The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual statement: the Coulomb's force (or gravitational force) acts along the line joining a couple of particles (in usual 3D space), so the direction of 4-vector Coulomb's force is carefully investigated, it is found that Maxwell's equations can be derived from classical Coulomb's force and the orthogonality. The second clue, a 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the 4-vector force reduces to 3, however we prove that 4-vector Coulomb's force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the 4-vector Coulomb's force, hinting that this missing undefined component is a hidden variable. The third clue, the best way to study the hidden variable is to establish a new concept: Z-space, in which the undefined component of 4-vector Coulomb's force can be clearly defined as the hidden variable for the quantum mechanics. At the last, the undefined component is regarded as a fluctuating source that contributes to Lorentz force, so that the quantum wave equation can be derived out in the ensemble space of particle motion from the relativistic Newton's second law.
The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual statement: the Coulomb's force (or gravitational force) acts along the line joining a couple of particles (in usual 3D space), so the direction of 4-vector Coulomb's force is carefully investigated, it is found that Maxwell's equations can be derived from classical Coulomb's force and the orthogonality. The second clue, a 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the 4-vector force reduces to 3, however we prove that 4-vector Coulomb's force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the 4-vector Coulomb's force, hinting that this missing undefined component is a hidden variable. The third clue, the best way to study the hidden variable is to establish a new concept: Z-space, in which the undefined component of 4-vector Coulomb's force can be clearly defined as the hidden variable for the quantum mechanics. At the last, the undefined component is regarded as a fluctuating source that contributes to Lorentz force, so that the quantum wave equation can be derived out in the ensemble space of particle motion from the relativistic Newton's second law.
According to the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, but we found that the electromagnetic force of the Maxwell's theory can not completely satisfy this orthogonality, this incompletion leads us to find that the electromagnetic force has two independent components in the 4 dimensional space time. A 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the force reduces to 3, while the electromagnetic force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the electromagnetic force. This missing undefined component may serve as a hidden variable which quantum mechanics is eager to find for a long time. The primary purpose of this paper is to strictly proof that the electromagnetic force has two independent components in the 4 dimensional space time. We also briefly discuss the possibility that the undefined component of the electromagnetic force serves as a hidden variable for quantum mechanics.
Re-examination of the work of Max Karl Planck has revealed hidden variables in his famous quantum work, consistent with Einstein's famous sentiment that quantum mechanics is incomplete due to the existence of "hidden variables". The recent discovery of these previously hidden variables, which have been missing from the foundational equations of quantum theory for more than one hundred years, has important implications for all the sciences as well as for understanding the interactions of electromagnetic radiation with matter. Planck's quantum formula, E = hν, is missing the variable for measurement time. Planck had included the missing time variable in his earlier electromagnetic work, but omitted it in his famous work that sparked the quantum revolution. Restoration of measurement time to Planck's quantum formula produces the more complete, E = h~ ν t. The numerical value Planck calculated for his action constant "h" takes on new meaning as an energy constant "h~" for light. Planck's energy constant is the mean energy of a single oscillation of light, namely 6.626 X 10-34 J/oscillation. The mean oscillation energy of light is constant, and does not vary with frequency or wavelength. The photon, as historically defined, is a time dependent packet of energy, based on the arbitrary measurement time of one second. An arbitrary, one second increment of energy cannot be a truly indivisible and elementary particle of nature. Omission of the time variable from Planck's quantum formula contributed to numerous paradoxes in quantum mechanics, such as uncertainty relating to formulations involving time, wave-particle duality, the need for normalization of wave functions, lack of dimensions for the fine structure constant, and irreconcilability of quantum mechanics and general relativity (Einstein's gravitational theory). Many of these paradoxes are simplified or eliminated altogether with a re-interpretation of quantum mechanics with Planck's hidden time variable and energy constant.
The nondeterministic character of quantum measurement can, and should, be taken to imply a deeper 'hidden variable' description of a system, which reproduces quantum theory when the unknown values of the variables are marginalised over. Differences in measurements on identically prepared systems then represent differences in the hidden variables of the systems. Not to seek the hidden variables, as the Copenhagen interpretation of quantum mechanics arbitrarily instructs, is to give up all hope of improvement in advance, and is contrary to the purposes of science. Correspondingly, it can never be proven that hidden variables don't exist; the most that can be done is to place hypothetical restrictions on them and prove that the resulting theory cannot be marginalised into quantum theory - implying that the hidden variables violate the restriction. The best known example is Bell's theorem, which rules out all local hidden-variable theories and explains why the variables are so coy: it is not easy to isolate and influence something nonlocal. A promising way forward is to proceed from the Dirac theory of the electron in its natural, geometric language of Clifford algebra. This approach, due to Hestenes, suggests that the free electron is in fact a massless point particle executing zitterbewegung at the speed of light, with radius the electron Compton wavelength. This proposal improves the correspondence of the physics with the formalism and resolves many paradoxes; it also hints that the hidden variables are concerned with those parameters needed to define the electron orbit completely. These ideas all represent a demystification of quantum theory. In the 19th century, microscopes advanced to the point at which a new phenomenon, today called Brownian motion after its chronicler, could be seen. The small particles, newly made visible ('dust' particles), were observed to jiggle around in a manner the scientists could not predict, for no apparent reason. Motion of any individual dust particle could not be predicted; however, statistical details of the motion, such as the average (drift) velocity or the mean square velocity, were reproducible. The scientists of the day, probably without realising it, made an assumption: that there was a reason for the jiggling, and that if they could find this, they could predict the precise motion of individual dust particles. They never said Maybe the dust particles just behave like that and there isn't a why; maybe we can go no further and this is the end of the line. 79
