indicated that the Dirac probability/field tensor and its closed system condition closes the gap with General Relativity quite a bit.

A single-particle Hamiltonian independent of the particle's coordinate ensures the particle conserves momentum, i.e., is free. This free-particle Hamiltonian is completely determined by Lorentz covariance of its energy-momentum and the particle's rest-energy value; such a free particle has velocity which vanishes when its momentum vanishes. Dirac required his free-particle Hamiltonian to be inhomogeneously linear in momentum, which contrariwise produces velocity that is independent of momentum; he also required his Hamiltonian's square to equal the above relativistic Hamiltonian's square, forcing many observables to anticommute and breach the quantum correspondence principle, as well as forcing the speed of any Dirac "free particle" to be c times the square root of three, which remains true when the particle interacts electromagnetically. The quantum correspondence principle breach causes a Dirac "free particle" to exhibit spontaneous acceleration that becomes unbounded in the classical limit; an artificial "spin" is also made available. Unlike the Dirac Hamiltonian, the nonrelativistic Pauli Hamiltonian is free of unphysical anomalies. Its relativistic extension is worked out via Lorentz-invariant upgrade of its associated action functional at zero particle velocity, and is obtained in closed form when there is no applied magnetic field; when there is, a successive approximation scheme must be used.

When a particle is in constant acceleration, it has been suggested it has a Rindler horizon given by c^2/ a, where a is the proper acceleration. The Rindler event horizon tells us that we cannot receive information outside the horizon during the time period in which we are accelerating at this uniform rate. If we accelerate uniformly, sooner or later we will reach the speed of light, or at least very close to it. In this paper, we will look more closely at the Rindler horizon in relation to Haug’s newly-suggested maximum velocity for matter and see that there likely is a minimum Rindler horizon for a particle with mass that is accelerating; this minimum Rindler horizon may, in fact, be the Planck length.

Refraction is treated classically, which is not physically realistic. Unlike optical reflection that is well understood refraction, is a more difficult problem exposing a major missing piece of quantum mechanics. Refraction normally is treated either classically or as a non-relativistic perturbation response. Recently it became apparent where this property finds its quantum origin in a full relativistic quantum description.

Recent experimental research has shown that mass is linked to Compton periodicity. We suggest a new way to look at mass: Namely that mass at its most fundamental level can simply be seen as reduced Compton frequency over the Planck time. In this way, surprisingly, neither the Planck constant nor Newton’s gravitational constant are needed to observe the Planck length, nor in any type of calculation, except when we want to convert back to old and less informative mass measures such as kg. The theory gives the same predictions as Einstein’s special relativity theory, with one very important exception: anything with mass must have a maximum velocity that is a function of the Planck length and the reduced Compton wavelength. For all observed subatomic particles, such as the electron, this velocity is considerably above what is achieved in particle accelerators, but always below the speed of light. This removes a series of infinity challenges in physics. The theory also offers a way to look at a new type of quantum probabilities. As we will show, a long series of equations become simplified in this way.

In this paper, a simple Zitterbewegung electron model, proposed in a previous work, is presented from a different perspective that does not require advanced mathematical concepts. A geometric-electromagnetic interpretation of mass, relativistic mass, De Broglie wavelength, Proca, Klein-Gordon and Aharonov-Bohm equations in agreement with the model is proposed. Starting from the key concept of mass-frequency equivalence a non-relativistic interpretation of the 3.7 keV deep hydrogen level found by J. Naudts is presented. Abstract According to this perspective, ultra-dense hydrogen can be conceived as a coherent chain of bosonic electrons with protons or deuterons at center of their Zitterbewegung orbits. The paper ends with some examples of the possible role of ultra-dense hydrogen in some aneutronic low energy nuclear reactions.

I show how many connections of Γ are presently existing from R to β as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the tensor connection is true through its output method using a wide variety but small amount of tensor calculus methods and number theory. You will patently see the formations of operator functions throughout the application as these two mathematical methods work together.

A single-particle Hamiltonian independent of the particle's coordinate ensures the particle conserves momentum, i.e., is free. Lorentz-covariance of that Hamiltonian's energy-momentum specifies it up to the particle's rest energy; the free particle it describes has speed below c and constant velocity parallel to its conserved momentum. Dirac took his free-particle Hamiltonian to have the same squared value as that relativistic one, but unwittingly blocked Lorentz-covariance of his Hamiltonian's energy-momentum by requiring it to be inhomogeneously linear in momentum. The Dirac "free particle" badly flouts relativity and even physical cogency; its velocity direction is extremely nonconstant, while its speed is fixed to c times the square root of three even when it interacts electromagnetically. Both its rest energy and total energy can be negative, and its velocity components and rest energy are artificially correlated by being mutually anticommuting; its alleged "spin" is an artifact of the anticommutation of its velocity components. Unlike the Dirac Hamiltonian, the nonrelativistic Pauli Hamiltonian is apparently physically sensible for particle speed far below c. Its relativistic extension is worked out via Lorentz-invariant upgrade of its associated action functional at zero particle velocity, and is obtained in closed form if there is no applied magnetic field; a successive approximation scheme must otherwise be used.

In modern physics, it is assumed that the Planck length is a derived constant from Newton's gravitational constant, the Planck constant and the speed of light, l_p=Sqrt(G*hbar/c^3). This was first discovered by Max Planck in 1899. We suggest a way to find the Planck length independent of any knowledge of Newton's gravitational constant or the Planck constant, but still dependent on the speed of light (directly or indirectly).

We suggest a way to find the Planck length by finding the Compton wavelength of the electron from Compton scattering, and then measuring the proton-electron ratio using cyclotron frequency. This gives us the Planck length using a Cavendish apparatus with no knowledge of Newton's gravitational constant. The Planck length is indeed important for gravity, but Newton's gravitational constant is likely a composite constant.

In the past, there was an attempt to modify Newton’s gravitational theory, in a simple way, to consider relativistic effects. The approach was “abandoned” mainly because it predicted only half of Mercury’s precession. Here we will revisit this method and see how a small logical extension can lead to a relativistic Newtonian theory that predicts the perihelion precession of Mercury correctly. In addition, the theory requires much less mass to explain galaxy rotation than standard theories do, and is also interesting for this reason.

With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. We show here that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.

We develop a non-cooperative game-theoretic model for the problem of graph minor-embedding to show that optimal compiling of adiabatic quantum programs in the sense of Nash equilibrium is possible.

Abstract The path integral in quantum mechanics is a very important mathematical tools. It is widely applied in quantum electrodynamics and quantum field theory. But its basic concepts confuse all of us. The first thing is the propagation of the probability. The second is the path can be any paths you can draw. How this can work? In this article, a new definition of energy pipe streamline integral is introduced in which the mutual energy theorem and the mutual energy flow theorem, mutual energy principle, self-energy principle, Huygens principle, and surface integral inner product of the electromagnetic fields are applied to offer a meaningful and upgraded path integral. The mutual energy flow is the energy flow from the emitter to the absorber. This energy flow is built by the retarded wave radiates from the emitter and the advanced wave radiates from the absorber. The mutual energy flow theorem guarantees that the energy of the photon go through any surface between the emitter and the absorber are all equal. This allow us to build many slender flow pipes to describe the energy flow. The path integral can be defined on these pipes. This is a updated path integral and it is referred as the energy pip streamline integral. The Huygens principle allow us to insert virtual current sources on any place of the pipes. Self-energy principle tell us that any particles are consist of 4 waves: the retarded wave, the advanced wave and another two time-reversal waves. All these waves are canceled and, hence, the waves do not carry or transfer any energy. Energy is only carried and transferred by the mutual energy flow. Hence, the mutual energy flow theorem is actually the energy flow theorem. Wave looks like probability wave, but mutual energy flow are real energy flow, it is not a probability flow. In this article the streamline integral is applied to photon which satisfy Maxwell equation. However, this concept can be easily widened to other particle for example electrons which satisfies the Schrödinger or Dirac equation.

Having elsewhere refuted Bell’s theorem irrefutably with elementary mathematics, we here advance Einstein’s ideas similarly with a classical Lorentz-invariant theory, observationally-indistinguishable from quantum mechanics. Given that our elementary theory is straight-forward and non-mysterious, we provide an Einsteinian—a specifically local and truly realistic—advance toward understanding the classical nature of physical reality at the quantum level. We thus resolve Bell’s dilemma in Einstein’s favor: as Bell half-expected, he and his supporters were being rather silly.

Using quantum computers to simulate polyatomic reaction dynamics has an exponential advantage in the amount of resources needed over classical computers. Here we demonstrate an exact simulation of the dynamics of the laser-driven isomerization reaction of assymetric malondialdehydes. We discretize space and time, decompose the Hamiltonian operator according to the number of qubits and use Walsh-series approximation to implement the quantum circuit for diagonal operators. We observe that the reaction evolves by means of a tunneling mechanism through a potential barrier and the final state is in close agreement with theoretical predictions. All quantum circuits are implemented through IBM's QISKit platform in an ideal quantum simulator.

Bell's famous inequality contradicts ours. But ours holds algebraically, experimentally, classically and quantum-mechanically: Bell's does not. So Bell's inequality is refuted on Bell's terms as we identify his naively-realistic error and correct it.

We derive a class of inequality relations, using both the sum uncertainty relations of su(2) algebra operators and the Schrodinger-Robertson uncertainty relation of partially transposed su(1, 1) algebra operators, to detect the three-mode entanglement of non-Gaussian states of electromagnetic field. These operators are quadratic in mode creation and annihilation operators. The inseparability condition obtained using su(2) algebra operators is shown to guarantee the violation of stronger separability condition provided by Schrodinger-Robertson uncertainty relation of partially transposed su(1, 1) algebra operators. The obtained inseparability condition is also shown to be a necessary condition for W type entangled states and it is used to derive the general form for a family of such inseparability conditions. An experimental scheme is proposed to test the violation of separability condition. The results derived for three-mode systems are generalized to multimode systems.

The Lamb shift was discovered by Willis Lamb and measured for the first time in 1947 by Lamb and Rutherford [1, 2, 3] on the hydrogen microwave spectrum. We suggest that the Lamb shift can be approximated by a very simple function that seems accurate enough for most experimenters working with elements where relativistic effects of the electron are minimal, that is up to element 80 or so. Even if our new approximation does not show anything new in physics, we think it can be useful for experimenters and students of quantum physics and chemistry; now everyone can calculate the Lamb shift on the back of an envelope.

It is known that quantum mechanics is one of the most successful theories in physics across the entire history of physics, nevertheless, many believe that its foundations are still not really understood like: wave-particle duality, interference, entanglement, quantum tunneling, uncertainty principle, vacuum catastrophe, wave collapse, relation between classical mechanics and quantum mechanics, classical limit, quantum chaos etc., and the continuous failures in the unify between relativity theory and quantum theory may be an indication about a problem in the foundations, this paper aims at discovering the first small step in the path of solving and understanding these quantum puzzles, in fact, the key to solving quantum puzzles is by understanding the reality of the motion and how it occurs. This paper proposes a model of motion with a new action principle like the principle of least action called "alike action principle". Actually, we have been able to deduce the principles of quantum mechanics so that the oddity of the quantum becomes easier to understand and interpret, for example, this paper proposes a solution to vacuum catastrophe and gives us the origin of dark energy, and shows that the basic law of motion must be broader than both quantum mechanics and classical mechanics.

One of the greatest unsolved problems in quantum mechanics is related to time operators. Since the Pauli objection was first raised in 1933, time has only been considered a parameter in quantum mechanics and not as an operator. The Pauli objection basically asserts that a time operator must be Hermitian and self-adjoint, something the Pauli objection points out is actually not possible. Some theorists have gone so far as to claim that time between events does not exist in the quantum world. Others have explored various ideas to establish an acceptable type of time operator, such as a dynamic time operator, or an external clock that stands just outside the framework of the Pauli objection. However, none of these methods seem to be completely sound. We think that a better approach is to develop a deeper understanding of how elementary particles can be seen, themselves, as ticking clocks, and to examine more broadly how they relate to time.

Today scientists believe that all “particles” also have a “wave nature” (and vice versa). This phenomenon has been verified not only for elementary particles, but also for the elementary particles that exist in compound particles like molecules and even atoms. You can consider light (the photons of the light beams) as a “wave-like energy”. This energy is a wave–particle, just containing elementary matter and speed. We can use Einstein, Planck equations to determine the amount of the energy which make up a sample photon. But, to date we cannot measure the matter, therefore we make a simple unit that let us to measure the matter.

The 2018 Physics Today essay competition invites participants to identify a ‘significant advance’ in his or her field since the millennium that deserves wider recognition among non-experts, and to write an essay that describes the advance, how it was made, and why it’s important[1]. This essay takes quantum mechanics to be the field of interest, introducing ‘non-experts’ to a new synthesis of math and physics, of geometry and fields, a computationally precise yet intuitive representation of wavefunctions and their interactions at all scales, allowing for a common sense interpretation of quantum phenomena and resolution of most if not all quantum paradoxes. It’s all about the wavefunction, the foundation, fundamental, quantum philosophy, quantum logic. As yet we are all non-experts.

In this paper, we will revisit the derivation of Heisenberg’s uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, “God does not throw dice.” His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton ‘clock’ frequency in elementary particles.

The particle and wave duality is solved through the self-energy and the mutual energy principles. Welch has introduced the time-domain reciprocity theorem in 1960. This author have introduced the mutual energy theorem in 1987. It has been proved that the above two theorems are same theorem in time-domain or in Fourier domain. This author believe there is an energy flow from transmitting antenna to the receiving antenna. Hence this theorem is a energy theorem instead of a mathematical theorem i.e. the reciprocity theorem. This author found that the mutual energy is the additional energy when the two waves are superposed comparing to the situation when the two waves alone stayed in the space. It is often asked that if the two waves are identical what is the energy after the two waves are superposed, 4 or 2 times? this author's answer are 2 or 4 depending whether the sources of the waves are involved or not. However this author noticed that a more important situation, which is the superposition of two waves: one is retarded wave sent from the emitter, another is the advanced wave sent from the absorber. This situation actually described the photon. This author have found that, instead there are two photons the retarded photon and the advanced photon like some author believed, there is only one photon. The reason is that the two waves the retarded wave and the advanced wave they both bring one photon energy, which are sent to the space, but these energy are returned with the time-reversed waves. The additional energy because of the superpose process of the two waves is just with 1 photon's energy instead of 2 photon's energy. This energy is sent from the emitter to the absorber. These build this author's photon model. This photon model is proved by this author through the notice of the conflict between the energy conservation and both the superposition principle and the Maxwell equations for single charge. This conflict force this author introduced the mutual energy principle and the self-energy principle. Self-energy principle tell us the self-energy (the wave's energy before superposed) time-reversal return to its source and hence do not transfer any energy from emitter to the absorber. The mutual energy principle tell us that transferring the energy from the emitter to the absorber is only done by the mutual energy flow. This author also proved that the mutual energy flow theorem, which says that the energy transferred by mutual energy flow is equal in any surface between the emitter to the absorber. The wave function collapse process is explained by the two processes together the first is the self-energy time-reversal return to their sources (instead of the targets), the second is that the mutual energy flow brings a photon's energy package from emitter to the absorber. The wave's probability property is also explained that because only when a retarded wave synchronized with an advanced wave the energy can be transferred. The photon energy is transferred only when the retarded wave (one of solution of Maxwell equations) and the advanced wave (another solution of the Maxwell equations) are synchronized, otherwise the two waves are returned by two time-reversal waves. Time-reversal wave are not satisfy Maxwell equations but satisfy the time-reversal Maxwell equations. Hence, 4 time-reversal Maxwell equations which describe the two additional time-reversal waves are added to Maxwell equations. Hence, the photon's package wave is consist of 4 waves which are corresponding to 4 self-energy flows. There are two additional energy flows, which are the mutual energy flows that is responsible for transferring the energy from emitter to the absorber. The time-reversal mutual energy flow which is responsible to bring the energy back from the absorber to the emitter if the absorber only obtained a half photon or a part of photon.

A quantum potential $V(x,t)$ of $\delta$-function type is introduced, to describe the inertial motion of a particle. Quantum-mechanically, it is in a bound state, though classically one seems to be free. The motion of the object (micro- or macroscopic) takes place according to the Huygens-Fresnel principle. The new position of the object (wave front) plays the role of the secondary sources that maintain the propagation. The mean value of the potential energy is $-mc^{2}$. We found that the de Broglie - Bohm quantum potential is the difference between the bound energy $E = - mc^{2}/2$ from the stationary case and our potential $V(x,t)$.

This is to present and discuss an alternative method for precise analytical determination of electron spin angular momentum 1/2. The method is based on the Lorentz-force acting on a point-like charge moved through the entire magnetic dipole-field of the electron. The result hbar/2 coincides with a previous result based on Lagrangian electrodynamics and confirms the "hidden" electromagnetic origin of spin angular momentum. Both methods reveal a key role of the "classical" electron radius.

Over the past few years I have presented a theory of modern atomism supported by mathematics [1, 2]. In each area of analysis undertaken in this work, the theory leads to the same mathematical end results as Einstein’s special relativity theory when using Einstein-Poincar ́e synchronized clocks. In addition, atomism is grounded in a form of quantization that leads to upper boundary limits on a long series of results in physics, where the upper boundary limits traditionally have led to infinity challenges. In 2014, I introduced a new concept that I coined “time-speed” and showed that this was a way to distinguish mass from energy. Mass can be seen as time-speed and energy as speed. Mass can also be expressed in the normal way in form of kg (or pounds) and in this paper we will show how kg is linked to time-speed. Actually, there are a number of ways to describe mass, and when they are used consistently, they each give the same result. However, modern physics still does not seem to understand what mass truly is. This paper is mainly aimed at readers who have already spent some time studying my mathematical atomism theory. Atomism seems to offer a key to understanding mass and energy at a deeper level than modern physics has attained to date. Modern physics is mostly a top-down theory, while atomism is a bottom-up theory. Atomism starts with the depth of reality and surprisingly this leads to predictions that fit what we can observe.

In this short note we present a possible connection between the proton radius and the proton mass using the fine structure constant. The Hagedorn temperature is related to the energy levels assumed to be required to free the quarks from the proton, where hadronic matter is unstable. We also speculate that there could be a connection between the Hagedorn temperature and the Planck temperature through the fine structure constant. Whether there is something to this, or it is purely a coincidence, we will leave to others and future research to explore. However, we think these possible relationships are worth further investigation.

Clauser-Horne (CH) inequality, Eberhard inequality, and Clauser-Horne-Shimony-Holt (CHSH) inequality are used to determine whether quantum entanglement can contradict local realism. However, the "finite statistics" loophole is known to allow local realism to violate these inequalities if a sample size is small and not "large enough" [1]. Remarkably though, this paper shows that this loophole can still cause a violation in these inequalities even with a very large sample size, e.g. a 2.4 sigma violation of CH inequality and Eberhard inequality was achieved despite 12,000,000 total trials in a Monte Carlo simulation of a local realist photonic experiment based on Malus' law. In addition, this paper shows how Eberhard inequality is especially vulnerable to this loophole when combined with an improper statistical analysis and incorrect singles counts, e.g. a 13.0 sigma violation was achieved with the same large sample size, and furthermore, a 26.6 sigma violation was produced when a small, acceptable 0.2% production rate loophole was applied. Supplementally, this paper demonstrates how the finite statistics loophole allows a bigger violation in a smaller sample size despite the sample size being "large enough", e.g. a CHSH violation of 4.4 sigma (2.43 +/- 0.10) was achieved with 280 total trials, and 4.0 sigma (2.16 +/- 0.04) with 3,000 total trials. This paper introduces the aforementioned loopholes as plausible local realist explanations to two observed violations reported by Giustina, et al. [2], and Hensen, et al. [3].

In his recent work, physicist Mike McCulloch has derived what he has coined “Quantized Inertia” from Heisenberg’s uncertainty principle. He has published a series of papers indicating that Quantized Inertia can predict everything from galaxy rotations (without relying on the concept of dark matter) to the EM drive; see [1, 2, 3, 4]. Clearly, it is an interesting theory that deserves some attention until proven or disproven. We think McCulloch has several excellent insights, but it is important to understand the fundamental principles from which he has derived his theory. We will comment on the derivation in his work and suggest that it could be interpreted from a different perspective. Recent developments in mathematical atomism appear to have revealed new concepts concerning the Planck mass, the Plank length, and their link to special relativity, gravity, and even the Heisenberg principle. We wonder if Quantized Inertia is compatible with the atomist view of the world and, if so, how McCulloch’s theory should be interpreted in that light.

Mike McCulloch has derived Newton's gravity from Heisenberg's uncertainty principle in an innovative and interesting way. Upon deeper examination, we will claim that his work has additional important implications, when viewed from a different perspective. Based on recent developments in mathematical atomism, particularly those exploring the nature of Planck masses and their link to Heisenberg's uncertainty principle, we uncover an insight on the quantum world that leads to an even more profound interpretation of the McCulloch derivation than was put forward previously.

In this paper we show that Heisenberg’s uncertainty principle, combined with key principles from Max Planck and Einstein, indicates that uncertainty collapses at the Planck scale. In essence we suggest that the uncertainty principle becomes the certainty principle at the Planck scale. This can be used to find the rest-mass formula for elementary particles consistent with what is already known. If this interpretation is correct, it means that Einstein’s intuition that “God Does Not Throw Dice with the Universe” could also be correct. We interpret this to mean that Einstein did not believe the world was ruled by strange uncertainty phenomena at the deeper level, and we will claim that this level is the Planck scale, where all uncertainty seems to collapse. The bad news is that this new-found certainty can only can last for one Planck second! We are also questioning, without coming to a conclusion, if this could have implications for Bell’s theorem and hidden variable theories.

Quantum entanglement is of great importance to quantum cryptography and computation. So far, all experimental demonstrations of entanglement are designed to check Bell's inequality which is based on Bell's formulation for EPR paradox. In this note, we specify the assumptions needed in Bell's mathematical argument. We then show the contradictions among these assumptions. As a result, it becomes very easy to see that Bell's inequality is trivial.

The simplest measurements in physics are binary; that is, they have only two possible results. An example is a beam splitter. One can take the output of a beam splitter and use it as the input of another beam splitter. The compound measurement is described by the product of the Hermitian matrices that describe the beam splitters. In the classical case the Hermitian matrices commute (are diagonal) and the measurements can be taken in any order. The general quantum situation was described by Julian Schwinger with what is now known as ``Schwinger's Measurement Algebra''. We simplify his results by restriction to binary measurements and extend it to include classical as well as imperfect and thermal beam splitters. We use elementary methods to introduce advanced subjects such as geometric phase, Berry-Pancharatnam phase, superselection sectors, symmetries and applications to the identities of the Standard Model fermions.

In this paper, we derive a maximum velocity for anything with rest-mass from Heisenberg’s uncertainty principle. The maximum velocity formula we get is in line with the maximum velocity formula suggested by Haug in a series of papers. This supports the assertion that Haug’s maximum velocity formula is useful in considering the path forward in theoretical physics. In particular, it predicts that the Lorentz symmetry will break down at the Planck scale, and shows how and why this happens. Further, it shows that the maximum velocity for a Planck mass particle is zero. At first this may sound illogical, but it is a remarkable result that gives a new and important insight into this research domain. We also show that the common assumed speed limit of v < c for anything with rest-mass is likely incompatible with the assumption of a minimum length equal to the Planck length. So one either has to eliminate the idea of the Planck length as something special, or one has to modify the speed limit of matter slightly to obtain the formula we get from Heisenberg’s uncertainty principle.

