The expectation value of the total energy of a wave packet, associated with the speed (moments) space by means of the Lorentz transformation, allows us to obtain by means of quantum wave formulation an energetic expression equivalent, and at the same time less restricted (more versatile and informative), to the one obtained by means of a corpuscular treatment. On the one hand, the energetic formants of the matter appear, on the other the expression in undulatory terms of it, of that which we call mass, and finally an additional phase factor as the last vestige of the undulatory nature after the formation process, that is to say, as an accrediting element of that nature, and mechanism of restitution of it, responsible for the wave-corpuscle duality, of the related creation-annihilation processes, and of the relations among the different generations of elementary particles, as it was shown in https://vixra.org/abs/2003.0001.
The expectation value of the total energy of a wave packet, associated with the speed (moments) space by means of the Lorentz transformation, allows us to obtain by means of quantum wave formulation an energetic expression equivalent, and at the same time less restricted (more versatile and informative), to the one obtained by means of a corpuscular treatment. On the one hand, the energetic formants of the matter appear, on the other the expression in undulatory terms of it, of that which we call mass, and finally an additional phase factor as the last vestige of the undulatory nature after the formation process, that is to say, as an accrediting element of that nature, and mechanism of restitution of it, responsible for the wave-corpuscle duality, of the related creation-annihilation processes, and of the relations among the different generations of elementary particles, as it was shown in https://vixra.org/abs/2003.0001.
In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E ¯ ω = E ¯ k + E ¯ f , which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation ( E=m c 2 =hν ), i.e. to explain through m the intimate sense of the first equivalence, which explains what ν is in the second one.
The theory of relativity represents fields of force as structural properties of space-time, and a field of force is the arena in which the presence of energy is detectable. Energy manifests itself in the physical world as radiation, and Einstein established its fundamental identity with mass.1 This has since been demonstrated experimentally by the annihilation of elementary particles and their conversion into y-rays and the reverse process of conversion of y-rays into pairs of electrons and positrons ('pair production') as observed by Blackett and Occhialini. It is hardly surprising, therefore, that both matter and energy should appear to us in the same phenomenal forms, as particles and as waves. The universal interconnectedness of things is here again exemplified. Space-time structure, in the form of curvature of differing degrees, appears as field, and field, by what Teilhard would call 'complexification', organizes itself into material particles. The contemporary theory of matter, notwithstanding disputes and controversies still current about the concepts involved, unquestionably represents the atom as a complicated organization of fields of force describable without misrepresentation as an energy complex. This being so, an unbroken continuity between space-time, field, energy and matter is established, as a series of forms or manifestations of the real, each a more complex elaboration of its predecessor in the series. The progression is effected, to borrow again from Teilhard, by a process of self-enfoldment (enroulement sur soi-meme) of the prior form: curvature of space gives field, the structure or complexity of the field (as we are about to find) takes the form of waves (or radiation), further complication of these, by superposition, produces wave-packets or particles, and the intricate organization of particles into a single energy system constitutes the atom.
In the wave-particle duality, a free particle can be considered as a wave packet. Is there a wave property that corresponds to the rest mass of the particle? This is an interesting question that has not been extensively explored before. We suggest that this problem may be approached by treating the rest mass on the same footing as energy and momentum. Here we demonstrate that, by assuming that the matter wave of a particle behaves like a photon, one could derive the mass-energy relation from the solution of a simplified wave equation. This solution suggests that the rest mass of a particle is associated with a "transverse wave number", which characterizes the radial variation of the wave function in the transverse plane. This finding has several appealing features. For example, it shows a consistent geometrical relationship between mass, energy and momentum in both the wave and particle perspectives. Also, it predicts that a massless particle must travel at the constant speed of light. Furthermore, from a philosophical point of view, this model suggests that the mass-energy relation attributed to the special theory of relativity may have a root in the wave-particle duality. Indeed, it is shown that the Klein-Gordon equation can be derived naturally based on this model.
Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric potential where this particle is confined, the vector potential of the electromagnetic radiation, and the gravitational potential. In the gravitational field of a black hole, the velocity of a quantum particle is directed to the Schwarzschild boundary from the outside and from the inside, without passing this boundary. When the very strong gravitational field of a large agglomeration of matter has spherical symmetry with a radius smaller than the Schwarzschild radius, the quantum particles in the central region are crushed up to quasi-uniform distributions of matter, exploding with velocities much larger than the light velocity, towards the Schwarzschild boundary, but decelerating in the gravitational field and reaching this boundary only in an infinite time. The matter of a black hole has the tendency to concentrate around the Schwarzschild boundary, with a radius proportional to its mass. In this framework, we believe that our universe is a huge black hole, with the explosion of its central matter as the Big Bang-inflation process, and an increasing radius on account of an absorption of matter from the Total Universe, where our universe has been formed. In a gravitational wave, the time-space interval in the first-order approximation is the product of a gravitational invariant including the amplitude tensor, and a coordinate invariant including the polarization vector. The gravitational invariant describes a rotation of the metric tensor around the direction of the propagation of this wave, with spin 2, as a gravitational quantum called graviton. The coordinate invariant describes a matter rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.
The interference of laser photons (λ=532 nm) when they pass through two slits of the same width has been studied. The interference is observed up to the value S≈11 mm between the slits. Based on this, the assumption has been made that all elementary particles are soliton formations of the electromagnetic field. Solitons of classical physics exhibit the properties of a wave and a corpuscle, thus, we have an explanation of the corpuscular-wave nature of elementary particles as a phenomenon of classical physics. For the formation of solitons, the presence of a medium with the properties of dispersion and nonlinearity is necessary, and this contradicts the foundations of SRT. In this regard, a number of problems related to the foundations of SRT have been analyzed. It has been established that SRT does not pass the verification by the correspondence principle, since at low speeds the Lorentz transformation of time does not pass into the Galilean transformation. This means that SRT cannot be a physical theory. The reader’s attention is drawn to the fact that the relationship between the mass of a body and its internal energy, as well as the dependence of the mass of a body on the speed of its motion, do not belong to the problems of the theory of relativity, and therefore, their experimental confirmation cannot be an argument in favor of SRT. It is shown that the idea of the independence of the speed of quanta on the speed of the frame has a direct experimental refutation – the results of measuring the rotation periods of Io (a satellite of Jupiter) taking into account the addition and subtraction of velocities make it possible to obtain results for the speed of light with an accuracy of 1% of the reference value. This is a direct experimental refutation of the SRT.