The Lorentz transformation of special relativity is based on velocity. Although this velocity may be differentiated by time, the notion of force is not needed to obtain the Lorentz matrix for a particle with rest mass. In particular, in special relativity one considers frames moving at constant velocities. In the case of a photon, the Lorentz transformation preserves the form of Maxwell’s electromagnetic equations. As a result, there does not seem to be a focus on force, rather the emphasis is on the two 4-vectors (p,E) and (x,t) for a particle with rest mass and photon. Nevertheless, a particle with momentum (and the capability to interact) imparts an impulse. In fact, one may think of energy changing due to an impulse (which includes force). Thus from an information point of view, one may ask: Does this force which creates a change in energy/momentum “disappear” as the particle/photon moves at constant speed only to “reappear” when it strikes a surface? If not, where is the information of this force stored? We argue it is associated with a change in energy and momentum of a free particle which in turn is linked to an internal ruler/clock i.e. the quantum frequency and wavelength from exp(-iEt+ipx) which preserves the force because a spatial probability distribution is created (for the wavelength). This force is linked with a direction i.e. the direction of p through the two dimensionality of exp(ipx). Thus, we argue that the force does not disappear, rather it is manifest in the internal clock and ruler which define spacetime for the free quantum particle, but in a probabilistic manner with the distribution being deterministic to ensure it maps to spatial invariance. One might at first find it surprising that force, usually associated with acceleration (i.e. deterministic motion) is now associated with probability cos(px) in space (, but deterministic probability, not random), but E,p and x,t are intertwined through the Lorentz invariant -Et+px for both a particle with rest mass and photon, so if E and p change, it is not necessarily surprising that t,x also change. Thus an impulse may change p and E, but then remains manifest in the system through the internal clock and ruler gradations in such a way that speed is still constant on average.
Until the introduction of Special Relativity by Hendrik Antoon Lorentz, Herman Minkovski and Albert Einstein in 1905 and General Relativity by Albert Einstein in 1916, Physics has been 3-Dimensional. After this period, Physics became in generally 4-Dimensional with the time as the fourth dimension. For that reason it is remarkable that till now quantum physics has been described by 3-dimensional equations like the Schrodinger wave equation and the relativistic Dirac equation. In this article the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions and the complex conjugated vector probability function will be published. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time 300 years ago. More than 200 years ago before the Dirac Equation had been published. A Return to the Inception of Physics. The time of Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics which was in Harmony with Science and Religion. The Universal Path, the Leitmotiv, the Universal Concept in Physics. Newton found the concept of “Universal Equilibrium” which he formulated in his famous third equation Action = - Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity. The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrodinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrodinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason these material waves in Schrodinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrodinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function. In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrodinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values. Key words : General Relativity; Quantum Physics; Dirac Equation; Gravitational-Electromagnetic Interaction; Black Holes; Gravitational-Electromagnetic Confinement; Electromagnetism; Quantum Optics
Article includes “Linking radioactive dating to origin of the universe” or “How dinosaurs committed scientific heresy & exterminated the Big Bang” Vector-tensor-scalar geometry’s important insights into 1) Cancer, 2) The origin of the moon In a newsletter discussing “Automated discovery of fundamental variables hidden in experimental data” (Chen, B., Huang, K., Raghupathi, S. et al. Automated discovery of fundamental variables hidden in experimental data. Nat Comput Sci 2, 433–442 (2022). Cosmos Magazine attributed the following statement to co-author Qiang Du, “What other laws are we missing simply because we don’t have the variables?” According to Cosmos, another co-author (Hod Lipson) argues that scientists may be misinterpreting or failing to understand many phenomena simply because they don’t have a good set of variables. All of this reminds me of the Hidden Variables associated with Albert Einstein’s doubts about quantum mechanics. I’ve been thinking about hidden variables for perhaps twenty or more years and it seems that their combination with the Mobius strip, figure-8 Klein bottle, base 2 mathematics, vector-tensor-scalar geometry, and Wick rotation might unite quantum mechanics and relativity. The union would result in explanation of particles existing in two or more places at once being due to our frame of reference. It would also explain wave-particle duality and, on a universal scale, why there was no Big Bang. The section on vector-tensor-scalar geometry is very important since it provides insights into 1) cancer, and 2) the origin of the moon. The yet-to-be-discovered underlying physics of the wave function proposed in this comment predicts exactness in outcomes, not probability or randomness. Quantum mechanics says particles can, according to our frame of reference, be in two or more places at once. This frame of reference is necessarily restricted to our present understanding of quantum mechanics which Albert Einstein and his colleagues claimed to be incomplete. Hidden Variables are presently hypothetical factors based on the belief that the theory of quantum mechanics is incomplete. Their identification would lead to exact predictions, not just probabilities, for the outcomes of measurements. Albert Einstein is the most famous proponent of hidden variables. Their existence would vindicate his belief that quantum mechanics is lacking something. It’s proposed here that electronics’ binary digits (1’s and 0’s) are those hidden variables. Despite Bell’s theorem and the more recent Pusey–Barrett–Rudolph theorem, hidden variables can be a valid theory since the following boxed explanation of unification of all time periods allows the existence of both “retarded” waves going forwards in time and the disfavoured “advanced” waves travelling back in time and this permits quantum entanglement of every form of mass if, as shown, gravitational waves interacting with electromagnetic waves is responsible for production of mass. The misperception that the universe is expanding is accounted for by retarded/advanced shift.