We embolden the idea that the Dirac 4 × 4 γ-matrices are four-vectors where the space components (γ i) represent spin and the forth component (γ 0) should likewise represent the time component of spin in the usual four-vector formalism of the Special Theory of Relativity. With the γ-matrices as four-vectors, it is seen that the Dirac equation admits two kinds of wavefunctions – (1) the usual four component Dirac bispinor ψ and (2) a scalar four component bispinor φ. Realizing this, and knowing forehand of the existing mystery as to why Leptons and Neutrinos come in pairs, we seize the moment and make the suggestion that the pair (ψ, φ) can be used as a starting point to explain mystery of why in their three generations [(e ± , ν e), (µ ± , ν µ), (τ ± , ν τ)], Leptons and Neutrinos come in doublets. In this suggestion, the scalar-bispinor φ can be thought of as the Neutrino while the usual Dirac bispinor ψ can be thought of as the Lepton.

This Toroidal Solenoid Electron model describe the electron as an infinitesimal electric charge moving at the speed of light along a helical path. From this semiclassical model, we can derive all the electron characteristics as the electron magnetic moment, the g-factor, its natural frequency, the value of Quantum Hall Resistance and the value of the Magnetic Flux Quantum. In this new work, we obtain other features such as the helicity, the chirality, the Schwinger limits and, especially, the Toroidal Moment of the electron. The experimental detection of the Toroidal Moment of the electron could be used to validate this model. The toroidal moment of the electron is a direct consequence of Helical Solenoid Electrón model and it is calculated qualitatively and quantitatively. This feature of the electron (and any other subatomic particle) is not contained in the standard model, but appears as a requirement to explain the violation of the parity symmetry of the subatomic particles. The existence of a toroidal moment has been experimentally verified in nuclei of heavy atoms and also serves as basis to explain the dark matter.

Abstract<br>Abstract Textbook theory says that the Canonical Commutation Relation derives from the homogeneity of space. This paper shows that the Canonical Commutation Relation does not derive from homogeneity of space or the homogeneity symmetry itself, but derives from a duality viewpoint of homogeneity, seen both from the viewpoint of position space, and from the viewpoint of momentum space, combined. Additionally, a specific particular fixed scale factor, relating position space with momentum space is necessary. It is this additional scaling information which enables complementarity between the system variables and makes the system unitary. Without this particular scaling, the Canonical Commutation Relation is left non-unitary and broken. Indeed, unitarity is separate information, unconnected and logically independent of the quantum system's underlying symmetry. This single counter-example contradicts the current consensus that foundational symmetries, underlying quantum systems, are ontologically, intrinsically and unavoidably unitary. And thus removes ‘unitary ontology’, as reason, for axiomatically imposing unitarity (or self-adjointness) — by Postulate — on quantum mechanical systems.<br><br>Keywords<br>foundations of quantum theory, quantum mechanics, wave mechanics, Canonical Commutation Relation, symmetry, homogeneity of space, unitary.

Atomic electron transition appears leaping from one energy level to another. The issue is, atomic particles are too small and too fast for our detectors to recognize their action and identity. I believe it is due to the sensors can only detect and register the repeated trajectory. Particle would have to revolving on the same orbit long enough. Otherwise, it would not trigger the reaction of the detectors. Transitional trajectory is short, and it does not repeat. It can not be detected, hence, jump.

According to Feynman, we should make nature to be quantum mechanical to simulate it better. Simulating quantum systems in a computer had been remained a challenging problem to tackle. It's mainly in case of a large quantum system. However, Feynman's 1982 conjecture that `physics can be simulated using a quantum computer other than using a Turing machine or a classical computer' has been proved to be correct. It is widely known that quantum computers have superior power as compared to classical computers in simulating quantum systems efficiently. Here we report the experimental realization of quantum tunneling through potential barriers by simulating it in the IBM quantum computer, which here acts as a universal quantum simulator. We take a two-qubit system for visualizing the tunneling process, which has a truly quantum nature. We clearly observe the tunneling through a barrier by our experimental results. This experiment inspires us to simulate other quantum mechanical problems which possess such quantum nature.

This note briefly outlines how numbers that appear to be totally and independently random switch to become deterministic at the Planck scale. In other words, God does not play dice.

A fifth force, the Cohesion Force, becomes necessary when building a toy universe based on a fully deterministic, Euclidean, 4-torus cellular automaton using a constructive approach. Each cell contains one integer number forming bubble-like patterns propagating at speeds at least equal to that of light, interacting and being reemitted constantly. The collective behavior of these integers looks like patterns of classical and quantum physics. The four forces of nature plus the new one are unified. In particular, the graviton fits nicely in this framework. Although essentially nonlocal, it preserves the no-signalling principle. This flexible model predicts three results: i) if an electron is left completely alone (if even possible), still continues to emit low frequency fundamental photons; ii) neutrinos are Majorana fermions; and, last but not least, iii) gravity is not quantized. Pseudocode first version implementing these ideas is contained in the appendix.

Here begins a precautionary tale from a creative life in STEM. Bringing an elementary knowledge of vectors to Bell (1964)—en route to refuting Bell’s inequality and his theorem—we aim to help STEM students study one of the strangest double-errors in the history of science. To that end we question du Sautoy’s (2016) claim that Bell’s theorem is as mathematically robust as they come.

A simple explanation is given for the continuation of the singlet state over large distances in an EPRBA experiment. The paper answers this question with clocks ticking in synchronized frequencies that can be carried by the particles.

Quantum Mechanics is all about wavefunctions and their interactions. If one seeks to understand Quantum Mechanics, then a deep intuitive understanding of wavefunctions and wavefunction collapse would seem essential, indispensable. That’s where it all starts, the causal origin of the quantum as manifested in the physical world. We introduce a wavefunction comprised of the geometric elements of the Pauli algebra of space - point, line, plane, and volume elements - endowed with quantized electromagnetic fields. Wavefunction interactions are described by the geometric product of geometric Clifford algebra, generating the Dirac algebra of flat Minkowski spacetime, the particle physicist’s S-matrix. Electromagnetic synthesis of four fundamental forces becomes apparent via this Geometric Wavefunction Interpretation (GWI).

What is proposed here is a simple modication in the quantum protocol [1] for achieving instantaneous teleportation of arbitrary quantum state from Alice to Bob even when Bob is several light years away. This modied quantum protocol is constructed by adding a step the in the celebrated quantum teleportation protocol [1]. It consists of the action of a unitary operator to be performed by Alice on the qubits in her possession before she does the Bell basis measurement. It is important to note that the existing quantum teleportation protocol [1] requires certain classical communication between the participants, Alice and Bob, and we are going to eliminate this classical communication through our modification. In the existing protocol [1] Alice requires sending the classical bits generated during her Bell basis measurement over a classical channel to Bob for Bob to use these classical bits to determine the exact recovery operation to be performed on the qubit(s) in his possession for creating the exactly identical copy of unknown quantum state that was with Alice and got destroyed during her Bell basis measurement. Alice cannot send the classical bits she obtained to Bob with the speed faster than that of light since it is the well known experimentally veried universal upper limit on the speed. We show that by incorporating suitable unitary operation to be performed by Alice on her qubits before the Bell basis measurement the requirement of the transmission of classical bits by Alice to Bob for the creation of the unknown quantum state by Bob at his place can be completely eliminated. Our modification in the teleportation protocols [1], [2] thus clearly demonstrates the enormous advantage of remaining in the quantum regime and avoiding the requirement of any classical communication for the teleportation of the quantum states.

This is a very short non-technical note pointing out a key finding from modern mathematical atomism, namely that the world is Binary, and that the Planck mass, the Planck length, and the Planck second are invariant entities. With Einstein-Poincare synchronized clocks, the speed of light (in a vacuum) is the same in every direction, it is isotropic and it is often represented with the character c. The speed of light is, per definition, exactly 299 792 458 m/s, a tremendous speed. We do not contest that this is the speed of light as measured with Einstein-Poincare synchronized clocks, but still we ask: ``Is this truly always the case?".

In the reading Nyambuya (2015), we proposed a hypothetical state of the Hydrogen atom whose name we coined 'Neutronium'. That is to say, in the typical Hydrogen atom, the Electron is assumed to orbit the Proton, while in the Neutronium, the converse is assumed, i.e., the Proton orbits the Electron. In the present reading, we present some seductive argument which lead us to think that this Neutronium may actually be the usual Neutron that we are used to know. That is to say, we show that under certain assumed conditions, a free Neutronium may be unstable while a non-free Neutronium is stable in its confinement. Given that a free Neutron is stable in it confinement of the nucleus and unstable where free with a lifetime of ∼ 15 min, one wonders whether or not this Neutronium might be the Neutron if we are to match the lifetime of a free Neutronium to that of a free Neutron.

Quantum mechanics differential equations are based on the de Broglie postulate. This paper presents the repercussions on quantum mechanics differential equations when the de Broglie wavelength is replaced by a relation between the radius and the relativistic energy of a particle. This relation results from a theoretical work about the interaction of charged particles, where the particles are modelled as focal points of rays of fundamental particles with longitudinal and transversal angular momentum. Interaction of subatomic particles is described as the interaction of the angular momenta of their fundamental particles. The relationship between the solution of the differential equation for a radial Coulomb field and the Correspondence Principle is presented. All four known forces are the result of electromagnetic interactions, so that only QED is required to describe them. The potential well of an atomic nucleus is shown with the regions that are responsible for the four type of interactions defined in quantum mechanics. Also the compatibility of the gravitation model derived in the theoretical work with quantum mechanics is shown, model where gravitation is the result of the reintegration of migrated electrons and positrons to their nuclei.

In our previous publications we argue that finite mathematics is fundamental, classical mathematics (involving such notions as infinitely small/large, continuity etc.) is a degenerate special case of finite one, and ultimate quantum theory will be based on finite mathematics. We consider a finite quantum theory (FQT) based on a finite field or ring with a large characteristic $p$ and show that standard continuous quantum theory is a special case of FQT in the formal limit $p\to\infty$. Space and time are purely classical notions and are not present in FQT at all. In the present paper we discuss how classical equations of motions arise as a consequence of the fact that $p$ changes, i.e. $p$ is the evolution parameter.

Abstract A fully deterministic, Euclidean, 4-torus cellular automaton is presented axiomatically using a constructive approach. Each cell contains one integer number forming bubble-like patterns propagating at speeds at least equal to that of light, interacting and being reemitted constantly. The collective behavior of these integers looks like patterns of classical and quantum physics. In this toy universe, the four forces of nature are unified. In particular, the graviton fits nicely in this framework. Although essentially nonlocal, it preserves the no-signalling principle. This flexible model predicts three results: i) if an electron is left completely alone (if even possible), still continues to emit low frequency fundamental photons; ii) neutrinos are Majorana fermions; and, last but not least, iii) gravity is not quantized. Pseudocode implementing these ideas is contained in the appendix. This is the first, raw, version of this document. I expect to make corrections in future releases.

The widely held expectation that quantum physics breaks down below the Planck length ($10^{-33}$ cm) is brought into question. A possible experiment is suggested that might test its validity at a sub-Planckian length scale.

For photon we have obtained the results that the waves of photon obey the mutual energy principle and self-energy principle. In this article we will extended the results for photon to other quantum. The mutual energy principle and self energy principle corresponding to the Schrödinger equation are introduced. The results are that a electron, for example, travel in the empty space from point A to point B, there are 4 different waves. The retarded wave started from point A to infinite big sphere. The advanced wave started from point B to infinite big sphere. The return waves corresponding to the above both waves. There are 5 different flow corresponding to these waves. The self-energy flow corresponding to the retarded wave, the self-energy flow corresponding to the advanced wave. The return flows corresponding to the above two return waves. The mutual energy flow of the retarded wave and the advanced wave. It is found that the the mutual energy flow is the energy flow or the charge intensity flow or electric current of the the electron. Hence the electron travel in the empty space is a complicated process and do not only obey one Schrödinger equation. This result can also extend to to Dirac equations.

Bell's inequality is usually considered to belong to mathematics and not quantum mechanics. We think that this makes it difficult to understand Bell's theory. Thus in this paper, contrary to Bell's spirit (which inherits Einstein's spirit), we try to discuss Bell's inequality in the framework of quantum theory with the linguistic Copenhagen interpretation. And we clarify that whether or not Bell's inequality holds does not depend on whether classical systems or quantum systems, but depend on whether a kind of simultaneous measurements exist or not. And further we assert that our argument ( based on the linguistic Copenhagen interpretation) should be regarded as a scientific representation of Bell's philosophical argument (based on Einstein's spirit).

Exact solutions to the stationary spherically symmetric Newton-Schroedinger equation are proposed in terms of integrals involving $generalized$ Gaussians. The energy eigenvalues are also obtained in terms of these integrals which agree with the numerical results in the literature. A discussion of infinite-derivative-gravity follows which allows to generalize the Newton-Schroedinger equation by $replacing$ the ordinary Poisson equation with a $modified$ non-local Poisson equation associated with infinite-derivative gravity. We proceed to replace the nonlinear Newton-Schroedinger equation for a non-linear quantum-like Bohm-Poisson equation involving Bohm's quantum potential, and where the fundamental quantity is $no$ longer the wave-function $ \Psi$ but the real-valued probability density $ \rho$. Finally, we discuss how the latter equations reflect a $nonlinear$ $feeding$ loop mechanism between matter and geometry which allows us to envisage a ``Schwarzschild atom" as a spherically symmetric probability cloud of matter which curves the geometry, and in turn, the geometry back-reacts on this matter cloud perturbing its initial distribution over the space, which in turn will affect the geometry, and so forth until static equilibrium is reached.

Abstract:<br>In 2008 Tomasz Paterek et al published experiments demonstrating that quantum randomness results from logical independence. The job of this paper is to derive implications for Matrix Mechanics. Surprisingly (and apparently unwittingly), the Paterek experiments imply that faithful representation of (non-random) pure states contradicts the Quantum Postulate which imposes unitary, Hermitian and Hilbert space mathematics on all states. Paterek's Boolean formalism asserts and demands a non-unitary environment for pure states, which is freely restricted to logically independent unitary structure, wherever the creation of mixed states demands unitarity. Consequently, the Paterek experiments contradict the Quantum Postulate which imposes unitary, Hermitian and Hilbert space structures, axiomatically as blanket ontology, across the whole theory. Examination of the ‘non-unitary to unitary transition’ reveals the machinery of quantum indeterminacy. That machinery involves self-referential circularity, inaccessible history, and the geometrical ambiguity of perfect symmetry. The findings here provide answers for researchers studying Foundations of Quantum Mechanics; they make intuitive good sense of indeterminacy; they provide reason and significance for observable operators and eigenvectors; and they should be helpful for those interested in the Measurement Problem, the EPR paradox and possibly those looking for a method to quantize Gravity.<br><br>Keywords:<br>foundations of quantum theory, quantum randomness, quantum indeterminacy, logical independence, self-reference, logical circularity, mathematical undecidability.

The photon energy transfer is from point to point. But the wave according to the Maxwell equation spreads from the source point to the entire empty space. In order to explain this phenomenon the concept of wave function collapse is created. This concept is very rough, if there are many partition boards with small holes between the emitter charge and the absorber charge. The light is clear can go through all these small holes from emitter to the absorber. But according to the concept of the wave function collapse the wave must collapse N times if there are N holes on the partition boards. Collapse one is strange enough, if the wave collapse N times, that is unbelievable! In another article we have proved that the photon energy is actually transferred by the “mutual energy flow” which is point to point instead of spread to the entire space. Since energy can be transferred by the mutual energy flow, the concept of the wave function collapse is not necessary. In order to build the mutual energy flow it is required to build the self-energy flow also. The self-energy flow is spread to the entire empty space. What will do for the self-energy flow, it is possible the self-flow also collapse to the absorber. However if self-energy flow collapse we have also meet the same problem as the whole wave collapse that means if there are partition sheets with N holes, the self-energy flow has to collapse N times. In the article about mutual energy principle we have propose another possibility in which the self-energy flow instead collapse, we believe it is returned. It is returned with a time reversal process, hence the self-energy dose not contributed to the energy transfer of the photon. The return process can be seen as also a collapse process, however it is collapse to the source of the wave instead of the target of the wave. In this article we will discuss the self-energy flow and the time reversal process in details.

An introduction is given to the geometry and harmonics of the Golden Apex in the Great Pyramid, with the metaphysical and mathematical determination of the fine-structure constant of electromagnetic interactions. Newton's gravitational constant is also presented in harmonic form and other fundamental physical constants are then found related to the quintessential geometry of the Golden Apex in the Great Pyramid.

“What the Hell is Going On?” is Peter Woit’s ‘Not Even Wrong’ blog post of July 22nd 2017, a commentary on Nima Arkani-Hamed’s view of the present barren state of LHC physics, the long-dreaded Desert. This paper addresses the roots of the quandary which are fundamental, branching deep into the measurement problem and the enigmatic unobservable character of the wavefunction, and the confusion generating an ongoing proliferation of quantum interpretations.

An experimental non-model determination of the number of electrons participating in a chemical bond has been achieved. This determination corroborates the valence theory of Lewis and coincides with the current state of the art. The relationship between a normalized bond area and its bond energy is used to precisely characterize selected organic molecules. The mass fusion of bonding electrons with its mass loss or gain, is the probable origin of the chemical energy. As a consequence, a probable geometric meaning of thermodynamic functions is provided.

Quantum information-theoretic approach has been identied as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In the following paper we try to find relationship between a general quantum mechanical observable and von Neumann entropy. We find that the expectation values and the uncertainties of the observables have bounds which depend on the entropy. The results also show that von Neumann entropy is not just the uncertainty of the state but also encompasses the information about expectation values and uncertainties of any observable which depends on the observers choice for a particular measurement. Also a reverese uncertainty relation is derived for n quantum mechanical observables.

In the Aharonov-Bohm effect for a magnetic solenoid a moving charged particle seems to be influenced by the 4-potential in a region where there are no fields in the laboratory frame of reference. The 4-potential should be transformed to the frame of reference of the particle before computing the fields. There is an E field in its frame of reference. The field accelerates a moving charged particle. One of the components of the acceleration vector is in the same direction as the particle's velocity in the first frame of reference. The resulting longitudinal displacement in the path integral, when scaled in units of the de Broglie wavelength for the particle, is approximately the same as the phase of the Aharonov-Bohm solution for long paths. The scalar solution does not require transformation. It follows from the static Coulomb solution and the Newton equations.

The author believes there are spacetime particles(STP) which can sense all matter particles ubiquitously. Matter particles will change their states collided by STP . The underlying property of mass is a statistical property emerging from random impact in spacetime. We propose a mass interaction principle (MIP) which states any particle with mass m will involve a random motion without friction, due to random impacts from spacetime. Each impact changes the amount nh (n is any integer) for an action of the particle. Starting from the concept of statistical mass, we propose the fundamental MIP. We conclude that inertial mass has to be a statistical property, which measures the diffusion ability of all matter particles in spacetime. We prove all the essential results of special relativity come from MIP. Speed of light in the vacuum need no longer any special treatment. Instead, speed of STP has more fundamentally physical meaning, which represents the upper limit of information propagational speed in physics. Moreover, we derive the uncertainty relation asserting a fundamental limit to the precision regarding mass and diffusion coefficient. Within this context, wave-particle duality is a novel property emerging from random impact by STP. Further more, an interpretation of Heisenberg’s uncertainty principle is suggested, with a stochastic origin of Feynman’s path integral formalism. It is shown that we can construct a physical picture distinct from Copenhagen interpretation, and reinvestigate the nature of spacetime and reveal the origin of quantum behaviours from a realistic point of view.

Eschewing naive realism, we define true (classical/quantum) realism:= some existents (ie, some Bell-beables) may change interactively. We then show that Bell's mathematical ideas re local causality—from his 1964:(1)-(2) to his 1990a:(6.9.3)—are valid under true realism. But we refute Bell's analyses (and his ‘local realism’), as we resolve his consequent ‘action-at-a-distance’ dilemma in favor of true locality:= no influence propagates superluminally. In short: defining beables by properties and values—and allowing that locally-causal interactions may yield new beables—we predict the probabilities of such interaction outcomes via equivalence-classes that are weaker (hence more general) than the corresponding classes in EPR/Bell. In this way delivering the same results as quantum theory and experiment—using EPRB, CHSH, GHZ and 3-space—we also advance QM's reconstruction in spacetime with a new vector-product for geometric algebra. True local realism thus supports local causality, resolves Bell's dilemma, negates nonlocality, demystifies QM, rejects naive realism, eliminates the quantum/classical divide (since observables are clearly beables; being or not being, prior to an interaction, but certainly existing thereafter), etc: all at the level of undergraduate math and logic, and all contra the analyses and impossibility-claims of Bell and many others. We also show that Bayes' Law and Malus' Law hold, undiminished, under true local realism and the quantum.

The ergodic second-order approach of entropy gradient maximization, applied on the problem of a quantum bosonic system, does not provide dynamic equations for pure fermionic system. The first-order dynamic equation results for a system of bosonic and fermionic \dofs interacting by a conservation of a common sum of quantum occupation numbers.

Relativistic extension of the Pauli Hamiltonian is ostensibly achieved by minimal coupling of electromagnetism to the free-particle Dirac Hamiltonian. But the free-particle Pauli Hamiltonian is pathology-free in its nonrelativistic domain, while the free-particle Dirac Hamiltonian yields completely fixed particle speed which is greater than c, spin orbit torque whose ratio to kinetic energy tends to infinity in the zero-momentum limit, and mega-violation of Newton's First Law in that limit. Furthermore, relativistic extension of the Pauli Hamiltonian is unique in principle because inertial frame hopping can keep the particle nonrelativistic. That extension is indeed readily achieved by upgrading the terms of the Pauli Hamiltonian's corresponding action to appropriate Lorentz invariants. The resulting relativistic Lagrangian yields a canonical momentum that can't be analytically inverted in general, but a physically-sensible successive-approximation scheme applies. For hydrogen and simpler systems approximation isn't needed, and the result, which includes spin-orbit coupling, is as transparently physically sensible as the relativistic Lorentz Hamiltonian is, a far cry from the Dirac Hamiltonian pathologies.

The square-root Klein-Gordon operator,√(m^2− ∇^2), is a non-local operator with a natural scale inversely proportional to the mass (the Compton wavelength). There is no fundamental reason to exclude negative energy states from a “square-root” propagation law. We find several possible Hamiltonians associated with √(m^2− ∇^2) which include both positive and negative energy plane wave states. It is possible to satisfy the equations of motion with commutators or anticommutators. For the scalar case, only the canonical commutation rules yield a stable vacuum. We investigate microscopic causality for the commutator of the Hamiltonian density. We find that despite the non-local dependence of the energy density on the field operators, the commutators of the physical observables vanish for space-like separations. Hence, Pauli’s result can be extended to the non-local case. Pauli explicitly excluded √(m^2− ∇^2) because this operator acts non-locally in the coordinate space. The Mandelstam representation offers the possibility of avoiding the difficulties inherent in minimal coupling (Lorentz invariance and gauge invariance). We also compute the propagators for the scattering problem and investigate thesolutions of the square-root equation in the Aharonov-Bohm problem.

