In various articles1 2, 3 , the author developed a mathematical model showing interesting applications in physics. The following article analyzes the coordinates transformation produced by a vectorial pseudo-rotation. The invariant quantities after a pseudo-rotation and the Doppler effect for light are also presented. Still, the paper's main purpose is to deduce the matter wave equation as the natural consequence of intrinsic properties of the "physical world" and its Hnumber representation. Ever since de Broglie formulated his hypothesis, the physics of matter waves was playing an important role in the field of the measurement technique4 . In the last decade, matter waves optics enabled numerous applications ranging from basic science to navigation or detection systems technologies.
In various articles1 2, 3 , the author developed a mathematical model showing interesting applications in physics. The following article analyzes the coordinates transformation produced by a vectorial pseudo-rotation. The invariant quantities after a pseudo-rotation and the Doppler effect for light are also presented. Still, the paper's main purpose is to deduce the matter wave equation as the natural consequence of intrinsic properties of the "physical world" and its Hnumber representation. Ever since de Broglie formulated his hypothesis, the physics of matter waves was playing an important role in the field of the measurement technique4 . In the last decade, matter waves optics enabled numerous applications ranging from basic science to navigation or detection systems technologies.
Momentum and Kinetic Energy equations are developed from the hypothesis that oppositely directed components of harmonically oscillating pseudo standing waves pass through a quantum particle center and can be represented by Longitudinal Matter Waves that carry the particle’s momentum and energy. The Doppler effect on the component wave lengths allows the net forward momentum and kinetic energy to increase with speed well beyond classical values. De Broglie (1925) issues with stationary wavelength and moving pulse rate are resolved in a different manner. Because a quantum particle is considered to be nothing more than the sum of “in” and “out” matter waves focused through its center, whatever happens to these matter waves determines the future location of that center. This opens the door to physical explanations for gravity, interference, and the slowdown of light in transparent mediums. Gravity, for example, is shown in section 6, to possibly be caused by the local gradient in matter wave speed near a large body like earth.
The theory is based on a new hypothesis on the nature of matter. This hypothesis is that the elementary particles, atoms, and molecules we have found in nature are not part of the real world, but constitute information about the real world. They are the wave components of a generalized Fourier analysis of our observations (which in the final analysis are always space-time distributions of photon- or particle-counter clicks). This Fourier analysis should be so general that every observation can be expressed in its terms; it thereby becomes axiomatic. Physicists of past generations, with their sound instincts, were intuitively approaching this most general and most powerful possible analysis of our observations. With the discovery of quantum mechanics, this development had advanced so far that the precise formulation of this ultimate analysis could be guessed. The model which can guide us to this mathematical formulation is that of an ideal optical observation on a physical object. This observation is made by illuminating the object with a finite number of laser beams of known amplitude and phase, and observing the amplitude and phase of the finite number of light beams emerging from the object space. The assumption that this is all the information we can ever obtain about the object leads to a wave function of the object which consists of light waves, extrapolated from the photon detectors back to the object space. It is suggested that these light waves should be presented as a product of amplitudes in a 4n-dimensional space, where n is the number of light quanta in the signal. Most important, force, or interaction, can then be described as a linear transformation in this space. The actual mathematical formalism proposed on the basis of that model is Xf=dtitdf. X is the Hamiltonian of the whole universe with ${n}_{0}\ensuremath{\cong}{10}^{80}$ particles. It is a $4{n}_{0}\ifmmode\times\else\texttimes\fi{}4{n}_{0}$ linear matrix operator. f is a 4n0-component vector wave function representing waves traveling at the speed of light. The coordinates are the homogeneous coordinates (xj,yj,zj,uj) of the n0 particles in the closed universe. The eigenvalue $\ensuremath{\omega}$, in $Xf=\ensuremath{\omega}f$, is a $4{n}_{0}\ifmmode\times\else\texttimes\fi{}4{n}_{0}$ Hermitian matrix. It can be divided into ${n}_{0}\ifmmode\times\else\texttimes\fi{}{n}_{0}$, 4 \ifmmode\times\else\texttimes\fi{} 4 submatrices, each representing a complete set of dynamic and inertial quantities of elementary particles, or interaction quanta between particles. $\frac{\mathrm{it}df}{\mathrm{dt}}=\ensuremath{\omega}f$ is therefore a complete expression of the dynamic conservation laws. A special orthogonal transformation ${\ensuremath{\alpha}}_{0}$ transforms the solution into a standard solution with eigenvalue ${\ensuremath{\omega}}_{0}$, representing n0 identical elementary particles. The assumption that the universe is of maximum probability then leads to simple explicit expressions for all matrix elements of ${\ensuremath{\omega}}_{0}$. This means that the energy levels of all n-particle systems (atoms or molecules) of the theory can be directly calculated. The equations demand relations between cosmological constants and atomic constants. In a universe of the size and mass of our observed universe, the elementary particle would have to be the size of the proton.