This work-in-progress paper consists of four points which relate to the foundations and physical realization of quantum computing. The first point is that the qubit cannot be taken as the basic unit for quantum computing, because not every superposition of bit-strings of length n can be factored into a string of n-qubits. The second point is that the “No-cloning” theorem does not apply to the copying of one quantum register into another register, because the mathematical representation of this copying is the identity operator, which is manifestly linear. The third point is that quantum parallelism is not destroyed only by environmental decoherence. There are two other forms of decoherence, which we call measurement decoherence and internal decoherence, that can also destroy quantum parallelism. The fourth point is that processing the contents of a quantum register “one qubit at a time” destroys entanglement.

In this paper, we shall describe the delayed-choice experiment first proposed by Wheeler and then analyze the experiment based on both our interpretation of what is happening and the Wheeler/Feynman interpretation. Our interpretation includes wave-function collapse due to a measurement, while the Wheeler/Feynman interpretation attempts to avoid wave-function collapse in a measurement, as part of their explanation, to preserve consistent unitarity. in quantum processes. We will also show that there are severe consequences for quantum computing if there is no wave function collapse due to a measurement.

Negating the classical/quantum divide in line with Bell's hidden-variable ideas, we resolve Bell's ‘action-at-a-distance' dilemma in accord with his hopes. We identify the resultant theory as clear local realism (CLR), the union of Bohr's ‘measurement' insight, Einstein locality and Bell beables. Our method follows: (i) consistent with Bohr's insight, we replace EPR's elements of physical reality with Bell's beables; (ii) we let Bell's beable λ denote a pristine particle's total angular momentum; (iii) validating Malus' Law in our quantum-compatible equivalence relations, we deliver the hopes of Bell and Einstein for a simple constructive model of EPRB; (iv) we then derive the correct results for CHSH and Mermin's version of GHZ; (v) we thus justify EPR's belief that additional variables would bring locality and causality to QM. In short, advancing Bell's ideas in line with his expectations: we amend EPR, resolve Bell's dilemma, negate nonlocality, endorse Einstein's locally-causal Lorentz-invariant worldview, demystify the classical/quantum divide, etc. CLR: clear via Bohr's insight, local via Einstein locality, realistic via Bell beables.

Spirituality is often seen as a part of religion, it is about rules for dealing with the spirits from the point of view of God the almighty, the creator of our universe. Of course, these rules have been written down by humans which are accepted to be so-called inspired and speaking the words of that same God. Whereas the point of view these rules are taking has to do with eternal good and bad, the morality and dangers of dealing with spirits and engaging with deamons; the point of view expressed in this book is a scientic one. It tries to descipher rules spirits have to obey and it lays down the foundations for behavioral psychology, devoid of good and evil, from the point of view of physical charges. I wish to advocate the point of view that nobody is good or evil, we can all do things which many people accept to be good or evil, but there is no such thing as intrinsically good or bad people. There are on the other hand, strong and weak ones, those with grand visions and small ones, quick and slow thinkers and so on.

This paper examines various alternatives for what the fine structure constant might represent. In particular, we look at an alternative where the fine structure constant represents the radius ratio divided by the mass ratio of the electron, versus the proton as newly suggested by Koshy [5], but here derived and interpreted based on Haug atomism (see [7]). This ratio is remarkably very close to the fine structure constant, and it is a dimensionless number. We also examine other alternatives such as the proton mass divided by the Higgs mass, which also appears as a possible candidate for what the fine structure constant might represent.

Simulating Bell correlations by Monte Carlo methods can be time-consuming due to the large number of trials required to produce reliable statistics. For a noisy vector model, formulating the vector threshold crossing in terms of geometric probability can eliminate the need for trials, with inferred probabilities replacing statistical frequencies.

In an article recently published in Vixra: http://vixra.org/abs/1704.0365. Its author (Mario Hieb) conjectured the possible relationship of Feigenbaum's constant delta with the fine-structure constant of electromagnetism (Sommerfeld's Fine-Structure Constant). In this article it demonstrated, that indeed, there is an unequivocal physical-mathematical relationship. The logistic map of double bifurcation is a physical image of the random process of the creation-annihilation of virtual pairs lepton-antilepton with electric charge; Using virtual photons. The probability of emission or absorption of a photon by an electron is precisely the fine structure constant for zero momentum, that is to say: Sommerfeld's Fine-Structure Constant. This probability is coded as the surface of a sphere, or equivalently: four times the surface of a circle. The original, conjectured calculation of Mario Hieb is corrected or improved by the contribution of the entropies of the virtual pairs of leptons with electric charge: muon, tau and electron. Including a correction factor due to the contributions of virtual bosons W and Z; And its decay in electrically charged leptons and quarks.

Single atom cavity quantum electrodynamics grants access to nonclassical photon statistics, while electromagnetically induced transparency exhibits a dark state of long coherence time. The combination of the two produces a new light field via four-wave mixing that shows long-lived quantum statistics. We observe the new field in the emission from the cavity as a beat with the probe light that together with the control beam and the cavity vacuum is driving the four-wave mixing process. Moreover, the control field allows us to tune the new light field from antibunching to bunching, demonstrating our all-optical control over the photon-pair emission.

A transformation of the conditional equation for the magnetic flux quantum $\vec{\Phi}_{0} = \frac{2\pi}{e} \hspace{2} \vec{\hbar}/2$ yields the conditional equation for the quantum of electromagnetic canonical angular momentum: $ \frac{e}{2 \pi} \hspace{2} \vec{\Phi}_{0} = \vec{\hbar}/2$.

We suggest that gravitation is an emergent phenomenon which origin is the information signal associated with quantum fields acting like test particles. We have shown how the metric (Lamè) coefficients emerge as position & time operator mean value densities. The scalar curvature of the space-time in the case of a Bose-Einstein condensate or super- fluid/conductor is calculated and an experimentally verifiable prediction of the theory is made.

It is found that the Poynting theorem is conflict with the energy conservation principle. It is a bug of the Poynting theorem. The Poynting theorem is derived from Maxwell equations by using the superimposition principle of the fields. Hence, this bug also existed at either in superimposition principle or in the Maxwell equations. The Poynting theorem is corrected in this article. After the correction the energy is not quadratic and hence the field is also not linear. The concept of the superposition of fields need also to be corrected. Hence the new definitions for the inner product and cross product are proposed. The corrected Poynting theorem become the mutual energy formula, it is strongly related to the mutual energy theorems. It is shown that starting from the mutual energy formula, the whole electromagnetic theory can be reconstructed. The Poynting theorem can be proved from the mutual energy formula by adding pseudo items. The Maxwell equations can be derived from Poynting theorem as sufficient conditions. Hence if the mutual energy formula is corrected, the Maxwell equations still can be applied with knowing its problem. Most the problems originally caused by Maxwell equations are solved. Examples of this problems are: (1) electric field infinity which need to be re-normalized in quantum physics; (2) collapse of the electromagnetic field, the waves has to be collapsed to its absorber, otherwise the energy is not conserved; (3) the emitter can send energy without absorber, this is conflict to the direct interaction principle and absorber theory; (4) if our universe is not completely opaque, the charges will continually send energy to the outside of our universe, our universe will have a continual loss of energy. However there is no testimony supporting that our universe is opaque. The new theory supports the existence of advanced wave, hence also strongly support the absorber theory and transactional interpretation of quantum physics. It can offer an equation for photon and a good explanation for the duality of the photon. If photon and electromagnetic field obeys the mutual energy formula, it is very possible that all other quanta also obey their similar mutual energy formula. Hence the mutual energy formula can be applied as a principle or axiom for the electromagnetic theory and quantum physics. According to this theory the asychronous retarded wave and the asychronous advanced wave of electromagnetic fields both are an ability or probability waves, which is also partly agree with Copenhagen interpretation.

<p>‘... all this action at a distance business will pass [like the ether]. If we're lucky it will be to some big new development like the theory of relativity. Maybe someone will just point out that we were being rather silly, with no big new development. But anyway, I believe the questions will be resolved,' after Bell (1990:9). ‘Nobody knows where the boundary between the classical and quantum domain is situated. More plausible to me is that we'll find that there is no boundary: the hidden-variable possibility,' after Bell (2004:28-29).</p> <p><b>Abstract:</b> Studying Bell's work, using classical analysis and author-date referencing suited to undergraduate STEM students, we arrive at a new classical theory: local realistic quantum mechanics. Adjusting EPR to accord with Bohr's insight, and accepting Bell's principles (but not his false inferences), our method follows: (i) we allow Bell's pristine λ (and its pairwise twin μ) to be classical fair-coin vectors in 3-space; (ii) we complete the QM account of EPR correlations in a classical way; (iii) we deliver Bell's hope for a simple constructive model of EPRB; (iv) we justify EPR's belief that additional variables would bring locality and causality to QM's completion; (v) we refute key claims that such variables are impossible; (vi) we show that interactions between particles and polarizers are driven by the total angular momentum; (vii) we bypass Pauli's vector-of-matrices, but retain all the tools of the quantum trade. In short, under local realism: classically deriving the related results of quantum theory, we classically endorse Einstein's locally-causal Lorentz-invariant worldview.</p>

\begin{abstract} It is analytically determined that the smallest theoretically possible nonzero canonical electromagnetic angular momentum $\hbar/2$ arises when an electron is inserted into one magnetic flux quantum. The analysis further reveals how magnetic flux quantization is inherently linked up with angular momentum quantization. Bohr's correspondence principle is satisfied. \end{abstract}

In this paper we discuss and calculate the mass gap. Based on the mass gap we are redefining what a kilogram may truly represent. This enables us to redefine the Planck constant in what we consider to be more fundamental units. Part of the analysis is based on recent developments in mathematical atomism. Haug [1, 2, 3] has shown that all of Einstein’s special relativity mathematical end results [4] can be derived from two postulates in atomism. However, atomism gives some additional boundary conditions and removes a series of infinite challenges in physics in a very simple and logical way. While the mass gap in quantum field theory is an unsolved mystery, under atomism we have an easily defined, discrete, and “exact” mass gap. The minimum rest-mass that exists above zero is 1.1734 × 10^(−51) kg, assuming an observational time window of one second. Under our theory it seems meaningless to talk about a mass gap without also talking about the observational time window. The mass gap in one Planck second is the Planck mass. Further, the mass gap of just 1.1734 × 10^(−51) kg has a relativistic mass equal to the Planck mass. The very fundamental particle that makes up all mass and energy has a rest-mass of 1.1734 × 10^(−51) kg. This is also equivalent to a Planck mass that lasts for one Planck second.

Adjusting EPR (to accord with Bohr's insight), and accepting Bell's principles (but not his false inferences), we:— (i) complete the QM account of EPR correlations in a classical way; (ii) deliver Bell's hope for a simple constructive model of EPRB; (iii) justify EPR's belief that additional variables would bring locality and causality to QM's completion; (iv) refute key claims that such variables are impossible — including CHSH, Mermin's three-particle always-vs-never variant of GHZ, and this: in the context of Bell's theorem ‘it's a proven scientific fact that a violation of local realism has been demonstrated theoretically and experimentally,' (Annals of Physics Editors, 2016). In short: we refute Bell's theorem and endorse Einstein's locally-causal Lorentz-invariant worldview.

It is shown, utilizing dimensional analysis, that the quantization of electric charge can be explained, in a fundamentally consistent manner, as a manifestation of the quantization of the intrinsic vibrational energy of the fabric of spacetime by a non-Planckian "action" in sub-Planckian spacetime. It is found that this conceptualization of the elementary charge provides a natural explanation of some of the more vexing questions that have plagued quantum electrodynamics since its inception. A possible experiment is suggested that might test for the presence of such a non-Planckian "action" in gravitational radiation.

A new model of the electron with Helical Solenoid geometry is presented. This new model is an extension of the Parson’s Ring Electron Model and the Hestenes’ Zitter Electron Model. In this new electron model, the g-factor appears as a simple consequence of the geometry of the electron. The calculation of the g-factor is performed in a simple manner and we obtain the value of 1.0011607. This value of the g-factor is more accurate that the value provided by the Schwinger’s factor.

Analytical determination of the magnetic flux included in the electron's dipole field - with consideration of magnetic flux quantization - reveals that it precisely comprises one magnetic flux quantum $\Phi_{0}$. The analysis further delivers a redefinition of classical electron radius $r_{e}$ by a factorized relation among electron radius $r_{e}$, vacuum permeability $\mu_{0}$, magneton $\mu_{B}$ and fluxon $\Phi_{0}$, exclusively determined by the electron's quantized magnetic dipole field: \begin{center} $r_{e} =\mu_{0}\hspace{1} \mu_{B}\hspace{1}(\Phi_{0})^{-1}= e^{2}/ 4 \pi \epsilon_{0} m_{e} c^{2}$ \end{center} The single fluxon electron model further enables analytical determination of its vector potential at $r_{e}$: $\vec{A}_{re} = \vec{\Phi}_{0}/2\pi r_{e}}$ and canonical angular momentum: $ e \vec{A}_{re}\hspace{2} 2 \hspace{2}\pi r_{e} %= e \hspace{2}\vec{\Phi_{0}} 2 \hspace{2}\pi = \hbar/2$.\\ Consideration of flux-quantization supports a toroidal electron model.

Alice prepares two large qubit-ensembles E1 and E2 in the following states: She individually prepares each qubit of E1 in |0> or |1>, the eigenstates of Pauli-z operator Z, depending on the outcome of an unbiased coin toss. Similarly, she individually prepares each qubit of E2 in |+> or |-> the eigenstates of Pauli-x operator X. Bob, who is aware of the above states preparation procedures, but knows neither which of the two is E1 nor Alice's outcomes of coin tosses, needs to discriminate between the two maximally mixed ensembles. Here we argue that Bob can partially purify the mixed states (E1, E2), using the information supplied by central limit theorem. We will show that, subsequently Bob can discriminate between ensembles E1 and E2 by individually rotating each qubit state about the x-axis on Bloch sphere by a random angle, and then projectively measuring Z. By these operations, the variance of sample mean of Z measurement outcomes corresponding to the ensemble E1 gets reduced. On the other hand, qubit states in E2 are invariant under the x-rotations and therefore the variance remains unaltered. Thus Bob can discriminate between the two maximally mixed ensembles. We analyse the above problem both analytically as well as numerically, and show that the latter supports the former.

We discuss finite quantum theory (FQT) developed in our previous publications and give a simple explanation that standard quantum theory is a special case of FQT in the formal limit $p\to\infty$ where $p$ is the characteristic of the ring or field used in FQT. Then we argue that FQT is a more natural basis for quantum computing than standard quantum theory.

A two-dimensional vector can be made from a constant signal component plus a randomly oriented noise component. This simple model can exploit detection and post-selection loopholes to produce Bell correlations within 0.01 of the theoretical cosine expected from quantum mechanics. The model is shown to be in accord with McEachern's hypothesis that quantum correlations are associated with processes which can provide only one bit of information per sample.

In this paper we are combining Heisenberg's uncertainty principle with Haug's suggested maximum velocity for anything with rest-mass. This leads to a suggested exact boundary condition on Heisenberg's uncertainty principle. The uncertainty in position at the potential maximum momentum for subatomic particles as derived from the maximum velocity is half of the Planck length.

By oblique reflection of circularly polarized photons on a rotating cylindrical mirror the frequency of the reflected photons is shifted against the ferquency of incident photons by nearly twice the rotational frequency $n$ of the mirror: $\Delta \nu = 2\hspace{2} n \hspace{2}\sin \alpha$, where $\alpha$ is the axial angle of incidence. $\Delta \nu$ can be substantially enhanced by multiple reflections between counter-rotating coaxial mirrors.

The ensemble interpretation attributes the wave appearances of particles to their statistical characteristics. This has increasingly interested scientists. However, the ensemble interpretation is still not a scientific theory based on mathematics. Here, based on the double-slit experiment, a mathematical framework for the ensemble interpretation is constructed. The Schrodinger equation and the de-Broglie equation are also deduced. Analysis shows that the wave appearance of particles is caused by the statistical properties of these particles; the nature of the wave function is the average least action for the particles in a position.

A suggestion is proposed to solve the dispute about light momentum in transparent materials: when photons show wave features, the momentum of light conforms to Minkowski's viewpoint; when photons show particle features, the momentum of light accords with Abraham's thought.

Abstract In this article the authors will build the model of photon in time-domain. Since photon is a very short time wave, the authors need to build it in the time domain. In this photon model, there is an emitter and an absorber. The emitter sends the retarded wave. The absorber sends advanced wave. Between the emitter and the absorber the mutual energy current is built through the combination of the retarded wave and the advanced wave. The mutual energy current can transfer the photon energy from the emitter to the absorber and hence the photon is nothing else but the mutual energy current. This energy transfer is built in 3D space, this allow the wave to go through any 3D structure for example the double slits. The authors have proved that in the empty space, the wave can be seen approximately as 1D wave and can transfer energy from one pointer to to another point without any wave function collapses. That is why the light can be seen as light line. That is why a photon can go through double slits to have the interference. The duality of photon can be explained using this photon model. The total energy transfer can be divided as self-energy transfer and the mutual energy transfer. It is possible the self-energy current transfer half the total energy and it also possible that the part of self-energy part has no contribution to the energy transferring of the photon. In the latter, the self-energy items is canceled by the advanced wave of the emitter current and the retarded wave of the absorber current or canceled by the returned waves. This return wave is still satisfy Maxwell equations or at least some time-reversed Maxwell equations. Furthermore, the authors found the photon should satisfy the Maxwell equations in microcosm. Energy can be transferred only by the mutual energy current. In this solution, the two items in the mutual energy current can just interpret the line or circle polarization or spin of the photon. The traditional concept of wave function collapse in quantum mechanics is not needed in the authors’ photon model. The authors believe the concept of the traditional wave collapse is coursed by the misunderstanding about the energy current. Traditionally, there is only the energy current based on Poynting vector which is always diverges from the source. For a diverged wave, hence, there is the requirement for the energy to collapse to its absorber. After knowing that the electromagnetic energy is actually transferred by the mutual energy current, which is a wave diverging in the beginning and converging in the end, then the wave function collapse is not needed. The concept energy is transferred by the mutual energy current can be extended from photon to any other particles for example electron. Electrons should have the similar mutual energy current to carry their energy from one place to another and do not need the wave function to collapse.

Interactions are produced, at small scale, by Lorentz transformations around extra dimensions. As a simple example, we include simultaneously a "Kaluza-Klein fth dimension" and minimal coupling in Klein-Gordon equation applied to Hydrogen (all equations can be written in dimensionless form). Instead of solving the last separable equation for f(R), we require one more eigeinvalue equation, and require that the eccentricity of the system vanishes, to deduce the energy levels. With 4 spatial dimensions, there are naturally 6 rotations and 2 angular momenta (a classical one with parity+ and a spin with parity-). The SO(4) degeneracy and Schrodinger's energy levels are deduced, but the ne structure requires a modication : we give an example with a linear equation. We observe that the extra degree of freedom naturally disappears at classical scale (objects made of a large number of elementary particles). We then observe that the quantum principle of minimal coupling (here produced by Lorentz transformations) is analogous to a modication of the metric inside the wave function. We use the corresponding metric (no coordinate singularity, the central one being naturally solved by the Lorentz transformation with extra dimensions) to describe gravitation : the deduced equation of motion reduces, in the low eld approximation, to the equation given by general relativity. More generally, extra dimensions may be usefull in particles physics : conservation of lepton numbers could be understood as conservation of momentum along other dimensions, and unconvenient divergences could be solved.

We demonstrate that if one adheres to a method akin to Dirac's method of arriving at the Dirac equation -- then, the Dirac equation is not the only equation that one can generate but that there is a whole new twenty four equations that Dirac left out. Off these new equations -- interesting is that; some of them violate C, P, T, CT, CP, PT and CPT-Symmetry. If these equations are acceptable on the basis of them flowing from the widely -- if not universally accepted Dirac prescription, then, the great riddle of why the preponderance of matter over antimatter might find a solution.are acceptable on the basis of them flowing from the widely -- if not universally accepted Dirac prescription, then, the great riddle of why the preponderance of matter over antimatter might find a solution.

We demonstrate (show) that the Dirac equation – which is universally assumed to represent only spin 1/2 particles; can be manipulated using legal mathematical operations – starting from the Dirac equation – so that it describes any general spin particle. If our approach is acceptable and is what Nature employs, then, as currently obtaining, one will not need a unique and separate equation to describe particles of different spins, but only one equation is what is needed – the General Spin Dirac Equation. This approach is more economic and very much in the spirit of unification – i.e., the tie-ing together into a single unified garment – a number of phenomenon (or facets of physical and natural reality) using a single principle, which, in the present case is the bunching together into one theory (equation), all spin particles into the General Spin Dirac Equation.

The present reading is the first in a series where we suggest a Dirac equation for the Proton. Despite its great success in explaining the physical world as we know it, in its bare form, not only is the Dirac equation at loss but fails to account e.g. for the following: (1) Why inside hadrons (Proton in this case) there are three, not four or five quarks; (2) Why quarks have fractional electronic charges; (3) Why the gyromagnetic ratio of the Proton is not equal to two as the Dirac equation requires. In the present reading, we make an attempt to answer the first question of why inside the proton, there are three, not four or five quarks.

The present reading is the second in a series where we suggest a Dirac equation for the Proton. Despite its great success in explaining the physical world as we know it, in its bare form, not only is the Dirac equation at loss but fails to account e.g. for the following: (1) Why inside hadrons there are three, not four or five quarks; (2) Why quarks have fractional charges; (3) Why the gyromagnetic ratio of the Proton is not equal to two as the Dirac equation requires. In the present reading, we make an attempt to answer the second question of why quarks have fractional charges. We actually calculate the exact values of the charges of these quarks.

The present reading is the third in series where we suggest a Dirac equation for the Proton. Despite its great success in explaining the physical world as we know it, in its bare form, not only is the Dirac equation at loss but fails to account e.g. for the following: (1) Why inside hadrons there are three, not four or five quarks; (2) Why quarks have fractional charges; (3) Why the gyromagnetic ratio of the Proton is not equal to two as the Dirac equation requires. In the present reading, we make an attempt to answer the third question of why the gyromagnetic ratio of the Proton is not equal to two as the Dirac equation requires. We show that from the internal logic of the proposed theory -- when taken to first order approximation, we are able to account for 55.7% [2.000000000] of the Proton's excess gyromagnetic ratio [3.585 694 710(50)]. The remaining 44.3% [1.585 694 710(50)] can be accounted as a second order effect that has to do with the Proton having a finite size.

Our present understanding as revealed to us from Einstein's Special Theory of Relativity (STR) and experimental philosophy, informs us that a massive particle can never ever attain the light speed barrier: c. Massive particles are (according to the STR) eternally incarcerated to travel at sub-luminal speeds. On the other hand, Einstein's STR does not forbid the existence of particles that travel at superluminal speeds. Only massless particles can travel at the speed of light and nothing else. In the present reading, we demonstrate that it should in-principle be possible to have massive particles travel at the speed of light. Our investigations suggest that all light (Electromagnetic radiation or any particle for that matter that travels at the speed of light) may very well be comprised of two massive particle-antiparticle coupled pair.

Since it was discovered some 84 years ago, the Dirac equation is understood to admit 4x1 component wavefunctions. We demonstrate here that this same equation does admit 4x4 component wavefunctions as-well.

In the year 1928, the pre-eminent British physicist -- Paul Adrien Maurice Dirac, derived his very successful equation now popularly known as the Dirac equation. This unprecedented equation is one of the most beautiful, subtle, noble and esoteric equations in physics. One of its greatest embellishments is embedded in that this equation exhibits a perfect symmetry -- which amongst others -- requires, that the Universe contain as much matter as antimatter, or that, for every known fundamental particle, there exists a corresponding antiparticle. We show here that the Dirac theory in its bare form -- without the need of the Pauli Exclusion Principle; can -- via, its internal logic -- beautifully explain the stability of the Dirac Void -- i.e., the empty Dirac Sea. There is no need for one to `uglify' Dirac's otherwise beautiful, self-contained and consistent theory by indiscriminately stuffing the Dirac vacuum with an infinite amount of invisible negative energy in-order to prevent the positive energy Electron from falling into the negative energy state.

This open letter challenges Annals of Physics' Editors and Bell's supporters on this front: in the context of Bell's theorem -- after AoP (2016:67) -- ‘it's a proven scientific fact that a violation of local realism has been demonstrated theoretically and experimentally.' We show that such claims under the Bellian canon are curtailed by its foundation on a naive realism that is known to be false; ie, under Bohr's old insight (in our terms), a test may disturb the tested system. Further: (i) We define a general all-embracing local realism -- CLR, commonsense local realism -- the union of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). (ii) Under CLR, with EPR-based variables (and without QM), a thought-experiment delivers a local-realistic account of EPRB and GHZ in 3-space. (iii) Under EPR, mixing common-sense with undergrad math/physics in the classical way so favored by Einstein, we interpret QM locally and realistically. (iv) We find the flaw in Bell's theorem: Bell's 1964:(14a) ≠ Bell's 1964:(14b) under EPRB. (v) EPR (1935) famously argue that additional variables will bring locality and causality to QM's completion; we show that they are right. (vi) Even more famously, Bell (1964) cried ‘impossible' against such variables; we give the shortest possible refutation of his claim. (vii) Using Bell's (1988:88) moot gloss on a fragment of von Neumann's work, we conclude: ‘There's nothing to Bell's theorem -- nor Bellian variants like CHSH (1969), Mermin (1990), Peres (1995); nor Bellian endorsements like those by Bricmont, du Sautoy, Goldstein et al., Maudlin, Norsen, Shimony -- it's not just flawed, it's silly; its assumptions nonsense; it's not merely false but foolish' and misleading. (viii) Our results accord with common-sense, QM, Einstein's principles, EPR's belief and Bell's hopes and expectations.

An open letter to Bellians and the Annals of Physics' Editors re -- it's a proven scientific fact: a violation of local realism has been demonstrated theoretically and experimentally -- after AoP (2016:67). EPR (1935) famously argue that additional variables will bring locality and causality to QM's completion; we show that they are right. Even more famously, Bell (1964) cried ‘impossible' against such variables; we give the shortest possible refutation of his claims. With EPR-based variables (and without QM), an old thought-experiment delivers a commonsensical locally-causal account of EPRB and GHZ in 3-space. We then name the flaw in Bell's theorem – Bell's error -- Bell's 1964:(14a) ≠ Bell's 1964:(14b) under EPRB. Thus, given Bell's (1988:88) gloss on a snippet of von Neumann's work, ‘There's nothing to Bell's theorem -- nor variants like CHSH (1969), Mermin (1990), Peres (1995) -- it's not just flawed, it's silly; not merely false but foolish.' In short, we show that the whole Bellian canon -- with its no-name brand of local realism -- is all of those, and misleading too. Under EPR, mixing common-sense with undergrad math/physics in the classical way so favored by Einstein, we interpret QM locally and realistically. We thus define a new brand of local realism -- CLR, commonsense local realism -- the union of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). Long may EPR rule OK we say.

There seems to be nothing short of a {\it double whammy} hitting the users of probability, and among them physicists, especially those involved in the foundations of quanta. First is the instant instinctual reaction that phenomena which interest one do sharply and clearly divide into the {\it dichotomy} of {\it two and only two} alternatives of being {\it either} ``deterministic", {\it or} on the contrary, being ``probabilistic". However, there is also a second, prior and yet deeper trouble, namely, the ``probabilistic" case is strongly believed to be equally clear and well-founded as is the ``deterministic" one. And the only difference seen between the two is that the latter can talk also about ``individual" phenomena, while the former can only do so about large enough ``ensembles" for which, however, it is believed to be equally clear, precise and rigorous with the ``deterministic" approach. Or briefly, ``probabilistic'' is seen as nothing else but the ``deterministic'' on the level of ``ensembles" ... \\ The fact, however, is that there is a {\it deep gap} between the empirical world of ``random" phenomena, and on the other hand, theories of ``probability". Furthermore, any attempt to bridge that gap does inevitably involve {\it infinity}, thus aggravating the situation to the extent that even today, and even if not quite realized by many, theories of ``probabilities" have a {\it shaky} foundation. \\ This paper tries to bring to the awareness of various users of ``probabilities", and among them, to physicists involved in quanta, the fact that - seemingly unknown to them - they are self-inflicted victims of the mentioned double whammy.

EPR (1935) famously argue that additional variables will bring locality and causality to QM's completion; we show that they are right. More famously, Bell (1964) cried 'impossible' against such variables; we give the shortest possible refutation of his theorem. With EPR-based variables -- and no QM -- a thought-experiment delivers common-sense locally-causal accounts of EPRB and GHZ in 3-space. We then find the flaw in Bell's theorem: Bell's 1964:(14a) does not equal Bell's 1964:(14b). Thus, at odds with EPR (and us), Bell's unrealistic theorem and its many variants (eg, Mermin, Peres) miss their mark. In short, mixing common-sense with undergrad math and physics in the classical way so favored by Einstein, we interpret QM locally and realistically. Long may EPR rule OK we say.

Rebooting Einstein's ideas about local-causality, an engineer brings local-causality to quantum theory via operators and variables in 3-space. Taking realism to be the view that external reality exists and has definite properties, his core principle is common-sense local realism (CLR): the union of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). Endorsing Einstein-separability — system X is independent of what is done with system Y that is spatially separated from X — Bell's famous mission is advanced. That is, by means of parameters λ, a more complete specification of EPRB's physics is successful. A consequent locally-causal refutation of Bell's theorem allows EPRB correlations to be explained in a classical way, in line with Einstein's ideas, without reference to Hilbert space, quantum states, etc. Conclusion: Bell's theorem is based on a mathematical error; an error in reduction is inconsistent with Bell's opening assumptions.

To the undoubted displeasure of very many detractors, this research program has heretofore focused on aspects of physics so fundamental that many of said detractors do not even acknowledge the program as physics. This paper responds to detractors' criticisms by continuing the program in the same direction and style as earlier work. We present one new quantitative result regarding the big bang and we find a particularly nice topic from fluid dynamics for qualitative treatment. A few other topics are discussed and we present quantitative results regarding the fine structure constant and the differential operator form of $\hat{M}^3$. This paper is somewhat reiterative as it calls attention to directions for further inquiry and continues to leave the hashing out of certain details to either a later effort or the eventual publication of results by those who have already hashed it out, possibly several years ago by now.

In present paper we confirm our previous result [4] that Planck constant is adiabatic invariant of electromagnetic field propagating on the adiabatically changed Finslerian manifold. Direct calculation from cosmological parameters gives value h=6x10(-27) (erg s). We also confirm that Planck constant (and hence other fundamental constants which depend on h) is varied on time due to changing of geometry. As an example the variation of the fine structure constant is calculated. Its relative variation ((da/dt)/a) consist 1.0x10(-18) (1/s). We show that on the Finsler manifold characterized by adiabatically changed geometry, classical free electromagnetic field is quantized geometrically, from the properties of the manifold in such manner that adiabatic invariant of field is ET=6x10(-27)=h. Electrodynamic equations on the Finslerian manifold are suggested. It is stressed that quantization naturally appears from these equations and is provoked by adiabatically changed geometry of manifold. We consider in details two direct consequences of the equations: i) cosmological redshift of photons and ii) effects of Aharonov -- Bohm that immediately follow from equations. It is shown that quantization of system consists of electromagnetic field and baryonic components (like atoms) is obvious and has clear explanation.

In this paper we suggest that one single fundamental particle exists behind all matter and energy. We claim that this particle has a spatial dimension and diameter equal to the Planck length and a mass equal to half of the Planck mass. Further, we will claim this particle is indivisible, that is it was never created and can never be destroyed. All other subatomic particles, in spite of having much lower masses than the Planck mass, are easily explained by the existence of such an indivisible particle. Isaac Newton stated that there had to be a fundamental particle, completely hard, that could not be broken down. He also claimed that light consisted of a stream of such particles. Newton’s particle theory was very similar to that of the ancient atomists Democritus and Leucippus. However, the atomist view of an indivisible particle with spatial dimensions has generally been pushed aside by modern physics and replaced with hypothetical point particles and the mysterious wave-particle duality.

In present paper we evaluate the fine structure constant variation which should take place as the Universe is expanded and its curvature is changed adiabatically. This changing of the fine structure constant is attributed to the energy lost by physical system (consist of baryonic component and electromagnetic field) due to expansion of our Universe. Obtained ratio (d alpha)/alpha = 1. 10{-18} (per second) is only five times smaller than actually reported experimental limit on this value. For this reason this variation can probably be measured within a couple of years. To argue the correctness of our approach we calculate the Planck constant as adiabatic invariant of electromagnetic field, from geometry of our Universe in the framework of the pseudo- Riemannian geometry. Finally we discuss the double clock experiment based on Al+ and Hg+ clocks carried out by T. Rosenband et al. (Science 2008). We show that in this particular case there is an error in method and this way the fine structure constant variation can not be measured if the fine structure constant is changed adiabatically.

In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.

The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box wavefunctions as trial wavefunctions, with the size of the box as the variation parameter, approximate eigenenergies and the corresponding eigenfunctions are obtained for the one dimensional free harmonic oscillator.

Anybody who has ever studied quantum mechanics knows that it is a very counterintuitive theory, even though it has been an incredibly successful theory. This paper aims to remove this counterintuitiveness by showing that the laws of quantum mechanics are a natural consequence of classical Newtonian mechanics combined with the digital universe hypothesis of Konrad Zuse and Edward Fredkin. We also present a possible way to test the digital universe hypothesis.

The problem with introducing the particle trajectories into Quantum Physics is the need of the violation of the Energy Conservation law. The latter law must hold, because the Noether's theorem requires it for the case of homogeneous time. Therefore, the wonder is happening, provided, that the David Bohm's theory is proved. But latter proof is there, in [M. Ringbauer et al.: Nature Physics, 2015] together with my explanation in the present manuscript. Enjoy! All rights Reserved!

The quantum energy levels of electron inside of the box with the infinite barriers at point 0 and l is considered. The situation is then extended to the thee dimensions. Quantum mechanics of such so called quantum billiard does not involve the retarded wave functions (the retarded Green functions) and it means that the quantum pressure is instantaneous at the walls of the box. The instantaneous process is equal to the action at a distance, or to the existence of the superluminal signals inside of the quantum box. The similar situation is in case of the Casimir effect between two capacitor plates.

G. Adenier and A.Y. Khrennikov (2016) show that a recent ``loophole free'' CHSH Bell experiment violates no-signaling equalities, contrary to the expected impossibility of signaling in that experiment. We show that a local realism setup, in which nature sets hidden variables based on forecasts, and which can violate a Bell Inequality, can also give the illusion of signaling where there is none. This suggests that the violation of the CHSH Bell inequality, and the puzzling no-signaling violation in the CHSH Bell experiment may be explained by hidden variables based on forecasts as well.

The electromagnetic shift of energy levels of H-atom electrons is determined by calculating the mean square amplitude of oscillation of an electron coupled to the relic photon fluctuations of the electromagnetic field. Energy shift of electrons in H-atom is determined in the framework of non-relativistic quantum mechanics. The

Fermi's golden rule is of great importance in quantum dynamics. However, in many textbooks on quantum mechanics, its contents and limitations are obscured by the approximations and arguments in the derivation, which are inevitable because of the generic setting considered. Here we propose to introduce it by an ideal model, in which the quasi-continuum band consists of equaldistant levels extending from $-\infty $ to $+\infty $, and each of them couples to the discrete level with the same strength. For this model, the transition probability in the first order perturbation approximation can be calculated analytically by invoking the Poisson summation formula. It turns out to be a \emph{piecewise linear} function of time, demonstrating on one hand the key features of Fermi's golden rule, and on the other hand that the rule breaks down beyond the Heisenberg time, even when the first order perturbation approximation itself is still valid.

In this note we are rewriting the reduced mass formula into a form that potentially gives more intuition on what is truly behind the reduced mass.

Abstract:<br> In 2008, Tomasz Paterek et al published ingenious research, proving that quantum randomness is the output of measurement experiments, whose input commands a logically independent response. Following up on that work, this paper develops a full mathematical theory of quantum indeterminacy. I explain how, the Paterek experiments imply, that the measurement of pure eigenstates, and the measurement of mixed states, cannot both be isomorphically and faithfully represented by the same single operator. Specifically, unitary representation of pure states is contradicted by the Paterek experiments. Profoundly, this denies the axiomatic status of Quantum Postulates, that state, symmetries are unitary, and observables Hermitian. Here, I show how indeterminacy is the information of transition, from pure states to mixed. I show that the machinery of that transition is unpreventable, logically circular, unitary-generating self-reference: all logically independent. Profoundly, this indeterminate system becomes apparent, as a visible feature of the mathematics, when unitarity --- imposed by Postulate --- is given up and abandoned.<br><br>Keywords:<br>foundations of quantum theory, quantum mechanics, quantum randomness, quantum indeterminacy, quantum information, prepared state, measured state, pure states, mixed states, unitary, redundant unitarity, orthogonal, scalar product, inner product, mathematical logic, logical independence, self-reference, logical circularity, mathematical undecidability.

In this paper we show that the Larmor formula at the Planck scale is simply the Planck power multiplied by $\frac{1}{2\pi}$. The Larmor formula is used to describe the total power radiated by charged particles that are accelerating or decelerating. \citet{Hau16h} has recently shown that the Coulomb's electrostatic force is the same (at least mathematically) as the gravitational force at the Planck scale. The findings in this paper strengthen the argument that electricity is not so special and that at the Planck scale, we likely only have one force and thereby only one power as well.

Ever since the celebrated 1964 paper of John Bell, the statement that "Quantum systems violate the Bell inequalities", [1,2], has a very large support among quantum physicists as well as others claiming some knowledge about quanta. Amusingly, it has so far escaped the general notice that, if indeed, quanta do violate that Bell inequalities, then - due to elementary facts of Logic - they must also violate {\it all} other valid mathematical relations, thus among them, the equation 0 = 0. Here the respective elementary facts of Logic are presented.

Recently in [3] it was shown that the so called Bell Inequalities are {\it irrelevant} in physics, to the extent that they are in fact {\it not} violated either by classical, or by quantum systems. This, as well known, is contrary to the claim of John Bell that the mentioned inequalities {\it would be} violated in certain quantum contexts. The relevant point to note in [3] in this regard is that Bell's mentioned claim, quite of a wider acceptance among quantum physicists, is due to a most simple, elementary and trivial {\it mistake} in handling some of the involved statistical data. A brief presentation, simplified perhaps to the maximum that still presents the essence of that mistake, can be found in [10], see also [9]. The present paper tries to help in finding a way to the understanding of the above by quantum physicists, an understanding which, typically, is obstructed by an instant and immense amount and variety of ``physical intuitions" with their mix of ``physics + philosophy" considerations which - as an unstoppable avalanche - ends up making a hopeless situation from one which, on occasion, may in fact be quite simple and clear, as shown in [3] to actually happen also with the Bell Inequalities story. The timeliness of such an attempt here, needless to say not the first regarding the Bell Inequalities story, is again brought to the fore due to the no less than {\it three} most freshly claimed to be fundamental contributions to the Bell Inequalities story, [4,5,13], described and commented upon in some detail in [6].

In a previous paper of this author [1], I introduced a novel way of looking at and extending at quantum field theory to a general curved spacetime satisfying mild geodesic conditions. The aim of this paper is to further extend the theory and clarify the construction from a physical point of view; in particular, we will study the example of a single particle propagating in a general external potential from two different points of view. The reason why we do this is mainly historical given that the interacting theory is after all well defined by means of interaction vertices and the Feynman propagator and therefore also applicable to this range of circumstances. However, it is always a pleasure to study the same question from different points of view and that is the aim of this paper.

The experiments, conducted by the author; demonstrate the physical equivalence between the repulsion between two powerful Neodymium magnets and reverse Casimir effect (nanoscale) and macroscopic scale (The spherical shell of actual observable Universe); and as measuring weight on an electronic balance of this repulsive force, it causes the appearance of a fictitious mass; dependent on the repulsive force between the two magnets. One of these magnets is positioned above the balance; while the other slowly magnet is positioned right in the perpendicular axis that would link the centers of both circular magnets. (Circular disks). There is no difference between this experiment and the physical results of the experiments carried out at the microscopic level and measured experimentally: The reverse Casimir effect of a conducting spherical shell. The actual comportment of the Universe to macroscopic scales; with the manifestation of an accelerated expansion and the emergence of a fictitious mass, which does not exist; the so-called dark matter. The three physical phenomena with identical results are equivalent; so they could have a common physical origin. In the article, we have inserted links to videos uploaded to youtube that let you see the whole experimental process and its results. The last experiment is made with other balance; more shielded against interference magnetism and the magnet placed over the balance. The videos are explained in Spanish. They are welcome English subtitles.

We offer a new look on multiparticle theory which was initiated in a recent philosophical paper [1] of the author. To accomplish such feature, we start by a revision and extension of the single particle theory as well relativistically as nonrelativistically. Standard statistics gets an interpre- tation in terms of symmetry properties of the two point function and any reference towards all existing quantization schemes is dropped. As I have repeatedly stated and was also beautifully explained by Weinberg, there is no a priori rationale why quantum field theory should take the form it does in a curved spacetime; there is no reason why the straightforward generalizations of the Klein Gordon and Dirac theory should have some- thing to do with the real world. Perhaps, if we were to look differently at the flat theory, a completely satisfactory class of relativistic quantum theories would emerge. These may not have anything to do with quantum fields at all except in some limit.

In this paper the design and coding of a local hidden variables model is presented that violates the Clauser, Horne, Shimony and Holt, $|$CHSH$|$ $\leq 2$ inequality. Numerically we find with our local computer program, CHSH $\approx 1 + \sqrt{2}$.

The concept of "potentia" as proposed by Heisenberg to understand the structure of quantum mechanics, has just remained a fanciful speculation as of now. In this paper we provide a physically consistent and a mathematically justified ontology of this model based on a fundamental role played by the discrete subgroups of the relevant Lie groups. We show that as such, the space of "potentia" arises as a coexisting dual space to the real three dimensional space, while these two sit piggyback on each other, such that the collapse of wave function can be understood in a natural manner. Quantum nonlocality and quantum jumps arise as a natural consequence of this model.

The road on the foundations of science in general consists in (a) making precise what the assumptions are one makes resulting from our measurements (b) holding a “good” balance between theoretical assumptions and genericity of predictions (c) saying as precisely as possible what you mean. Unfortunately, recent work where these three criteria are met is scarce and I often encounter situations where physicists talk about different things in the same words or the other way around, identify distinct concepts (even without being aware of it), or introduce unnecessary hypothesis based upon a too stringent mathematical interpretation of some observation. In this work, I will be as critical as possible and give away those objections against modern theories of physics which have become clear in my mind and therefore transcend mere intuition. All these objections result from the use of unclear language or too stringent assumptions on the nature of reality. Next, we weaken the assumptions and discuss what I call process physics; it will turn out that Bell’s concerns do find a natural solution within this framework.

We unify the Bohr energy formula with the Leibniz continuity theorem in order to get the aufbau of photon. During the electron transition in this model the photon is created by the continual way. The oscillation of parity of K-meson is discussed.

De Broglie waves were originally derived from the Lorentz Transformation of a standing wave, $e^{-i \omega t}$, that has no space dependence. It is shown here that a suitable, physically reasonable, standing wave can be constructed from physical waves that propagate at c, subject to the condition that any field line of the wave vector exists on the surface of a sphere at rest in the comoving frame. This result contradicts the classical picture of a point particle emitting a far field that propagates radially away from it, and it is argued that, while the present construction of de Broglie waves is both local and realistic, Bell Inequalities cannot be derived in de Broglie's context.

Errors in the paper "Black-body laws derived from a minimum knowledge of Physics" are described. The paper claims that the density of the thermal current in any number of spatial dimensions is proportional to the temperature to the power of 2(n-1)/(n-2), where n represents the number of spatial dimensions. However, it is actually proportional to the temperature to the power of n + 1. The source of this error is in the claim that the known formula for the fine-structure constant is valid for any number of spatial dimensions, and in the subsequent error that the physical dimensions of Planck's constant become dependent on n.

Today's science provides quite a lean picture of time as a mere geometric evolution parameter. I argue that time is much richer. In particular, I argue that besides the geometric time, there is creative time, when objective chance events happen. The existence of the latter follows straight from the existence of free-will. Following the french philosopher Lequyer, I argue that free-will is a prerequisite for the possibility to have rational argumentations, hence can't be denied. Consequently, science can't deny the existence of creative time and thus that time really passes.

We report some nonsmooth dynamics of a Bloch state in a one-dimensional tight binding model with the periodic boundary condition. After a sudden change of the potential of an arbitrary site, quantities like the survival probability of the particle in the initial Bloch state show cusps periodically, with the period being the Heisenberg time associated with the energy spectrum. This phenomenon is a nonperturbative counterpart of the nonsmooth dynamics observed previously (Zhang and Haque, arXiv:1404.4280) in a periodically driven tight binding model. Underlying the cusps is an exactly solvable model, which consists of equally spaced levels extending from $-\infty$ to $+\infty$, between which two arbitrary levels are coupled to each other by the same strength.

In this work gravicommunication (GC) is introduced, as a new form of communication (different from the gravitational waves), which involves gravitons (elementary particles of gravitation). This research is based on quantum modification of the general relativity. The modification includes effects of production /absorption of gravitons, which turn out to have small, but finite mass and electric dipole moment. It is shown, that such gravitons form the dipole Bose-Einstein condensate, even for high temperature. The theory (without fitting parameters) is in good quantitative agreement with cosmological observations. In this theory we got an interface between gravitons and ordinary matter, which very likely exist not only in cosmos, but everywhere, including our body and, especially, our brain. Subjective experiences are considered as a manifestation of that interface. A model of such interface is presented and some new experimentally verifiable aspects of natural neural systems are considered. According to the model, GC can be superluminal, which will solve the problem of quantum entanglement. Probable applications of these ideas include health (brain stimulation), new forms of communication, computational capabilities, energy resources and weapons. Potential social consequences of these developments can be comparable with the effects of discovery and applications of electricity. Some developed civilizations in the universe may already master gravicommunication (with various applications) and so should we.

In this article some observed objects in the experiment and the way of compatibility classical relationships between empirical observations from the view points of the plasma physics have been investigated, the plasma physics equations rooted in classical physics and quantum mechanics equations; given that the possibility of separation and direct observation the spin of free electron is one of the most discussable issues in the quantum philosophy during the last few decades, this paper has been studied some of technical and scientific issues of the experiment.