More than a hundred years ago, a series of discoveries, especially in physics, began to subtly (or maybe not) reveal some mysterious properties of matter, properties that in some fashion or other were not acceptable to our established way of perceiving Reality. Strangely enough, these properties were not taken seriously by science because they pointed to a reality that seemed too fantastical to be true, a reality that seemed to have no substance or permanence. These so called mysterious properties matter, for lack of a better word, turn out to be fundamentally related to the following discoveries: The ambiguous wave-particle duality. As in de Broglie matter-waves and the Compton properties of particles. The ubiquitous appearance of the cycle constant (τ=2π=C⁄r) in physical mathematical relations. The general applicability of the Fourier Transform to represent/model physical motion and other natural processes. The Heisenberg Uncertainty Principle and its mysterious constraint between conjugate variables, momentum and position for example. Quantum Mechanics and its collapse of the wavefunction. The surprising mass-energy equivalence. As in Einstein’s E=mc^2. The perplexing isotropy of the speed of light. The mind boggling time dilation and length contraction of Einstein’s Special Relativity (SR). The contradictory fabric of SR/GR’s spacetime and its assignment of properties to the void. The surprisingly discrete nature of atomic properties. As in Quantum Mechanics (QM). Needless to say, no matter what science has tried in order to fit the above discoveries into our physical world, their implications continue to elude an intuitively acceptable explanation in material terms. This monograph, although not necessarily in chronological order, is a recapitulation of previous monographs written by the author in an attempt at a single-source theoretical explanation/clarification for the above mentioned list of “mysterious” properties of matter, in terms of one fundamental set of properties, the motional geometry of matter.
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what the wave function represents. Besides the statistical meaning suggested by the Copenhagen interpretation, does the wave function represent any physical motion? For photon, we know it is an electro-magnetic wave. But what about particles with rest mass, such as an electron? To investigate the physical nature of matter wave, we propose that: (1) Like the photon, a particle is an excitation wave of a real physical field. (2) Different types of particles are different excitation modes of the same field. Based on this thinking, we show that the concept of quantum mechanics can be a natural extension of classical mechanics. By critically analyzing the transition from classical physics to quantum physics, we found a new physical meaning for the quantum wave function. This work suggests that various quantum wave equations, including the Klein-Gordon equation, the Dirac equation and the Schrodinger equation, could have a common base relating to the Basic Wave Equation of the matter wave. This work has some interesting implications. It suggests a possible way to explain the origin of visible matters and dark matters in our universe.
A hypothesis is put forward according to which the formulas of Relativity are a consequence of the laws of quantum physics and may be applied only to quantum objects. According to the wave - particle duality quantum bodies are simultaneously the waves and considered in the present research with a use of the wave equation and requirement of its Lorentz‘s invariance. The property of invariance with respect to the Lorentz’s transform is analysed in hyperbolic coordinates in an area of complex numbers. An examination showed that formulas of relativistic kinematics can be obtained based on the condition of equality of the amplitudes and phases of the wave, observed from different inertial frames. There is no need to introduce the concept of a unified entity of space-time, but the return to the idea of aether and matter waves de Broglie occurs. The physical model becomes borrowed partly from quantum field theory. It is assumed that the moving particle binds to a wave of the aether disturbance, and only this wave acts on the other particle like an electromagnetic field pushes an electrical charge. The model of colliding elastic balls becomes inapplicable, but equations of relativity mechanics remain the same, however, with a new interpretation. The mass of a particle in all coordinate systems is constant, in exchange the expressions of energy and momentum alter relative the classical case, include the property of aether – coefficient c of the wave equation, and acquire relativistic forms.
Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by coordinate and momentum spinors. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Dirac equation the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Quantum mechanics describes interactions using complex wave functions that cannot be observed directly; only upon measurement do they translate into probabilities expressed as the squares of the magnitudes of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors. In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In the presence of a potential the momentum components cease to commute with each other. To neutralize this effect, the Schrödinger equation is supplemented by several equations with mixed partial derivatives on coordinates. Section 3 presents a version of quantum theory in spinor coordinate space. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. An equation of motion for the electron is proposed that is relativistically invariant. This novel equation permitted the construction of an actually invariant procedure for the second quantization of the fermion field in spinor coordinate space. Furthermore, it is demonstrated that the field operators are a combination of plane waves in spinor or vector space, with the coefficients of which being pseudospinors or pseudovectors. Furthermore, each plane wave possesses an additional coefficient in the form of a creation or annihilation operator. In vector space, these operators commute, whereas in spinor space they anticommutate. The paper presents the spinor and vector representations of the field operators in explicit form, comprising sets of 16 pseudospinors or 4 pseudovectors. An explicit form of the symmetric traceless tensor with spin two, zero mass and two polarizations are presented, which can serve as a model of the graviton. Section 5 presents Einstein's inhomogeneous equation, which features the Riemann tensor rather than the Ricci tensor, with the energy-momentum tensor of a charged particle having four indices rather than two. In the case where a particle of matter has a charge, another Riemann tensor is added to Einstein’s equation, in addition to the usual Riemann curvature tensor, which describes the additional curvature created for a charged particle by an electromagnetic field.