Packaged entanglement states encapsulate the necessary physical quantities as an entirety for completely identifying the particles. They are important for particle physics and matter teleportation. Here we proposed the new packaged entanglement states (of two particles and more than two particles) in which the charge does not conserve in the process of wave function collapse. We also discussed the particle teleportation and entanglement transfer using the new packaged entanglement states. It is shown that a particle always converts into its conjugating particle during the particle teleportation process.

Abstract<br>I show that, in general, the Fourier transform is necessarily self-referent and logically circular.<br><br>Keywords<br> self-reference, logical circularity, mathematical logic, Fourier transform, vector space, orthogonality, orthogonal, unitarity, unitary, imaginary unit, foundations of quantum theory, quantum mechanics, quantum indeterminacy, quantum information, prepared state, pure state, mixed state, wave packet, scalar product, tensor product.

Abstract: As opposed to the classical logic of true and false, when Elementary Algebra is treated as a formal axiomatised system, formulae in that algebra are either provable, disprovable or otherwise, logically independent of axioms. This logical independence is well-known to Mathematical Logic. Here I show that the imaginary unit, and by extension, all complex numbers, exist in that algebra, logically independently of the algebra's axioms. The intention is to cover the subject in a way accessible to physicists. This work is part of a project researching logical independence in quantum mathematics, for the purpose of advancing a complete theory of quantum randomness. Elementary Algebra is a theory that cannot be completed and is therefore subject to Gödel's Incompleteness Theorems.<br><br>keywords: mathematical logic, formal system, axioms, mathematical propositions, Soundness Theorem, Completeness Theorem, logical independence, mathematical undecidability, foundations of quantum theory, quantum mechanics, quantum physics, quantum indeterminacy, quantum randomness.

Abstract Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures are included so that quantum corrections and modifications to Navier-Stokes behavior can be derived. This leads to a small deviation in rigid body rotation for a cylindrically bound gas and the internal energy changes associated with vorticity give deviations in the Reynolds’ transport theorem. Some macroscopic observable features arising from this include variations in the specific heat, an anisotropic correction to thermal conductivity and a variation in optical scattering as a function of the declination from the axis of local vorticity. The improvements in magneto-optical traps suggests some interesting experiments to be done in higher temperature regimes where they are not usually employed. It is argued that the finite lifetime of observed vortices in ultracold bosonic gases is only apparent and these volume excluding structures persist in generating angular momentum and pressure in the cloud in a non-imageable form.

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory. As a consequence, coordinate wave functions of photons emitted by stars have cosmic sizes. This results in a paradox because predictions of the theory contradict observations. The reason of the paradox and its resolution are discussed.

The attempt of Schrödinger to describe elementary particles by wave packets is repeated by means nowadays available, that is to say, by applying the results of quantum field theory and especially by the explicit consideration of interaction.

Casimir's celebrated result that the conducting plates of an unpowered rectangular cavity attract each other with a pressure inversely proportional to the fourth power of their separation entails an unphysical unbounded pressure as the plate separation goes to zero. An unphysical result isn't surprising in light of Casimir's unphysical assumption of perfectly conducting plates that zero out electric fields regardless of their frequency, which he sought to counteract via a physically foundationless discarding of the pressure between the cavity plates when they are sufficiently widely separated. Casimir himself, however, emphasized that real metal plates are transparent to sufficiently high electromagnetic frequencies, which makes removal of the frequency cutoff that he inserted unjustifiable at any stage of his calculation. Therefore his physically groundless discarding of the large-separation pressure isn't even needed, and when it is left out a constant attractive pressure between cavity plates exists when their separation is substantially larger than the cutoff wavelength. The intact cutoff furthermore implies zero pressure between cavity plates when their separation is zero, and also that Casimir's pressure is merely the subsidiary lowest-order correction term to the constant attractive pressure between cavity plates that is dominant when their separation substantially exceeds the cutoff wavelength.

The general n-point information (n-pi) are introduced and equations for them are considered. The role of right and left invertible interaction operators occurring in these equations together with their interpretation is discussed. Some comments on approximations to the proposed equations are given. The importance of positivity conditions and a possible interpretation of n-pi in the case of their non-compliance, for essentially nonlinear interactions (ENI), are proposed. A language of creation, annihilation and projection operators which can be applied in classical as well as in quantum case is used. The role of the complex numbers and functions in physics is also a little elucidated.

Recently I proposed the linguistic interpretation of quantum mechanics, which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized. Hence, I propose the justification of the projection postulate in the linguistic interpretation.

Entanglement states are important for both basic research and applied research. However, these entanglement states usually relate to one or several of the particles' physical quantities. Here we theoretically show that a particle-antiparticle pair can form packaged entanglement states which encapsulate all the necessary physical quantities for completely identifying the particles. The particles in the packaged entanglement states are hermaphroditic and indeterminate. Thereafter, we gave a possible experimental scheme for testing the packaged entanglement states. Finally, we proposed a protocol for teleporting a particle to an arbitrarily large distance using the packaged entanglement states. These packaged entanglement states could be important for particle physics and useful in matter teleportation, medicine, remote control, and energy transfer.

The purpose of this paper is two-fold. First, we would like to write down algebraic expression for the wave function of general excited state of harmonic oscillator which doesn't include derivative signs (this is to be contrasted with typical physics textbook which only gets rid of derivative signs for first few excited states, while leaving derivatives in when it comes to Hermite polynomial for general n). Secondly, we would like to write similar expression for two dimensional case as well. In the process of tackling two dimensions, we will highlight the interplay between Cartesian and polar coordinates in 2D in the context of an oscillator. All of the above mentioned results have probably been derived by others but unfortunately they are not easily available. The purpose of this paper is to make it easier for both students and general public to look up said results and their derivations, should the need arise. We also attempt to illustrate different angles from which one could look at the problem and this way encourage students to think more deeply about the material.

The eight geometric objects of the electron impedance model, as fortuitous happenstance would have it, are those of the 3D Pauli subalgebra of the geometric interpretation of Clifford algebra. Given that impedance is a measure of the amplitude and phase of opposition to the flow of energy, and that quantum phase is the gauge parameter in quantum mechanics, one might consider an approach in which elements of an electron gauge group would be the phase shifters, the impedances of interactions between these geometric objects. The resulting 4D Dirac algebra is briefly examined in relation to the E8 exceptional Lie group.

Abstract<br>The homogeneity symmetry is re-examined and shown to be non-unitary, with no requirement for the imaginary unit. This removes symmetry, as reason, for imposing unitarity (or self-adjointness) -- by Postulate. The work here is part of a project researching logical independence in quantum mathematics, for the purpose of advancing a full and complete theory of quantum randomness.<br><br>Keywords<br>foundations of quantum theory, quantum physics, quantum mechanics, wave mechanics, Canonical Commutation Relation, symmetry, homogeneity of space, unitary, non-unitary, unitarity, mathematical logic, formal system, elementary algebra, information, axioms, mathematical propositions, logical independence, quantum indeterminacy, quantum randomness.

Recently it was proposed that quantum mechanics, if applied to macroscopic systems, would necessarily include a form of fortune telling or psychic phenomena. In this article, this claim is presented using formal quantum mechanics methods, and the results are analysed and found to be possible.

The homogeneity symmetry is re-examined and shown to be non-unitary. This is motivated by the prospect that logical independence in elementary algebra, entering quantum mathematics, will constitute the basis for a theory explaining quantum randomness. Keywords: foundations of quantum theory, quantum physics, quantum mechanics, wave mechanics, Canonical Commutation Relation, symmetry, homogeneity of space, unitary, non-unitary, unitarity, mathematical logic, formal system, elementary algebra, information, axioms, mathematical propositions, logical independence, quantum indeterminacy, quantum randomness.

Abstract As opposed to the classical logic of true and false, when elementary algebra is treated as a formal axiomatised system, formulae in that algebra are either provable, disprovable or otherwise, logically independent of axioms. This logical independence is well-known to Mathematical Logic. The intention here is to cover the subject in a way accessible to physicists. This work is part of a project researching logical independence in quantum mathematics, for the purpose of advancing a complete theory of quantum randomness.<br><br><b>Keywords</b> mathematical logic, formal system, axioms, mathematical propositions, Soundness Theorem, Completeness Theorem, logical independence, mathematical undecidability, foundations of quantum theory, quantum mechanics, quantum physics, quantum indeterminacy, quantum randomness.

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics.

We give an explicit matrix representation for the Hamiltonian of the Ising model in mutually orthogonal external magnetic fields, using as basis the eigenstates of a system of non-interacting spin~$1/2$ particles in external magnetic fields. We subsequently apply our results to obtain an analytical expression for the ground state energy per spin, to the fourth order in the exchange integral, for the Ising model in perpendicular external fields.

In this note, I analyse the code and the data generated by M. Fodje's simulation programs (written in Python, published in 2013 on Github) epr-simple and epr-clocked using appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH. The experimental efficiencies turn out to be approximately eta = 81% and gamma = 55% respectively, and the observed value of CHSH is (of course) well within the adjusted bounds. Fodjes' detection loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is very close to optimal, but the model shares the same defect as Pearle's - the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model, and the trick he uses is actually rather simple. But it does not lead to the optimal efficiency. Note: this is version 5 of a paper originally written in 2014. I recently submitted version 4 to the journal "Entropy" where it got rejected, rightly so. It has the status of "lab notes", a documentation of one or two experiments whose results are interesting but not worth publishing on their own. I will extract the few jewels in this work later and use them in a more ambitious paper about the results of the bigger research project of which these experiments were a small part.

In this paper the design and coding of a local hidden variables model is presented that violates the CHSH criterion in size larger than $1+\sqrt{2}$.

In the paper it is demonstrated that the particular form of CHSH S=E{A(1)[B(1)-B(2)]-A(2)[B(1)+B(2)]} with S maximally 2 and minimally -2, for A and B functions in {-1,1}, is not generally valid for local models. The nonzero probability that local hidden extra parameters violate the CHSH, is not eliminated with basic principles derived from the CHSH.

In 2015 the answer is still no. However this paper will look at what current physics has to say on this topic and what further questions need to be put forward to advance our enquiries. This work is a modified compilation of several posts that were originally published in the author's blogsite [1] on Gravity Control Propulsion (GCP) looking at several papers that deal with related topics with some ideas and speculations for further research.

We discuss at length the dynamical behavior of Grover's search algorithm for which all the Walsh-Hadamard transformations contained in this algorithm are exposed to their respective random perturbations inducing the augmentation of the dimension of the search space. We give the concise and general mathematical formulations for approximately characterizing the maximum success probabilities of finding a unique desired state in a large unsorted database and their corresponding numbers of Grover iterations, which are applicable to the search spaces of arbitrary dimension and are used to answer a salient open problem posed by Grover [L. K. Grover, Phys. Rev. Lett. \textbf{80}, 4329 (1998)].

Based on exact theory of quantum transition and precise numerical calculations, this paper demonstrates quantitatively that the Urbach tail in the diagram of light absorption coefficient of semiconductor versus photon energy are caused by energy nonconservation (ENC). This paper also points out that the light absorption is a non-example of Fermi golden rule; due to ENC the estimations on the dark energy and dark mass in our universe might be no longer to have big significance; ENC is a non-example of the first and second thermodynamic law.

Abstract We propose a space-time interaction principle (StIP) which states any particle with mass m will involve a random motion without friction, due to random impacts from space-time. Every impact changes the amount \hbar for an action of the particle. According to the principle, firstly, we prove the interaction coefficient must be \Re=\frac{\hbar}{2m_{ST}} deriving from Langevin's equation to the corresponding Fokker-Planck Hamiltonian, where m_{ST} is a space-time sensible mass of the particle. We can derive that an equation of motion for the particle will be the Schr\ddot{o} dinger equation, and prove that the space-time sensible mass m_{ST} reduce to the inertial mass in the non-relativistic quantum mechanics. Secondly, we show that there must exist the smallest mass \bar{m}_{ST} as the minimum of space-time sensible mass, provided the speed of light in vacuum as the maximum speed due to the postulation of special relativity. Furthermore, we estimate a magnitude of this \bar{m}_{ST} from microwave background radiation. Thirdly, an interpretation of Heisenberg's uncertainty principle is suggested, with a stochastic origin of Feynman's path integral formalism. It is shown that we can construct a physical picture distinct from Copenhagen interpretation, and reinvestigate the nature of space-time and reveal the origin of quantum behaviours from the materialistic point of view.

The discrimination of quantum operations is an important subject of quantum information processes. For the local distinction, existing researches pointed out that, since any operation performed on a quantum system must be compatible with no-signaling constraint, local discrimination between quantum operations of two spacelike separated parties cannot be realized. We found that, however, local discrimination of quantum measurements may be not restricted by the no-signaling if more multi-qubit entanglement and selective measurements were employed. In this paper we report that local quantum measurement discrimination (LQMD) can be completed via selective projective measurements and numerous seven-qubit GHZ states without help of classical communication if both two observers agreed in advance that one of them should measure her/his qubits before an appointed time. As an application, it is shown that the teleportation can be completed via the LQMD without classical information. This means that the superluminal communication can be realized by using the LQMD.

The dielectric with index of refraction n is inserted in the Planck blackbody. The spectral formula for photons in such dielectric medium and the equation for the temperature of photons is derived. The new equation is solved for the constant index of refraction. The photon flow initiates the osmotic pressure of he Debye phonons. The dielectric crystal surface works as the osmotic membrane with the Maxwell demonic refrigerator. Key words: Thermodynamics, blackbody, photons, phonons, dielectric medium, dispersion.

The discrimination of quantum operations is an important subject of quantum information processes. For the local distinction, existing researches pointed out that, since any operation performed on a quantum system must be compatible with no-signaling constraint, local discrimination between quantum operations of two spacelike separated parties cannot be realized. We found that, however, local discrimination of quantum measurements may be not restricted by the no-signaling if more multi-qubit entanglement and selective measurements were employed. In this paper we report that local quantum measurement discrimination (LQMD) can be completed via selective projective measurements and numerous seven-qubit GHZ states without help of classical communication if both two observers agreed in advance that one of them should measure her/his qubits before an appointed time. As an application, it is shown that the teleportation can be completed via the LQMD without classical information. This means that the superluminal communication can be realized by using the LQMD.

In this article we consider the variant of quantum mechanics (QM) which is based on the non-realism. There exists the theory of the modified QM introduced in [1] and [2] which is based on the non-realism, but it contains also other changes with respect to the standard QM (stQM). We introduce here the other non-realistic modification of QM (n-rQM) which contains the minimal changes with respect to stQM. The change consists in the replacement of the von Neumann`s axiom (ensembles which are in the pure state are homogeneous) by the anti-von Neumann`s axiom (any two different individual states must be orthogonal). This introduces the non-realism into n-rQM. We shall show that experimental consequences of n-rQM are the same as in stQM, but these two theories are substantially different. In n-rQM it is not possible to derive (using locality) the Bell inequalities. Thus n-rQM does not imply the non-locality (in contrast with stQM). Because of this the locality in n-rQM can be restored. The main purpose of this article was to show what could be the minimal modification of QM based on the non-realism, i.e. that the realism of stQM is completely contained in the von Neumann's axiom.

In 2007, and in a series of later papers, Joy Christian claimed to refute Bell's theorem, presenting an alleged local realistic model of the singlet correlations using techniques from geometric algebra (GA). Several authors published papers refuting his claims, and Christian's ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell's theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian claims to have a mathematical counterexample to a purely mathematical theorem. Each new version of Christian's model used new devices to circumvent Bell's theorem or depended on a new way to misunderstand Bell's work. These devices and misinterpretations are in common use by other Bell critics, so it useful to identify and name them. I hope that this paper can serve as a useful resource to those who need to evaluate new "disproofs of Bell's theorem". Christian's fundamental idea is simple and quite original: he gives a probabilistic interpretation of the fundamental GA equation a.b = (ab + ba)/2. After that, ambiguous notation and technical complexity allows sign errors t be hidden from sight, and new mathematical errors can be introduced.

We show that the complex number structure of the probability allows to express explicitly the relationship between the energy function H and the Laplace principle of equal ignorance (LPEI). This nonlinear relation- ship reflecting the measurement properties of the considered systems, to- gether with the principle of causality and Newton principle separating the dynamics from initial conditions, lead to the linear Schrodinger equation with the Max Born interpretation, for micro and macro systems!

From the dichotomy "nonlocality vs non-realism" which is the consequence of Bell Inequalities (BI) we shall choose the non-realism. We shall present here the modified Quantum Mechanics (modQM) in the axiomatic form. ModQM was introduced in [5] and we shall show its non-realism in the description of an internal measurement process. ModQM allows the restoration of locality, since BI cannot be derived in it. In modQM it is possible to solve: the measurement problem, the collapse problem, the problem of a local model for EPR correlations (see[5]). ModQM is a unique explicit realization of non-realism in QM. ModQM should be preferred as an alternative to the standard QM mainly since it restores the locality.

<b>Abstract:</b> I give a short explanation of how quantum mathematics representing pure states, is logically distinct from the mathematics of mixed states. And further: how standard quantum theory easily shows itself to contain logical independence. This work is part of a project researching logical independence in quantum mathematics, for the purpose of advancing a complete theory of quantum randomness.<br><br><b>Keywords:</b> quantum mechanics, quantum indeterminacy, quantum information, prepared state, wave packet, unitary, orthogonal, scalar product, mathematical logic, arithmetic, formal system, axioms, Soundness Theorem, Completeness Theorem, logical independence, mathematical undecidability, semantics, syntax.

The challenge of this essay was to demonstrate that the units of Planck’s constant are not [J x s]. Borrowing from the logic of the calibration, an attempt was made to find a complete set of small scale measuring sticks for each of time, space, mass, charge and temperature. This however was not possible unless we let the units of Planck’s constant be [J]. It appears that Planck et al forgot to incorporate measure-time into the famous energy equation, E = hν. The extra unit of [s] that is normally assigned to h actually belongs to a previously hidden measure-time variable. This logic suggests that Planck’s constant is an energy constant and not an action constant. After correcting this error, a complete set of unit measuring sticks, calibrated to the time scale of the cycle was calculated. A self-similar unit set was then calibrated to the time scale of the second. The scalability and self-similarity of these unit sets opens the door to the fractal paradigm, one of the main motivations for this research. This small change to the units of Planck’s constant has far reaching implications. All equations that contain h need to be reevaluated. All interpretations founded in unit analysis need to be reexamined. Much work still needs to be done to vindicate this approach.

For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of an accumulation-to-threshold process whose outcomes give predictions that are nearly identical to the given quantum theory. The model is neither local nor causal in spacetime, but is both local and causal is in a non-observable path space. The probabilistic nature of the squared wavefunction is a natural consequence of the model. We verify the model with simulations, and we discuss possible discrepancies from conventional quantum theory that might be detectable via experiment. Finally, we discuss the physical implications of the model.

It is argued that the lesson we should learn from Bell inequalities (BI) is not that Quantum Mechanics (QM) is nonlocal, but that QM contains an error which must be corrected. 1

In this paper we identify the superposition principle as a main source of problems in QM (measurement, collapse, non-locality etc.). Here the superposition principle for individual systems is substituted by the antisuperposition principle: no non-trivial superposition of states is a possible individual state (for ensembles the superposition principle is true). The modified QM is based on the anti-superposition principle and on the new type of probability theory (Extended Probability Theory [1]), which allows the reversible Markov processes as models for QM. In the modified QM the measurement is a process inside of QM and the concept of an observation of the measuring system is defined. The outcome value is an attribute of the ensemble of measured systems. The collapse of the state is substituted by the Selection process. We show that the derivation of Bell’s inequalities is then impossible and thus QM remains a local theory. Our main results are: the locality of the modified QM, the local explanation of EPR correlations, the non-existence of the wave-particle duality, the solution of the measurement problem. We show that QM can be understood as a new type of the statistical mechanics of many-particle systems.

The Heisenberg uncertainty principle is a consequence of the postulate that coordinate and momentum representations are related to each other by the Fourier transform. This postulate has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. We argue that the postulate is based neither on strong theoretical arguments nor on experimental data. A position operator proposed in our recent publication resolves inconsistencies of standard approach and sheds a new light on important problems of quantum theory. We do not assume that the reader is an expert in the given field and the content of the paper can be understood by a wide audience of physicists.

Abstract I comment on the background meaning, beneath Boolean encodings, used in the paper by Tomasz Paterek et al. Keywords foundations of quantum theory, quantum mechanics, quantum randomness, quantum indeterminacy, quantum information, prepared state, measured state, unitary, orthogonal, scalar product, mathematical logic, logical independence, mathematical undecidability. DOI: 10.13140/2.1.4703.4883

By modeling both the atom and the photon as capacitors, the correct energy levels are easily produced via extrapolation from Maxwell's, Gauss', Coulomb's and Ohm's laws — without the need to inject Planck's constant into the equation ad-hoc. In the case of the photon, Einstein's photoelectric equation is formulated as a result, with Planck's constant consequently occurring as an aggregate of fundamental constants. Analysis of these equations lends credence to Planck's fervent and controversial personal dogma that the constant which he himself had discovered is nothing but “a mathematical trick”. Further analysis shows that this model reconciles the wave-particle duality; wherein the wave properties of light and matter produce the particle-like aspects as a result of the laws of electrical engineering in conjunction with the uncertainty principle and Schrödinger's wave equations.

Quantum criticality is one of the corner stone assumptions of TGD. The value of Kähler coupling strength fixes quantum TGD and is analogous to critical temperature. TGD Universe would be quantum critical. What does this mean is however far from obvious and I have pondered the notion repeatedly both from the point of view of mathematical description and phenomenology. Superfluids exhibit rather mysterious looking effects such as fountain effect and what looks like quantum coherence of superfluid containers which should be classically isolated. These findings serve as a motivation for the proposal that genuine superfluid portion of superfluid corresponds to a large h_eff phase near criticality at least and that also in other phase transition like phenomena a phase transition to dark phase occurs near the vicinity.

A new variation on the Copenhagen interpretation of quantum mechanics is introduced, and its effects on the evolution of the Universe are reviewed. It is demonstrated that this modified form of quantum mechanics will produce a habitable Universe with no required tuning of the parameters, and without requiring multiple Universes or external creators.

A definition of G is derived using the product of two Planck point masses and a definition of hbar based on the speed of light in vacuum and geometry. The theoretical value of G is found to be 6.74981057667161 x 10^-11 m^3 kg^-1 s^-2 yielding a relative accuracy error of the CODATA 2010 G-value of -1.1255%. One experiment resulted in a value with a smaller relative accuracy error than the CODATA 2010 G-value of -0.5098%. Both rest and relativistic mass product equations are derived. These equations relate the relative spacetime spin frequency w_s, the relative orbital frequency w_o and (relativistic equation only) the Lorentz factor y describing relative linear speed of two bodies to the mass product. The Planck mass is a special case mass with w_sw_o = w_planck^2 = 1 s^-2. The theoretical value of the Planck mass was found to be 2.16039211144077 x 10^-8 kg. The relative accuracy error of the CODATA 2010 Planck mass value is 0.7461%. This error is attributed to use of the different definition of hbar. When derived from both hbar and G constants as well as the rest mass product equation, three kilogram unit definition candidates are all inconsistent. The candidate derived from the rest mass product equation is the only candidate that has equal second and meter exponents suggesting a kind of symmetry. This definition is considered the nominal kilogram unit definition. The other two candidates are considered to be artifacts of the hbar and G constants.

A deeper understanding of why the reduced Planck constant and Planck constant ("Planck constants") have the values they have as determined by experiments is developed. New definitions of the Planck constants are arrived at using the speed of light in vacuum and geometric considerations. The kilogram SI base unit is found to be derived from the SI base units second and meter. The values of the Planck constants determined by experiments and published by CODATA (2010) are found to both have a relative accuracy error of 0.3552%. A new kilogram definition is proposed and it is argued that since the kilogram will then be a derived SI unit, the kilogram should not be considered an SI base unit anymore.

We derive by the Schwinger source theory method, the power spectrum of photons, generated by charged particle moving within 2D sheet, with index of refraction n. Some graphene-like structures, for instance graphene with implanted ions, or, also 2D-glasses, are dielectric media, enabling the experimental realization of the Vavilov-Cherenkov radiation. The relation of the Vavilov-Cherenkov radiation to LED, where the 2D the additional dielectric sheet is the integral part of LED, is discussed. It is not excluded that LEDs with the 2D dielectric sheets will be the crucial components of detectors in experimental particle physics. 1 Introduction

The task to be carried out should be clear from the title. One motivation for this endeavour is coming from the fact that the usual version of quantum field theory is not acceptable. In the paper, above all, three intentions are pursued (a) an adequate consideration of the interaction (b) a proof that the means of classical field theory are sufficient (c) a new attempt to describe particles by stable wave packets.

In an earlier reading, we argued from a physical and number theoretic standpoint that an upper bound speed limit such as the speed of light implies the existence of a lower limit to the duration of events in the Universe. Consequently, this leads to a minimum characteristic length separation for events in the Universe. Herein, we argue that matter and energy that is in compliance with and in observance of the upper bound light speed limit is governed by the lower limiting uncertainty principle of Professor Werner Heisenberg. If there is a lower limiting uncertainty principle, we ask the natural and logical question 'What would an upper bound uncertainty principle mean?' We come to the interesting conclusion that an upper bound uncertainty principle must apply to particles that travel at speeds, equal to, or greater than the speed of light. Further, we argue that consequently, a tachyon must exist in a permanent state of confinement and must be intrinsically and inherently unstable in which event it oscillates between different states. These two requirements place quarks in a position to be good candidates for tachyons.

Quantum Electrodynamics (QED) is built on the original Dirac equation, an equation that exhibits perfect symmetry in that it is symmetric under charge conjugation (C), space (P) and time (T) reversal and any combination of these discrete symmetries. We demonstrate herein that the proposed Lorentz invariant Curved Spacetime Dirac Equations} (CSTD-Equations), while they obey (CPT) and PT-Symmetries, these equations readily violate C, P, T, CP and CT-Symmetries. Realizing this violation, namely the C-Violation, we take this golden opportunity to suggest that the Curved Spacetime Dirac Equations may help in solving the long standing riddle and mystery of the preponderance of matter over antimatter. We come to the tentative conclusion that if these CSTD-Equations are to explain the preponderance of matter over antimatter, then, photons are to be thought of as described by the flat version of this set of equations, while ordinary matter is to be explained by the positive and negatively curved spacetime versions of this same set of equations.

A semiclassical model of the electron is presented based on the Principle of Helical Motion (“A free electron always moves at the speed of light following a helical motion, with a constant radius, and with the direction of movement perpendicular to the rotation plane”). This model interprets the Zitterbewegung as a real motion that causes rotation of the electron spin and its magnetic moment. Based on this model, the quantum magnetic flux and quantum Hall resistance are obtained as parameters of the electron and special relativity theory is derived from the helical motion of the electron. Finally, a fix is proposed for the De Broglie’s wavelength that questions the very validity of the Dirac equation.

Justifying a local hidden variable theory requires an explanation of Bell's inequality violation. Ever since Bell derived the inequality to test the classical prediction on the correlation of two spin-1/2 particles, many experiments have observed the violation, and thus concluded against the local realism, while validating the non-locality of quantum entanglement. Still, many scientists remain unconvinced of quantum entanglement because the experiments have loopholes that could potentially allow a local realistic explanation. Upholding the local realism, this paper introduces how a precession of the spin would produce a cosine-like correlation function, and furthermore how it would also contribute to a fair sampling loophole. Simulating the precession in Monte Carlo method reveals that it can explain the observed Bell's violation using only classical mechanics.

In this work the usual formulation of the variational methods of Clas- sical Mechanics is slightly modified by describing space as an interface implementing instructions: these instructions, in the form of bit strings, determine the existence and the dynamics of classical systems and are global – that is, their information content is present at every point of space. These changes are then carried over to Feynman’s path integral formulation of non-relativistic Quantum Mechanics by recurring to the quantum superposition principle. The information content of the instructions is ex- panded to include spin; it then follows an interpretation within this framework of the collapse of the wave function in terms of splitting and merging of information and, as an illustration, of Wheeler’s delayed choice experiment.

Some variants of quantum theory theorize dogmatic “unimodal” states-of-being, and are based on hodge-podge classical-quantum language. They are based on <i>ontic</i> syntax, but <i>pragmatic</i> semantics. This error was termed semantic inconsistency [1]. Measurement seems to be central problem of these theories, and widely discussed in their interpretation. Copenhagen theory deviates from this prescription, which is modeled on experience. A <i>complete</i> quantum experiment is “<i>bimodal</i>”. An experimenter <i>creates</i> the system-under-study in <i>initial</i> mode of experiment, and <i>annihilates</i> it in the <i>final</i>. The experimental <i>intervention</i> lies beyond the theory. I theorize most rudimentary bimodal quantum experiments studied by Finkelstein [2], and deduce “bimodal probability density” π = |ψin>⊗<φfin| to represent <i>complete</i> quantum experiments. It resembles core insights of the Copenhagen theory.

Because of found mistakes, which we are lazy to correct, we need to check and recheck the foundations of Physics. As example of mistakes: "all" scientists used solution of dust collapse almost century, but it was wrong [Journal of Cosmology, 6, 1473-84, 2010]. Honest work on the errors, as I understand, has not begun. You postpone everything until the Second Coming? But God speaks: Matthew 25:26.

A critical inspection of quantum field theory will reveal that quantum field theory can be reconstructed only by means of classical field theory. In detail the following six assertions are claimed and proved: (1) Perturbation theory can be achieved by means of classical field theory. (2) Particles that are independent of one another are not correlated. This is especially true for the ingoing particles of scattering processes. (3) Outgoing particles in scattering processes are correlated. But the usual justification of quantum statistics is faulty. (4) In quantum field theory there is an amazing multitude of particle concepts. But a concise description of real existing elementary particles is lacking. (5) The path integral representation is not clearly defined in the particle picture of quantum mechanics. In the wave picture it is only another description of the expansion of a quantum state. (6) Functional representation is nothing else than a comprehensive version of perturbation theory.

Commonsense local realism (CLR) is the fusion of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). Advancing our case for a wholly CLR-based quantum mechanics, we use undergraduate maths and logic to factor the quantum entanglements in EPRB and Aspect (2002). Such factors (one factor relating to beables in Alice's domain, the other to beables in Bob's), refute Bell's theorem and eliminate the need for ‘t Hooft's superdeterminism. An obvious unifying algorithm (based on spin-s particles in a single thought-experiment) is foreshadowed and left as an exercise. That is, to emphasise the physical significance of our results, we here factor EPRB and Aspect (2002) separately and in detail.

Indefinite metric vectors are absolutely required as the physical states in Minkowski space because that is indefinite metric space and the physical space-time. For example, Maxwell equations are wave equations in Minkowski space. However, traditional Quantum theory ordinarily has been studied only in definite metric space, i.e., Hilbert space. There are no clear expression for indefinite metric vectors. Here we show a wave function example using Dirac's delta function for indefinite metric vectors in Minkowski space. In addition, we show the vectors can interfere with itself. This example also suggests indefinite metric will be absolutely required.

Generalizing Bell 1964:(15) to realizable experiments, CHSH (1969) coined the term “Bell's theorem”. Despite loopholes, but as expected, the results of such experiments contradict Bell's theorem to our total satisfaction. Thus, for us, at least one step in Bell's supposedly commonsense analysis must be false. Using undergraduate maths and logic, we find a mathematical error in Bell (1964) --- a false equality, uncorrected and thus continuing, undermines all Bell-style EPRB-based analyses, rendering them false. We again therefore predict with certainty that all loophole-free EPRB-style experiments will also give the lie to Bell's theorem.

Quantum theory (QT) which is one@@ of the basic theories of physics, namely in terms of Schrödinger's 1926 wave functions in general requires the field <b>C</b> of the complex numbers to be formulated. However, even the complex-valued description soon turned out to be insufficient. Incorporating Einstein's theory of Special Relativity (Schrödinger, Klein, Gordon, 1926, Dirac 1928) leads to an equation which requires some coefficients which are hypercomplex. Conventionally the Dirac equation is written using pairwise anti-commuting matrices. However, a unitary ring of square matrices <i>is</i> an - associative - hypercomplex algebra by definition. However, only the algebraic properties of the elements and their relations to one another are important. We hence replace the matrix formulation by a more symbolic one. In the case of the Dirac equation, these elements are called biquaternions. As an algebra over <b>R</b>, the biquaternions are eight-dimensional; as subalgebras, this algebra contains the division ring <b>H</b> of the quaternions at one hand and the algebra <b>C</b>⊗<b>C</b> of the bicomplex numbers at the other, the latter being commutative. As it will later turn out, <b>C</b>⊗<b>C</b> contains <i>pure non-real</i> subalgebras isomorphic to <b>C</b>. Within this paper, we first consider shortly the basics of the non-relativistic and the relativistic quantum theory. Then we introduce general hypercomplex algebras and also show how a relativistic quantum equation like Dirac's one can be formulated using hypercomplex coefficients. Subsequently, some algebraic preconditions for operations within hypercomplex algebras and their subalgebras will be examined. For our purpose equations akin the Schrödinger's one should be able to be set up and solved. Functions of complementary variables like <b>x</b> and <b>p</b> should be Fourier transforms of each other. This should hold within a purely non-real subspace which must hence be a subalgebra. Furthermore, it is an ideal denoted by <i>J</i>. It must be isomorphic to <b>C</b>, hence containing an internal identity element. The bicomplex numbers will turn out to fulfil these preconditions, and therefore, the formalism of QT can be developed within its subalgebras. We also show that bicomplex numbers encourage the definition of several different kinds of conjugates. One of these treats the elements of <i>J</i> precisely as the usual conjugate treats complex numbers. This defines a quantity what we call a modulus which, in contrast to the complex absolute square, remains non-real (but may be called `pseudo-real'). However, we do not conduct an explicit physical interpretation here but we leave this to future examinations.

Quantum theory (QT) which is one of the basic theories of physics, namely in terms of Schrödinger's 1926 wave functions in general requires the field <b>C</b> of the complex numbers to be formulated. However, even the complex-valued description soon turned out to be insufficient. Incorporating Einstein's theory of Special Relativity (Schrödinger, Klein, Gordon, 1926, Dirac 1928) leads to an equation which requires some coefficients which are hypercomplex. Conventionally the Dirac equation is written using pairwise anti-commuting matrices. However, a unitary ring of square matrices <i>is</i> an - associative - hypercomplex algebra by definition. However, only the algebraic properties of the elements and their relations to one another are important. We hence replace the matrix formulation by a more symbolic one. In the case of the Dirac equation, these elements are called biquaternions. As an algebra over <b>R</b>, the biquaternions are eight-dimensional; as subalgebras, this algebra contains the division ring <b>H</b> of the quaternions at one hand and the algebra <b>C</b>⊗<b>C</b> of the bicomplex numbers at the other, the latter being commutative. As it will later turn out, <b>C</b>⊗<b>C</b> contains <i>pure non-real</i> subalgebras isomorphic to <b>C</b>. Within this paper, we first consider briefly the basics of the non-relativistic and the relativistic quantum theory. Then we introduce general hypercomplex algebras and also show how a relativistic quantum equation like Dirac's one can be formulated using hypercomplex coefficients. Subsequently, some algebraic preconditions for operations within hypercomplex algebras and their subalgebras will be examined. For our purpose equations akin the Schrödinger's one should be able to be set up and solved. Functions of complementary variables like <b>x</b> and <b>p</b> should be Fourier transforms of each other. This should hold within a purely non-real subspace which must hence be a subalgebra. Furthermore, it is an ideal denoted by <i>J</i>. It must be isomorphic to <b>C</b>, hence containing an internal identity element. The bicomplex numbers will turn out to fulfil these preconditions, and therefore, the formalism of QT can be developed within its subalgebras. We also show that bicomplex numbers encourage the definition of several different kinds of conjugates. One of these treats the elements of <i>J</i> precisely as the usual conjugate treats complex numbers. This defines a quantity what we call a modulus which, in contrast to the complex absolute square, remains non-real (but may be called `pseudo-real'). However, we do not conduct an explicit physical interpretation here but we leave this to future examinations.

FQXi 2014 asks, ‘How should humanity steer the future?' Recalling false obstacles to medical progress in humanity's recent past — eg, impeding Semmelweis (b.1818), McClintock (1902), Marshall (1951) — we reply, ‘Steer by Logic.' Then — with Logic in view and other scientific disciplines in mind — we amplify our answer via an online coaching-clinic/challenge based on Einstein's work. With the future mostly physical, this physics-based challenge shows how we best steer clear of false obstacles — unnecessary barriers that slow humanity's progress. Hoping to motivate others to participate, here's our position: we locate current peer-reviewed claims of ‘impossible' — like those from days of old — and we challenge them via refutations and experimental verifications. The case-study identifies an academic tradition replete with ‘impossibility-proofs' — with this bonus: many such ‘proofs' are challengeable via undergraduate maths and logic. So — at the core of this clinic/challenge; taking maths to be the best logic — we model each situation in agreed mathematical terms, then refute each obstacle in like terms. Of course, upon finding ‘impossibilities' that are contradicted by experiments, our next stride is easy: at least one step in such analyses must be false. So — applying old-fashioned commonsense; ie, experimentally verifiable Logic — we find that false step and correct it. With reputable experiments agreeing with our corrections, we thus negate the false obstacles. Graduates of the clinic can therefore more confidently engage in steering our common future: secure in the knowledge that old-fashioned commonsense — genuine Logic — steers well.

We present a new explanation for a quantum eraser. Mathematical description of the traditional explanation needs quantum-superposition states. However, the phenomenon can be explained without quantum-superposition states by introducing unobservable potentials which can be identified as an indefinite metric vector. In addition, a delayed choice experiment can also be explained by the interference between the photons and unobservable potentials, which seems like an unreal long-range correlation beyond the causality.

This document is submitted as a partial requirement for the course Quantum Information and Computing, BITS Pilani. The phenomenon of NMR can be used to generate spin states of nuclei and these can be used as qubits for computational purposes, the speciality being, an ensemble of molecules must be utilized. This allows for an exponentiation in the processing power of the computer. The document explains about the setup, measurement and initialization of an NMR quantum computer.

The Quantum mechanics works but is not yet well understood. The difficulty in understanding lies not so much in the already very sophisticated mathematical formulations, but are much more rooted in the question of how the objects do that? Starting with the double-slit experiment, we will first provide the viewpoint of quantum mechanics. This leads us to the wave-particle duality. Photons have both wave and particle properties. Then we see the exact opposite: photons, electrons... are neither wave nor particle and address the question: Can we find truth from falsity? Can quantum mechanics be wrong in their conditions and yet lead to so excellent results? We then address the question of how good the mathematical prerequisites in classical physics is and how well they are fulfilled in quantum physics. Finally, we look at some very basic experiments from the point of view of the objects.

In classical electrodynamics the vacuum is defined as a region where there are no electric or magnetic fields. In such a region, a charged particle (such as an electron) will feel no effect — the Lorentz force is zero. The space external to a perfect (i.e., infinite) solenoid can be considered an electromagnetic vacuum, since E and B vanish there. While a non-zero vector potential A does exist outside the solenoid, it can exert no influence on the particle, and thus cannot be directly detected or quantified classically. However, in 1959 Aharonov and Bohm predicted that a vector field would exert a purely quantum-mechanical effect on the phase of the particle’s wave function, which in principle should be detectable. The predicted phase shift was not observed experimentally until 1986, when Tonomura brilliantly verified the effect using a microscopic solenoid. This paper provides a simplified explanation of the Aharonov-Bohm effect using a path-integral approach that is suitable for the advanced undergraduate.

The problem of angular momentum addition requires the calculation of Clebsch-Gordan coefficients. While systems involving small values of momenta and spin present no special problem, larger systems require extensive computational effort. This paper describes a straightforward method for computing the coefficients for any two-particle problem exactly by means of a simplified form of the recursion formula in a notation that is particularly accessible to the third- or fourth-year student. The method is summarized in a brief BASIC program.

With Bell (1964) and his EPR-based mathematics contradicted by experiments, at least one step in his supposedly commonsense theorem must be false. Defining commonsense local realism as the fusion of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively), we eliminate all such contradictions and make EPR correlations intelligible by completing the quantum mechanical account in a classical way. Thus refuting the famous inequality at the heart of Bell's mathematics, we show that Bell's theorem is limited by Bell's use of naive realism. Validating the classical mantra that correlated tests on correlated things produce correlated results without mystery, we conclude that Bell's theorem and related experiments negate naive realism, not commonsense local realism.

Hamiltonian Mechanics works for conserved systems. Quantum Mechanics is given in Hamiltonian language. In papers by Dekker and recently by A. Sergi, this problem was circumvented by complexifying the energy and interpreting the dissipative part as Imaginary part. Based on the Dekker model, a following interpretation is presented in Density-Operator language for Pseudo-Hermiticity. Proper forms of Quantum measures are provided, as there is need in this new formalism, namely correcting Pati and Zielinski, Wang.

Исходя из квантовых представлений об электромагнитных колебаниях, показана связь между поглощенной частью энергии квантов межзвездной средой и смещением спектров пропорциональных относительному расстоянию между источником и приемником квантов, а так же влияние на смещение спектров движения объектов относительно друг друга. Based on the concepts of quantum electromagnetic fluctuations, shows the relationship between the absorbed part photon energy of the interstellar medium and the displacement spectra are proportional to the relative distance between source and receiver rays, as well as the effect of the displacement spectra of the motion of objects relative to each other.

We show that when spin eigenfunctions are not fully orthonormal, Bell's inequality does allow local hidden variables. In the limit where spin eigenfunctions are Dirac orthonormal, we recover a significant extremal case. The new calculation gives a possible accounting for $\alpha_{\mathrm{MCM}}-\alpha_{\mathrm{QED}}$.

We show single photon and electron interferences can be calculated without quantum-superposition states by using tensor form (covariant quantization). From the analysis results, the scalar potential which correspond to an indefinite metric vector forms an oscillatory field and causes the interferences. The results clarify the concept of quantum-superposition states is not required for the description of the interference, which leads to an improved understanding of the uncertainty principle and resolution of paradox of reduction of the wave packet, elimination of infinite zero-point energy and derivation of spontaneous symmetry breaking. The results conclude Quantum theory is a kind of deterministic physics without ''probabilistic interpretation''.

As opposed to the classical logic of true and false, viewed as an axiomatised theory, ordinary arithmetic conveys the three logical values: provable, negatable and logically independent. This research proposes the hypothesis that Axioms of Arithmetic are the fundamental foundation running arithmetical processes in Nature, upon which physical processes rest. And goes on to show, in detail, that under these axioms, quantum mathematics derives and initiates logical independence, agreeing with indeterminacy in quantum experiments. Supporting arguments begin by explaining logical independence in arithmetic, in particular, independence of the square root of minus one. The method traces all sources of information entering arithmetic, needed to write mathematics of the free particle. Wave packets, prior to measurement, are found to be the only part of theory logically independent of axioms; the rest of theory is logically dependent. Ingress of logical independence is via uncaused, unprevented self-reference, sustaining the wave packet, but implying unitarity. Quantum mathematics based on axiomatised arithmetic is established as foundation for the 3-valued logic of Hans Reichenbach, which reconciles quantum theory with experimental anomalies such as the Einstein, Podolsky & Rosen paradox.

The conditions of the early universe are not known with any measure of certainty — they are only theories. Therefore, using the assumption that the estimated total energy of the observable universe is conserved, we propose a different lower limit for the gravitational energy; we attempt to unify the subatomic and the large scale universe into one coherent whole; thus, showing that the cosmos behaves like a quantum object. It uses a form of Bohr’s quantization to strengthen the unification of quantum gravity. Our model is simple, yet comprehensive.

The "Schrödinger cat" states supposed by quantum mechanics need not be considered intrinsically probabilistic or otherwise inconsistent with the existence of the particle in the physically real state assumed by classical physics. The further states contemplated by the formalism of standard quantum mechanics could be states, not of the particle itself, but of the apparatus - oscillatory disturbances induced by reaction as the particle is measured and mimicking the wave characteristics of a particle. If quantum states are understood in this way, much of what has seemed mysterious in quantum behaviour becomes consistent with local realism.

This note discusses recent weak measurements of the nested Mach-Zehnder interferometer, measurements that can be interpreted in terms of state vectors traveling both forwards and backwards in time. A complementary interpretation is presented, from the perspective of the scale invariant quantum Hall and far field photon impedances. A delayed choice variant on the recent experiment is proposed, distinguishing between these two and other interpretations.

In this short comment, by giving two numerical counterexamples directly contrary to the phase matching condition presented by Long \emph{et al.}, I show that Grover's conclusion that his algorithm can be extended to the case when the two phase inversions are replaced by arbitrary phases (Phys. Rev. Lett. {\bf 80}, 4329--4332, 1998) in a sense is correct.

For an initial uniform superposition over all possible computational basis states, we explore the performance of Grover's search algorithm geometrically when imposing a perturbation on the Walsh-Hadamard transformation contained in the Grover iteration. We give the geometric picture to visualize the quantum search process in the three-dimensional space and show that Grover's search algorithm can work well with an appropriately chosen perturbation. Thereby we corroborate Grover's conclusion that if such perturbation is small, then this will not create much of an impact on the implementation of this algorithm. We also prove that Grover's path cannot achieve a geodesic in the presence of a perturbation of the Fubini-Study metric.

For there to be $M> 1$ target items to be searched in an unsorted database of size $N$, with $M/N\ll 1$ for a sufficiently large $N$, we explore the performance of Grover's search algorithm when considering some possible situations that may arise in a four-complex-dimensional subspace, for which in the case of identical rotation angles $\phi=\theta$, we give the maximum success probabilities of finding a desired state and their corresponding numbers of Grover iterations in an approximate fashion. Our analysis reveals that the case of identical rotation angles $\phi=\theta$ is energetically favorable compared to the case $\left| {\theta - \phi } \right|\gg 0$ for boosting the probability to detect a desired state.

Abstract. A well-known experiment from 1986 involving entangled pairs is examined. The data, which until now have not been modeled quantitatively, is shown not to be in agreement with the quantum measurement postulate using von Neumann projectors. On the other hand, the data agree with the postulate using a more general positive operator valued measure (POVM). The peculiarity of the POVM proposed here is that it is only conditionally a POVM; i.e. it is not complete (trace-preserving) on the entire Hilbert space but only on a subset, although the POVM elements are positive semidefinite observables on the entire space. The state vector of the aforementioned experiment is in the subset where completeness holds. An extension of the conditional POVM is then applied to a proposed experiment involving three- particle Greenberger-Horne-Zeilinger (GHZ) entangled states. As with the Aspect experiment, completeness holds for the conditional POVM upon application to the GHZ state. Violation of the Bell inequality in the GHZ experiment does not occur upon application of von-Neumann projectors; however the conditional POVM allows for Bell inequality violation.

As first, a mechanism how quantum coherence in the brain can last long enough is shown. This mechanism is based on very light elementary particles. Then the arguments follow as why consciousness should be a quantum phenomenon and how such an introduction of quantum consciousness modifies the formalism of quantum mechanics. This can also be tested by an experiment. Without use of quantum mechanics it is shown how to atomize consciousness and how to explain the Libet experiment, and why a location of feeling of consciousness is an important paradox. It is also shown that panpsychism is an answer to many questions about consciousness. The author claims that consciousness is physically so fundamental that it is not a result of some complex phenomena, but it is so fundamental as quantum physics and space-time.

The predictions of Bell's inequalities, and their subsequent experimental verification in the form of correlations between spacelike separated events have led to the prevailing current view that `nature is non-local'. Here we examine the possibility that our current concept of locality may at present not be sufficiently differentiated, and that by using 'nature' synonymously with `spacetime' we may have missed an implication of special relativity which by rendering a more complete conception of locality permits such quantum correlations without either hidden variables or violations of locality.

This paper points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties.

This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties.

It was shown in [1], cited in the sequel as DRHM, that upon a correct use of the respective statistical data, the celebrated Bell inequalities cannot be violated by quantum systems. This paper presents in more detail the surprisingly elementary, even if rather subtle related basic argument in DRHM, and does so together with a few comments which, hopefully, may further facilitate its wider understanding.

We construct a Dirac theory on causal sets; a key element in the construction being that the causet must be regarded as emergent in an appropriate sense too. We further notice that mixed norm spaces are a key element in the construction allowing for negative norm particles and ``ghosts''.

In a Majorana basis, the Dirac equation for a free spin one-half particle is a 4x4 real matrix differential equation. When including the effects of the electromagnetic interaction, the Dirac equation is a complex equation due to the presence of an imaginary connection in the covariant derivative, related with the phase of the spinor. In this paper we study the solutions of the Dirac equation with the null and Coulomb potentials and notice that there is a real matrix that squares to -1, relating the imaginary and real components of these solutions. We show that these solutions can be obtained from the solutions of two non-linear 4x4 real matrix differential equations with a real matrix as the connection of the covariant derivative.

The measurement problem, the mechanism of quantum state reduction, has remained an open question for nearly a century. The 'quantum weirdness' of the problem was highlighted by the introduction of the Einstein-Podolsky-Rosen paradox in 1935. Motivated by Bell's Theorem, nonlocality was first experimentally observed in 1972 by Clauser and Freedman in the entangled states of an EPR experiment, and is now an accepted fact. Special relativity requires that no energy is transferred in the nonlocal collapse of these entangled two-body wavefunctions, that no work is done, no information communicated. In the family of quantum impedances those which are scale invariant, the Lorentz and centrifugal impedances, satisfy this requirement. This letter explores their role in the collapse of the wave function

This paper is intended to show the Schrodinger equation, within its structure, allows the manifestation of the wave function collapse within a very natural way of reasoning. In fact, as we will see, nothing new must be inserted to the classical quantum mechanics, viz., only the dialectics of the physical world must be interpreted under a correct manner. We know the nature of a physical system turns out to be quantical or classical, and, once under the validity of the Schrodinger equation to provide the evolution of this physical system, the dialectics, quantum or classical, mutually exclusive, must also be under context through the Schrodinger equation, issues within the main scope of this paper. We will show a classical measure, the obtention of a classical result, emerges from the structure of the Schrodinger equation, once one demands the possibility that, over a chronological domain, the system begins to provide a classical dialectic, showing the collapse may be understood from both: the structure of the Schrodinger equation as well as from the general solution to this equation. The general solution, even with a dialectical change of description, leads to the conservation of probability, obeying the Schrodinger equation. These issues will turn out to be a consequence of a general potential energy operator, obtained in this paper, including the possibility of the classical description of the physical system, including the possibility of interpretation of the collapse of the quantum mechanical state vector within the Schrodinger equation scope.

The logical structure of the standard model is isomorphic to the geometric structure of the modified cosmological model (MCM). We introduce a new particle representation scheme and show that it is invariant under CPT. In this representation spin arises as an ordinary physical process. The final character of the Higgs boson is predicted. Wavefunction collapse, the symmetry (anti-symmetry) of the wavefunction and some recent experimental results are discussed.

Starting with the Dirac-Maxwell’s equations in presence of electric and magnetic sources in an isotropic medium of dyons, we have derived the generalized octonion Maxwell’s equations in isotropic medium. And the octonion formulation of generalized electromagnetic fields in chiral medium has also been developed in compect, simple and consistent manner.

In this paper, we present several equations that generate the ratio of the sum of the roots of the masses of the quarks with respect to the electron, likewise the ratio of the sum of the masses of the quarks in relation to the mass of the electron. Both equations depend exclusively, and in a very simple and logical way from quantum dimensionless length derived from the fine structure constant to zero momentum; lengths in seven dimensions, the number of quarks and the three charges of color group SU(3).

In this paper we present a very simple formulas that generate the quark masses as a very direct functions sine and cosine of the Cabibbo angle. The accuracy of the results are very big in relation to the latest experimental values.

This paper is intended to show the Schrodinger equation, within its structure, allows the manifestation of the wave function collapse within a very natural way of reasoning. In fact, as we will see, nothing new must be inserted to the classical quantum mechanics, viz., only the dialectics of the physical world must be interpreted under a correct manner. We know the nature of a physical system turns out to be quantical or classical, and, once under the validity of the Schrodinger equation to provide the evolution of this physical system, the dialectics, quantum or classical, mutually exclusive, must also be under context through the Schrodinger equation, issues within the main scope of this paper. We will show a classical measure, the obtention of a classical result, emerges from the structure of the Schrodinger equation, once one demands the possibility that, over a chronological domain, the system begins to provide a classical dialectic, showing the collapse may be understood from both: the structure of the Schrodinger equation as well as from the general solution to this equation. The general solution, even with a dialectical change of description, leads to the conservation of probability, obeying the Schrodinger equation. These issues will turn out to be a consequence of a general potential energy operator, obtained in this paper, including the possibility of the classical description of the physical system, including the possibility of interpretation of the collapse of the quantum mechanical state vector within the Schrodinger equation scope.

We indicate how pursuit of a realist interpretation of Quantum Mechanics, starting from a simple and plausible physical principle and established Quantum Mechanics, leads to a physical picture almost as counter-intuitive but which among other things would if true confirm that the quest for a deterministic model of Quantum Mechanics is doomed to failure.

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to several paradoxes. The most striking of them is that coordinate wave functions of photons emitted by stars have cosmic sizes and strong arguments indicate that this contradicts observational data. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.

The Feynman path integral is an essential part of our mathematical description of fundamental nature at small scales. However, what it seems to say about the world is very much at odds with our classical intuitions, and exactly why nature requires us to describe her in this way is currently unknown. We will describe here a possibility according to which the path integral may be the spacetime manifestation of objects existing in a lower-dimensional analog of spacetime until they give rise to the emergence of spacetime objects under a process that is currently labeled a ‘Quantum Measurement’. This idea is based on a mathematical distinction which at present does not appear to be widely appreciated.

The probability of occurrence of an event or that of the existence of a physical state has no relative existence in the sense that motion is strongly believed to only exist in the relative sense. If the probability of occurrence of an event or that of the existence of a physical state is known by one observer, this probability must be measured to have the same numerical value by any other observer anywhere in the Universe. If we accept this bare fact, then, the probability function can only be a scalar. Consequently, from this fact alone, we argue that the quantum mechanical wavefunction can not be a scalar function as is assumed for the Schroedinger and the Klein-Gordon wavefunctions. This has fundamental implications on the nature of the wavefunction insofar as translations from one reference system to the other is concerned.

This paper presents a concise exposition of the Dimensional Theory, a novel framework which helps make sense out of the Copenhagen Interpretation as it explains the peculiarities of quantum mechanics in a way that is most consistent with that interpretation. \footnote{A recording of the talk based on this material can be viewed at http://youtu.be/GurBISsM308 }

Few years has passed from the latest formulation for the hierarchy of Planck constant. The original hypothesis seven years ago was that the hierarchy is real. In this formulation the imbedding space was replaced with its covering space assumed to decompose to a Cartesian product of singular finite-sheeted coverings of M⁴ and CP₂. </p><p> Few years ago came the realization that the hierarchy could be only effective but have same practical implications. The basic observation was that the effective hierarchy need not be postulated separately but follows as a prediction from the vacuum degeneracy of Kähler action. In this formulation Planck constant at fundamental level has its standard value and its effective values come as its integer multiples so that one should write hbar_eff=n×hbar rather than hbar= nhbar₀ as I have done. For most practical purposes the states in question would behave as if Planck constant were an integer multiple of the ordinary one. It was no more necessary to assume that the covering reduces to a Cartesian product of singular coverings of M⁴ and CP₂ but for some reason I kept this assumption. </p><p> In the recent formulation this assumption is made and the emphasis is on the interpretation of the multi-sheetedness (in the sense of Riemann surfaces) resulting as a multi-furcation for a preferred extremal taking place at the partonic 2-surfaces. This gives a connection with complexity theory (say in living systems), with transition to chaos, and with general ideas about fractality. Second quantization of the multi-furcation means accepting not only superpositions of branches as single particle states but also the analogs of many-particle states obtained by allowing several branches up to the maximum number. This revives the ideas of N-atom, N-molecule etc.. already given up as too adventurous. </p><p> The question whether gravitational Planck constant h_gr having gigantic values results as an effective Planck constant has remained open. A simple argument suggests that gravitational four-momentum could be identified as a projection of the inertial four-momentum to the space-time surface and that the square of the gravitational four-momentum obtained using the effective metric defined by the anti-commutators of the modified gamma matrices appearing in the modified Dirac equation naturally leads to the emergence of h_gr.

Still today the discussion about the foundations, physical interpretation, and real scope of quantum mechanics has never ceased. It would be wrong to dismiss these issues as mere philosophical problems, because questions of consistency and interpretation are not devoid of practical utility. We present the foundations and main properties of a positive definite phase space quantum mechanics. A new quantization procedure is proposed as well. This new interpretation/formulation eliminates conceptual and technical difficulties from quantum mechanics: (i) many paradoxes typical of the wave-particle duality, EPR experiments, macroscopic superpositions, and collapse of wavefunctions disappear; (ii) the elimination of the wavefunctions from quantum theory is in line with the procedure inaugurated by Einstein with the elimination of the ether in the theory of electromagnetism; (iii) it is useful in considering the classical limit, can treat mixed states with ease, and brings certain conceptual issues to the fore; (iv) confirms the ensemble interpretation of the wavefunctions, derives its statistical interpretation, corrects the temporal dependence of the old wavefunctions, and considers pure classical states --localizable states-- beyond the Hilbert space; (v) the quantum equation of motion is of the Liouville kind and star-products are not needed, simplifying the formalism; and (vi) eliminates the hypothetical external quantum field of the pilot wave interpretation, solving its problems on the status of probability, and correcting well-known inconsistencies of the Bohm potential. Finally, we offer some perspectives on future developments and research in progress.

In the reading Nyambuya (2009), it is shown that one can write down a general spin Dirac equation by modifying the usual Einstein energy-momentum equation via the insertion of the quantity ``s" which is identified with the spin of the particle. That is to say, a Dirac equation that describes a particle of spin \frac{1}{2}s\hbar\vec{\sigma} where \hbar is the normalised Planck constant, \vec{\sigma} are the Pauli 2 \times 2 matrices and s=(\pm 1, \pm2,\pm 3, \,\dots etc). What is not clear in this reading Nyambuya (2009) is how such a modified energy-momentum relation would arise in Nature. At the end of the day, the insertion by lathe of hand of the quantity ``s" into the usual Einstein energy-momentum equation, would then appear to be nothing more than speculation. In the present reading -- by making use of the curved spacetime Dirac equations proposed in the work Nyambuya (2008), we move the exercise of Nyambuya (2009) from the realm of speculation to that of plausibility

A non-unitary quantum theory describing the evolution of quantum state tensors is presented. Einstein’s equations and the fine structure constant are derived. The problem of precession in classical mechanics gives an example.

We consider a non-negative integer valued grading function on tensor products which aims to measure the extent of entanglement. This grading, unlike most of the other measures of entanglement, is defined exclusively in terms of the tensor product. It gives a possibility to approach the notion of entanglement in a more refined manner, as the non-entangled elements are those of grade zero or one, while the rest of elements with grade at least two are entangled, and the higher its grade, the more entangled an element of the tensor product is. The problem of computing and reducing the grade is studied in products of arbitrary vector spaces over arbitrary fields.

In explaining such phenomena as the redshift and even the fact that we can see stars and planets, the effect of wave packet spreading (WPS) of the photon wave function is not taken into account. Probably the main reason is a belief that WPS is not important since a considerable WPS would blur the images more than what is seen. However, WPS is an inevitable consequence of quantum theory and moreover this effect is also known in classical electrodynamics. So it is not sufficient to just say that a considerable WPS is excluded by observations. One should try to estimate the importance of WPS and to understand whether our intuition is correct or not. We explicitly demonstrate that a standard relativistic quantum-mechanical calculation shows that spreading in the direction perpendicular to the photon momentum is very important and cannot be neglected. Hence the physics of the above phenomena is not well understood yet. Possible approaches for solving the problem are discussed.

In this paper, we try to construct the famous Schrodinger equation of quantum mechanics in a very simple manner. It is shown that, even though the mathematical procedure of the construction may be correct, it is evident that the establishment of the Schrodinger equation is unreasonable in physics. We point out the application of the Schrodinger equation, in fact, will lead to the transformation of the studied system into an arbitrary variable pseudo physical system. This finding may help to uncover the nature of the nonlocality and Heisenberg's uncertainty principle of quantum mechanics. It is inevitable that the use of the Schrodinger equation will violate the law of conservation of energy. Hence, we argue that the Schrodinger equation is unsuitable to be applied to any physical systems.

Feynman proposed searching for -α^(1/2)=-0.08542455 with the ± sign on the -α^(1/2) for the positive and negative charge, and may be related to π, ϕ, 2 and 5. We found α^(1/2)≈±log e/Φπ=±0.0854372 where Φ=1/ϕ=2cos(π/5). I/FQHE R_xy=± Z_0/2αν_i α^(1/2)=±log e^(±ϕ/Kπ) where Φ-ϕ-e-π in Euler Identity and K~{3,37,61} from 2^((p-1)) (p-1)!∈2^n n! are linked to Quantum theories. The energy-mass formula E=mc^2 and special relativistic mass m=γ m_0 established the particle rest-mass m_0 , mass-ratio m_i/m_e , mass-defect ∆m . The rest-mass of a particle can be quantized by the fine structure constant and the proton-electron mass ratio β_(p/e)=(α^(-3/2)-2α^(1/2)+α^2/πϕ^2-ηα^3)lnπ . The hydrogen atomic rest-mass is m_(1_H )=m_(p+)+m_e (1-α^2 ln10) in the Quantum Gravity. The high-energy W^± boson α_W^(1/2)=≈±(1-αsin^2 θ_w)log F/Φπ , where Fransén-Robinson constant F=∫_0^∞□(dt/(Γ(t)))=2.80777⋯ replaced e=∑_(n=0)^∞□(1/(Γ(n)))=2.71828⋯ We get the g-factors of particles (Leptons and Baryons).

In this short note, the the key to unlocking the secrets of quantum physics will be elucidated by exploring the fundamentals of Schrodinger's wave mechanics approach to describing quantum phenomenon. We will show that de Broglie's wave-particle duality hypothesis which lies at the heart of Schrodinger's wave-function \psi produces a complex wave equation whose mathematical structure can be described by Euler's famous equation e^{i\theta}=cos(\theta)+isin(\theta) which basically describes a helical wave in 3D space. By comparing and contrasting the electromagnetic wave with that of a helical wave which Euler's equation represents, we may have discovered the geometric basis for spin and helicity and antimatter with negative energies that Dirac uncovered in his relativistic reformulation of Schrodinger's equation.

An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung’s hydrodynamic formulation of QM [1] and Louis de Broglie’s and David Bohm’s pilot wave models [2, 3]. The aims of the approach are as follows: 1) to have a clear ontology for QM, 2) to describe QM in a causal way, 3) to get rid of the wave-particle dualism in pilot wave theories, 4) to provide a theoretical framework for describing creation and annihilation of particles, and 5) to provide a possible connection between particle QM and virtual particles in QFT. These goals are achieved, if the wave function is replaced by a fluid of so called virtual particles. It is also assumed that in this fluid of virtual particles exist a few real particles and that only these real particles can be directly observed. This has relevance for the measurement problem in QM and it is found that quantum probabilities arise in a very natural way from the structure of the theory. The model presented here is very similar to a recent computational model of quantum physics [4] and recent Bohmian models of QFT [5, 6].

The often cited book [11] of Asher Peres presents Quantum Mechanics without the use of the Heisenberg Uncertainty Principle, a principle which it calls an "ill-defined notion". There is, however, no argument in this regard in the mentioned book, or comment related to the fact that its use in the realms of quanta is not necessary, let alone, unavoidable. A possible comment in this respect is presented here. And it is related to certain simple, purely logical facts in axiomatic theories, facts which are disregarded when using "physical intuition" and "physically meaningful" axioms or principles in the development of mathematical models of Physics, [16-18].

This article distills many of the essential definitions from the very thorough book, Clifford Algebras: An Introduction, by Dr D.J.H. Garling, with some minor additions.

The symmetry group of the 18-j(H) Wigner symbol is restructured by splitting two symmetry equations (Yutsis et al. 1962) into three generators. The symmetry groups of two 21-j Wigner symbols (Ponzano 1965) are complemented to form groups of order 8. This summarizes systematic evaluation of the automorphisms of the associated simple cubic graphs with McKay’s nauty program.

In order to understand nonlocal phenomena, the corresponding processes must be treated as scattering experiments and investigated in the frame of quantum field theory. Quantum mechanics is not sufficient for this task, because it is only concerned with the influence of a potential on a physical object. But in processes with nonlocal effects the role of interaction between physical objects must be sufficiently respected. – All this is shown first of all for the special case of the spin-1/2-experiment, and then generalized to arbitrary scattering processes.

It is easy to check that both algebraic equation Det(^p - m) = 0 and Det(^p + m) = 0 for 4-spinors u- and v- have solutions with (see paper) The same is true for higherspin equations. Meanwhile, every book considers the p0 = Ep only for both u- and v- spinors of the (see paper) representation, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of negative-energy solutions. Recent works of Ziino (and, independently, of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both s = 1/2 and higher spins particles.

Ever since quantum mechanics was first developed, it has been unclear what it really tells us about reality. A novel framework, based on 5 axioms, is presented here which offers an interpretation of quantum mechanics unlike any considered thus far: It is postulated that physical objects can exist in one of two distinct modes, based on whether they have an intrinsic actual spacetime history or not. If they do, their mode of existence is actual and they can be described by classical physics. If they do not, then their mode of existence is called actualizable and they must be described in terms of an equal-weight superposition of all possible actualizable (not actual) histories. The distinction is based on an axiom according to which there exists a limit in which spacetime reduces to a one-dimension reduced version, called areatime, and that objects which merely actualizably exist in spacetime actually exist in areatime. The operational comparison of the passage of time for such objects to the passage of time for a spacetime observer is postulated to be made possible by what is called an angular dual bilateral symmetry. This symmetry can be decomposed into the superposition of two imaginary phase angles of opposite sign. To mathematically describe the spacetime manifestation of objects which actually exist in areatime, each actualizable spacetime history is associated with an actualizable path, which in turn is associated with the imaginary phases. For a single free particle, the complex exponent is identified with a term proportional to its relativistic action, thus recovering the path integral formulation of quantum mechanics. Although based on some highly unfamiliar ideas, this framework appears to render at least some of the usual mysteries connected with quantum mechanics amenable to simple conceptual understanding. It also appears to connect the foundations of quantum theory to the foundation of the special theory of relativity while clarifying its relationship to the general theory of relativity and yields a testable prediction about a type of experiment, as yet unperformed, which under the current paradigm is utterly unexpected, namely, that the gravitational field of radiation is zero. The paper concludes with some speculations about how the theory may be extended to a metatheory of nature.

After a providing a review of the EPR paradox which draws a distinction between what is here called the locality and the in uence paradoxes, this paper presents a qualitative overview of a framework recently introduced by this author in which spacetime is assumed to emerge from areatime. Two key assumptions from this framework allow one to make the notion of quantum eects originating from `outside' spacetime intelligible. In particular, this framework assumes that until a quantum object is measured, it does not actually exist in spacetime and that there are connections between quantum particles in areatime which are independent of metric relations in spacetime. These assumptions are then shown to permit one to conceptually understand both the locality and the in uence paradoxes, and lead to the overall conclusion that spacetime is emergent in the sense that a very large number of discrete events which correspond to `measurements' in quantum mechanics aggregate to give rise on a large scale to the apparently smooth reality we experience in our daily lives.

The quantum superposition principle, which expresses the idea that a system can exist simultaneously in two or more mutually exclusive states is at the heart of the mystery of quantum mechanics. This paper presents an axiom, called the principle of actualizable histories, which naturally leads to the quantum superposition principle. However, in order to be applicable to massive systems, it requires introducing a novel distinction between actualizable and actual mass. By means of arriving in conjunction with two previously introduced axioms at the path integral formulation of quantum mechanics, it is shown that actualizable mass is the central concept of mass in quantum theory, whereas actual mass is the central concept in classical theories, and in particular general relativity. This distinction sharply segregates the domains of validity of the two theories, making it incompatible with any theory of quantum gravity which does not respect this segregation. Finally, an experiment is suggested to test this idea.

The quantum phase has profound effects on quantum mechanics but its physical origin is currently unexplained. This paper derives its general form from two physical axioms: 1) in the limit in which space goes to zero, spacetime reduces to a constant quantity of areatime, and 2) the proper time dimensions of areatime and of spacetime are orthogonal but can be compared to each other according to what will here be called an angular dual bilateral symmetry. The mathematical derivation and the explanation of the physical origin of the quantum phase from these two axioms is straightforward and implies that the quantum phase is intimately related to the quantization of spacetime.

This paper makes a case for ontology, the study of existence, to be explicitly and formally incorporated into foundational physics in general and the wave function collapse of quantum mechanics in particular. It introduces a purely ontological distinction between two modes of physical existence-actualizable and actual- into the conventional mathematical representation of the wave function collapse, and examines the implications of doing so, arguing that this may lead to insights that permit one to understand seemingly mysterious aspects of the wave function collapse, such as 'Schrödinger's cat paradox', as well as how quantum theory in general and Einstein's general theory of relativity relate to one another. A specific empirical prediction is given, which if conrmed, may move ontology outside the exclusive purview of philosophy.

The mass of a photon is one of the most intriguing ideas of theoretical physics, and their existence is consistently justified in the light of certain experimental data. In this paper the proposal for explanation of the nonzero photon mass in frames of the waveparticle duality is concisely presented. The standard formulation of the wave-particle duality is modified by the constant frequency field, which can be interpreted as the Zero-Point Frequency field.

Written at a level appropriate for an educated lay audience, this paper attempts to give a primarily conceptual overview of a framework recently introduced in reference [3] by this author, which attempts to clarify what quantum mechanics tells us about reality. Physicists may find this paper useful because it focuses on the central ideas of the framework at a conceptual level, thereby lessening their unfamiliarity, an unavoidable feature of truly novel ideas. The author hopes that this article will motivate physicists to seriously evaluate the mathematical details of the framework given in the original reference.

Fair sampling assumption is used in photonic tests of Bell inequalities. However, rigorous testing of this assumption is still to be performed. Here it is argued that without rigorous testing bias can be introduced that would mask indications of unfair sampling. For purpose of argument local realistic model for polarization entangled photons is outlined. According to model coincidence rate and correlation visibility are complementary.

The leading idea of this paper is to prove the theorem of Wigner with concepts and methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader acquainted with the essential features of the theorem and its proof. On the other hand it will turn out to be the core of the general proof.

In a previous preprint, [1], reproduced here within the appendix in its revised version, we were confronted, to reach the validity of the second law of thermodynamics for an unique collapse of an unique quantum object, to the necessity of an ensemble of measures to be accomplished within copies of identical isolated systems. The validity of the second law of thermodynamics within the context of the wave function collapse was sustained by the large number of microstates related to a given collapsed state. Now, we will consider just one pure initial state containing just one initial state of the quantum subsystem, not an ensemble of identically prepared initial quantum subsystems, e.g., just one photon from a very low intensity beam prepared with an equiprobable eigenset containing two elements, an unique observation raising two likelihood outcomes. Again, we will show the statistical interpretation must prevail, albeit the quantum subsystem being a singular, unique, pure state element within its unitary quantum subsystem ensemble set. This feature leads to an inherent probabilistic character, even for a pure one-element quantum subsystem object.

Academically, among students, an apparent paradox may arise when one tries to interpret the second law of thermodynamics within the context of the quantum mechanical wave function collapse. This is so because a quantum mechanical system suddenly seems to undergo, from a less restrictive state constructed from a superposition of eigenstates of a given operator, to a more restrictive state: the collapsed state. This paper is intended to show how this picture turns out to be a misconception and, albeit brie y, furtherly discuss the scope of Max Born's probabilistic interpretation within the second law of thermodynamics.

We discuss how, in the theoretical scenario presented in [1], the gravity screening and the gravity impulse which seem to be produced under certain conditions by high temperature superconductors are expected to be an entropic response to the ow of part of the system into a deeper quantum regime.

As argued earlier elsewhere, what is the Geometric Straight Line, or in short, the GSL, we shall never know, and instead, we can only deal with various mathematical models of it. The so called standard model, given by the usual linearly ordered eld R of real numbers is essentially based on the ancient Egyptian assumption of the Archimedean Axiom which has no known reasons to be assumed in modern physics. Setting aside this axiom, a variety of linearly ordered fields F_U becomes available for the mathematical modelling of the GSL. These elds, which are larger than R, have a rich self-similar structure due to the presence of infinitely small and infinitely large numbers. One of the consequences is the obvious relative and local nature of the long ongoing local versus nonlocal dichotomy which still keeps having foundational implications in quantum mechanics.

          In special experiments on slowing down soft electrons from the energy <i>E</i>₁ at the entry of a narrow slit down to <i>E</i>₂<<i>E</i>₁ in the exit there was drawn a conclusion that the source of the retardation radiation with the energy Δ<i>E</i>₁₂=<i>E</i>₁–<i>E</i>₂ in the opening of the narrow slit is not the passing by electrons, but a radiation due to inverse photoelectric effect of valence electrons in the stationary structure of the edge of the hole. Here we consider only central-axial flight of electrons via a narrow slit (of the width <0.2 μm) which generates quanta of light with the energy Δ<i>E</i>₁₂. If with the aid of external electrodes inside a wider slit (>2 μm) to create a field with the same retardation potential φ=Δ<i>E</i>₁₂ then despite of the same slowing down in it of central-axial flying by electrons there will be observed no emission of light quanta with the energy Δ<i>E</i>₁₂. This enables us to interpret in a different way the mechanism of induced radiation of matter under quantum transitions in it of particles. It looks such that the flying by electrons excites around themselves spherical zones of nonlinearity with radius ∼ 0.2 μm. The orbitals (with energies <i>E</i>₁ and <i>E</i>₂<<i>E</i>₁) of stationary valence electrons in the edge of the narrow orifice (of the width < 0.2 μm), falling in these zones, in accord with the Ritz combination rule gives from the difference of terms ν₁=<i>E</i>₁/<i>h</i> and ν₂=<i>E</i>₂/<i>h</i> the observed in experiments monochromatic radiation of the frequency ν₁₂=ν₁– ν₂. The passing of center-axial electrons via a wider gaps (>2 μm) is not affected by the nonlinearity zones of the orbitals of stationary valence electrons in the edge of the slit. Thence, despite of the dragging by the external field of the diaphragm φ=Δ<i>E</i>₁₂ in this case the flying by electrons does not radiate at the frequency ν₁₂=Δ<i>E</i>₁₂/<i>h</i>.

We consider electro-optical constructions in which the Casimir force is modulated in opposition to piezo-crystal elasticity, as in a stack of alternating tunably conductive and piezo layers. Adjacent tunably conducting layers tuned to conduct, attract by the Casimir force compressing the intermediate piezo, but when subsequently detuned to insulate, sandwiched piezo layers expand elastically to restore their original dimension. In each cycle some electrical energy is made available from the quantum zero point (zp). We estimate that the maximum power that could be derived at semiconductor THz modulation rates is megawatts/cm³ ! Similarly a permittivity wave generated by a THz acoustic wave in a single crystal by the acousto-optic effect produces multiple coherent Casimir wave mode overtones and a bulk mode. We model the Casimir effect in a sinusoidally graded medium finding it to be very enhanced over what is found in a multilayer stack for the equivalent permittivity contrast, and more slowly decreasing with scale, going as the wavelength 1/λ². Acoustic waves give comparable theoretical power levels of MW/cm³ below normal crystal damage thresholds. Piezo thermodynamic relations give conditions for effective coupling of the Casimir bulk mode to an external electrical load. Casimir wave modes may exchange energy with the main acoustic wave too, which may partially account for THz attenuation seen in materials. We outline feasibility issues for building a practical crystal power generator.

We consider the Bell's Theorem setup of Gill et. al. (2002). We present a \proof of concept" that if the source emitting the particles can predict the settings of the detectors with sufficiently large probability, then there is a scenario consistent with local realism that violates the Bell inequality for the setup.

It is intended here to propose descriptive explanations for the basic statistical concepts. Although most of them are highly familiar to us, their conventional descriptions have vague sides. Especially it was focused on the absolute probabilistic uncertainty which was characterized by momentum of the measurement device and the system which was measured.

Logical foundation for quantum theory is considered. I claim that quantum theory correctly represents Nature when mathematical physics embraces and indeed features, logical anomalies inherent in pure mathematics. This approach links undecidability in arithmetic with the logic of quantum experiments. The undecidablity occupies an algebraic environment which is the missing foundation for the 3-valued logic predicted by Hans Reichenbach, shown by him to resolve `causal anomalies' of quantum mechanics, such as: inconsistency between prepared and measured states, complementarity between pairs of observables, and the EPR-paradox of action at a distance. Arithmetic basic to mathematical physics, is presented formally as a logical system consisting of axioms and propositions. Of special interest are all propositions asserting the existence of particular numbers. All numbers satisfying the axioms permeate the arithmetic indistinguishably, but these logically partition into two distinct sets: numbers whose existence the axioms determine by proof, and numbers whose existence axioms cannot determine, being neither provable nor negatable. Failure of mathematical physics to incorporate this logical distinction is seen as reason for quantum theory being logically at odds with quantum experiments. Nature is interpreted as having rules isomorphic to the abovementioned axioms with these governing arithmetical combinations of necessary and possible values or effects in experiments. Soundness and Completeness theorems from mathematical logic emerge as profoundly fundamental principles for quantum theory, making good intuitive sense of the subject.

It is shown that the atomic number Z is prime at the beginning of the each s¹, p¹, d¹, and f¹ energy levels of electrons, with some fluctuation in the actinide and lanthanide series. The periodic prime number boundary of s¹, p¹, d¹, and f¹ is postulated to occur because of stability of Schrodinger�s wave equation due to a fundamental relationship with the Riemann-Zeta function.

Within quantum measurement there is the sharp dierence in the dynamics between the case when the eigenstate of the prepared quantum system is different from any of those of the measuring device, and on the other and, when it is the same with one of those of the measuring devices. It is argued that here one may face a "second measurement problem".

Quantum theory brought an irreducible lawlessness in physics. This is accompanied by lack of specication of state of a system. We can not measure states even though they ever existed. We can measure only transition from one state into another. We deduce this lack of determination of state mathematically, and thus provide formalism for maximum precision of determination of mixed states. However, the results thus obtained show consistency with Heisenberg's uncertainty relations.

Atomic structure model was proposed as a rotating stratified fl uidic matter field with the particles corresponded to solitary waves in the field. Mathematical formulation of the proposed structure was constructed on the model of thermal convection in rotating spherical shells of conducting fluids using magnetohydrodynamic Navier-Stokes Equations. Acceleration term was derived using Coulomb potential. Novel model showed that internal structure of atoms is subjected to complex fluid dynamics.

Quantum theory is a probabilistic theory, where certain variables are hidden or non-accessible. It results in lack of representation of systems under study. However, I deduce system's representation in probabilistic manner, introducing probability of existence w, and quantize it exploiting Schrödinger's quantization rule. The formalism enriches probabilistic quantum theory, and enables systems's representation in probabilistic manner.

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has solution containing imaginary part, which differs appreciably from known solution of KGE. In the present article we present numerical /computer solution of radial biquaternionic KGE (radialBQKGE); which differs appreciably from conventional Yukawa potential. Further observation is of course recommended in order to refute or verify this proposition.

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.

Using phion condensate model as described by Moffat [1], we consider a plausible explanation of (Tifft) intrinsic redshift quantization as described by Bell [6] as result of Hall effect in rotating frame. We also discuss another alternative to explain redshift quantization from the viewpoint of Weyl quantization, which could yield Bohr-Sommerfeld quantization.

In this paper we present four possible extensions of Bell's Theorem: Bayesian and Fuzzy Bayesian intrepretation, Information Fusion interpretation, Geometric interpretation, and the viewpoint of photon fluid as medium for quantum interaction.

In the present article, we argue that it is possible to generalize Schrödinger equation to describe quantization of celestial systems. While this hypothesis has been described by some authors, including Nottale, here we argue that such a macroquantization was formed by topological superfluid vortice. We also provide derivation of Schrödinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid dynamics interpretation.

This article shows, Synge-Weber's classical problem statement about two particles interacting by a signal can be reduced to the case where the same particle is located in two different points A and B of the basic space-time in the same moment of time, so the states A and B are entangled. This particle, being actual two particles in the entangled states A and B, can interact with itself radiating a photon (signal) in the point A and absorbing it in the point B. That is our goal, to introduce entangled states into General Relativity. Under specific physical conditions the entangled particles in General Relativity can reach a state where neither particle A nor particle B can be the cause of future events. We call this specific state Quantum Causality Threshold.

In this short paper, as an extension and consequence of Einstein-Podolski-Rosen paradox and Bell's inequality, one promotes the hypothesis (it has been called the Smarandache Hypothesis [1, 2, 3]) that: There is no speed barrier in the Universe and one can construct arbitrary speeds, and also one asks if it is possible to have an infinite speed (instantaneous transmission)? Future research: to study the composition of faster-than-light velocities and what happens with the laws of physics at faster-thanlight velocities?

There can be generated many paradoxes or quasi-paradoxes that may occur from the combination of quantum and non-quantum worlds in physics. Even the passage from the micro-cosmos to the macro-cosmos, and reciprocally, can generate unsolved questions or counter-intuitive ideas. We define a quasi-paradox as a statement which has a prima facie self-contradictory support or an explicit contradiction, but which is not completely proven as a paradox. We present herein four elementary quantum quasi-paradoxes and their corresponding quantum Sorites paradoxes, which form a class of quantum quasi-paradoxes.

In the light of some recent hypotheses suggesting plausible unification of thermostatistics where Fermi-Dirac, Bose-Einstein and Tsallis statistics become its special subsets, we consider further plausible extension to include non-integer Hausdorff dimension, which becomes realization of fractal entropy concept. In the subsequent section, we also discuss plausible extension of this unified statistics to include anisotropic effect by using quaternion oscillator, which may be observed in the context of Cosmic Microwave Background Radiation. Further observation is of course recommended in order to refute or verify this proposition.

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has solution containing imaginary part, which differs appreciably from known solution of KGE. In the present article we discuss some possible interpretation of this imaginary part of the solution of biquaternionic KGE (BQKGE); thereafter we offer a new derivation of biquaternion Schrödinger equation using this method. Further observation is of course recommended in order to refute or verify this proposition.

I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, to of the equation exhibits an asymmetry in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Moun - despite their acute similarities - exhibit an asymmetry in their mass is possible. The Moun is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible.

In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). We believe that the fact that this modification is consistent with the STR gives the present effort some physical justification that warrants further investigations. From the vantage point of unity, simplicity and beauty, it is natural to wonder why should there exist different equations to describe particles of different spins? For example, the Klein-Gordon equation describes spin-0 particles, while the Dirac Equation describes spin-1/2, and the Rarita-Schwinger Equation describes spin-3/2. Does it mean we have to look for another equation to describe spin-2 particles, and then spin-5/2 particles etc? This does not look beautiful, simple, or at the very least suggest a Unification of the Natural Laws. Beauty of a theory is not a physical principle but, one thing is clear to the searching mind - i.e., a theory that possesses beauty, appeals to the mind, and is (posteriori) bound to have something to do with physical reality if it naturally submits itself to the test of experience. The effort of the present reading is to make the attempt to find this equation.

A new nonlinear Schrödinger equation is obtained explicitly from the (fractal) Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy plane-wave solutions and solitons exist in the free particle case. One remarkable feature of this nonlinear Schrödinger equation based on a ( fractal) Brownian motion model, over all the other nonlinear QM models, is that the quantum-mechanical energy functional coincides precisely with the field theory one. We finalize by showing why a complex momentum is essential to fully understand the physical implications of Weyl's geometry in QM, along with the interplay between Bohm's Quantum potential and Fisher Information which has been overlooked by several authors in the past.

An electromagnetic wave with the wavelength lambda, which has some energy, descends on an electron and makes it move in the same direction of propagation of the wave. The wave makes the moving electron oscillate with a lower frequency. A simple analysis shows that this moving oscillating electron radiates, in the direction making angle theta with the direction of the incident wave, an electromagnetic wave which its wavelength is bigger by a factor proportional to lambda(1 − cos theta). The mechanism presented for pushing the electron, necessitates that Camton scattering to cease if the experiment is performed in vacuum. (I'm ready to prepare for doing such a critical test experiment in any university as a guest researcher.)

Since Berry demostrated that the standard description of adiabatic processes in quantum mechanics was incomplete, geometric phases have been studied in many areas of physics. Both adiabatic and non-adiabatic phase are described in detail, with the mathematical background. Then we study the qbit, that is the principal unit of information of the quantum computation, and its representation on the Bloch sphere. Finally we find the general expression for geometric phases for qbits. Those final expression are in fact related to the solid angle enclosed in the circuit on the Bloch sphere.

I have already earlier proposed the explanation of FQHE, anyons, and fractionization of quantum numbers in terms of hierarchy of Planck constants realized as a generalization of the imbedding space H = M⁴ x CP₂ to a book like structure. The book like structure applies separately to CP₂ and to causal diamonds (CD ⊂ M⁴) defined as intersections of future and past directed light-cones. The pages of the Big Book correspond to singular coverings and factor spaces of CD (CP₂) glued along 2-D subspace of CD (CP₂) and are labeled by the values of Planck constants assignable to CD and CP₂ and appearing in Lie algebra commutation relations. The observed Planck constant h, whose square defines the scale of M⁴ metric corresponds to the ratio of these Planck constants. The key observation is that fractional filling factor results if h is scaled up by a rational number. In this chapter I try to formulate more precisely this idea. The outcome is a rather detailed view about anyons on one hand, and about the Kähler structure of the generalized imbedding space on the other hand.

It is appropiate to start by quoting page xv �a first meaning of the novel hadronic mechanics is that of providing the first known methods for quantitative studies of the interplay between matter and the underlying substratum. The understanding is that space is the final frontier of human knowledge, with potential outcomes beyond the most vivid science fiction of today�. In this almost prophetic observations, Prof. Santilli has pointed out to the essential role of the substratum, its geometrical structure and the link with consciousness. In the present article, which we owe to the kind invitation of Prof. Santilli, we shall present similar views, specifically in presenting both quantum and hadronic mechanics as spacetime fluctuations, and we shall discuss the role of the substratum. As for the problem of human knowledge, we shall very briefly indicate on how the present approach may be related to the fundamental problem of consciousness, which is that of self-reference.

We review the relation between space-time geometries with torsion fields (the so-called Riemann-Cartan-Weyl (RCW) geometries) and their associated Brownian motions. In this setting, the metric conjugate of the tracetorsion one-form is the drift vector field of the Brownian motions. Thus, in the present approach space-time fluctuations as Brownian motions are -in distinction with Nelson�s Stochastic Mechanics- space-time structures. Thus, space and time have a fractal structure. We discuss the relations with Nottale�s theory of Scale Relativity, which stems from Nelson�s approach. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. In this work, the Schroedinger field is a torsion generating field. The potential functions on Schroedinger equations can be alternatively linear or nonlinear on the wave function, leading to nonlinear and linear creation-annihilation of particles by diffusion systems.

It is appropiate to start by quoting Prof. Santilli: �a first meaning of the novel hadronic mechanics is that of providing the first known methods for quantitative studies of the interplay between matter and the underlying substratum. The understanding is that space is the final frontier of human knowledge, with potential outcomes beyond the most vivid science fiction of today�. In this almost prophetic observation, Prof. Santilli has pointed out to the essential role of the substratum, its geometrical structure and the link with consciousness. In the present article, which we owe to the kind invitation of Prof. Santilli, we shall present similar views, specifically in presenting both quantum and hadronic mechanics as space-time fluctuations, and we shall discuss the role of the substratum. As for the problem of human knowledge, we shall very briefly indicate on how the present approach may be related to the fundamental problem of consciousness, which is that of self-reference.

We suggest that the electron is a wave in the whole process between the electron gun and the sensor. Between the two-slit and the sensor, the following two phenomena happen to the waves: interference and Fraunhofer diffraction. Due to these two phenomena, a considerably sharp shape of wave is finally made in front of the sensor, and a bright spot appears on the sensor. The experiment result that a bright spot appears at random can be explained by the abovementioned two phenomena and the �fluctuation� of the potential energy that the filament of the biprism makes. All are the wave motion phenomena, and, put simply, the particle called an electron does not exist.

The idea that configuration space CH of 3-surfaces, �the world of classical worlds�, could be realized in terms of number theoretic anatomies of single space-time point using the real units formed from infinite rationals, is very attractive.

We reintroduce the Riemann-Cartan-Weyl geometries with trace torsion and their associated Brownian motions on spacetime to extend them to Brownian motions on the tangent bundle and exterior powers of them. We characterize the diffusion of differential forms, for the case of manifolds without boundaries and the smooth boundary case. We present implicit representations for the Navier-Stokes equations (NS) for an incompressible fluid in a smooth compact manifold without boundary as well as for the kinematic dynamo equation (KDE, for short) of magnetohydrodynamics. We derive these representations from stochastic differential geometry, unifying gauge theoretical structures and the stochastic analysis on manifolds (the Ito-Elworthy formula for differential forms. From the diffeomorphism property of the random flow given by the scalar lagrangian representations for the viscous and magnetized fluids, we derive the representations for NS and KDE, using the generalized Hamilton and Ricci random flows (for arbitrary compact manifolds without boundary), and the gradient diffusion processes (for isometric immersions on Euclidean space of these manifolds). We solve implicitly this equations in 2D and 3D. Continuing with this method, we prove that NS and KDE in any dimension other than 1, can be represented as purely (geometrical) noise processes, with diffusion tensor depending on the fluid�s velocity, and we represent the solutions of NS and KDE in terms of these processes. We discuss the relations between these representations and the problem of infinite-time existance of solutions of NS and KDE. We finally discuss the relations between this approach with the low dimensional chaotic dynamics describing the asymptotic regime of the solutions of NS. We present the random symplectic theory for the Brownian motions generated by these Riemann-Cartan-Weyl geometries, and the associated random Poincare-Cartan invariants. We apply this to the Navier-Stokes and kinematic dynamo equations. In the case of 2D and 3D, we solve the Hamiltonian equations.

We review the relation between space-time geometries with torsion fields (the so-called Riemann-Cartan-Weyl (RCW) )geometries) and their associated Brownian motions. In this setting, the metric conjugate of the tracetorsion one-form is the drift vectorfield of the Brownian motions. Thus, in the present approach, Brownian motions, in distinction with Nelson�s Stochastic Mechanics, are spacetime structures. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a noncanonical quantum RCW geometry in state-space associated with the gradient of the quantum-mechanical expectation value of a self-adjoint operator given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wave function in terms of a RCW quantum geometry in state-space. We characterize the Schroedinger equation for both an observed and unobserved quantum systems in terms of the RCW geometries and Brownian motions. Thus, in this work, the Schroedinger field is a torsion generating field, and the U and R processes, in the sense of Penrose, are associated, the former to spacetime geometries and their associated Brownian motions, and the latter to their extension to the state-space of nonrelativistic quantum mechanics given by the projective Hilbert space. In this setting, the Schroedinger equation can be either linear or nonlinear. We discuss the problem of the many times variables and the relation with dissipative processes. We present as an additional example of RCW geometries and their Brownian motions counterpart, the dynamics of viscous fluids obeying the invariant Navier-Stokes equations. We introduce in the present setting an extension of R. Kiehn�s approach to dynamical systems starting from the notion of the topological dimension of one-forms, to apply it to the trace-torsion one-form whose metric conjugate is the Brownian motion�s drift vectorfield and discuss the topological notion of turbulence. We discuss the relation between our setting and the Nottale theory of Scale Relativity, and the work of Castro and Mahecha in this volume in nonlinear quantum mechanics, Weyl geometries and the quantum potential.

A theory of quantum mechanics in terms of a quantized spacetime shows that Einstein was correct in his debate with Bohr. The conflict of the axioms of quantum field theory and the axioms of general relativity may resolved by modifying both and equating quantum field theory with harmonic analysis on the complex space-time QAdS = U(3, 2)/U(3, 1)xU(1). This is consistent with the geometry of particle interactions introduced in Love

In [G2] a semiclassical model based on dark matter and hierarchy of Planck constants is developed for the fractionized principal quantum number n claimed by Mills [1] to have at least the values n =