The Schrödinger equation ensues from the following axiom: in Cartesian coordinates and in absence of gravitation, to the component , (), of the momentum tensor is associated the operator . We show here this equation is a particular case of the equation that governs, even in presence of gravitation, the oscillatory displacements of the points of the ether shown to be a specific elastic medium. That is to say that the Schrödinger equation of which the solutions are the scalar state functions is a particular case of the equation of the vectorial waves propagated in the ether. As shown in previous publications, a mobile particle is a superposition of these waves that form a globule moving like this particle; here we show, in particular that, in a bound state, it is the interferences of these waves that creates the so called “quantum states”. The ether elasticity theory therefore do not only generalizes the quantum mechanics, but also gives the physical signification of the quantum phenomena.
The Schrödinger equation ensues from the following axiom: in Cartesian coordinates and in absence of gravitation, to the component , (), of the momentum tensor is associated the operator . We show here this equation is a particular case of the equation that governs, even in presence of gravitation, the oscillatory displacements of the points of the ether shown to be a specific elastic medium. That is to say that the Schrödinger equation of which the solutions are the scalar state functions is a particular case of the equation of the vectorial waves propagated in the ether. As shown in previous publications, a mobile particle is a superposition of these waves that form a globule moving like this particle; here we show, in particular that, in a bound state, it is the interferences of these waves that creates the so called “quantum states”. The ether elasticity theory therefore do not only generalizes the quantum mechanics, but also gives the physical signification of the quantum phenomena.
One recalls that we have shown in our precedent publications that the ether is an elastic isotropic medium. One presents the exact equation and its non-relativistic approximation that govern the ether in presence of a Schwarzschild-Coulomb field to which is submitted a Par(m,e) (particle of mass m and of electric charge e ). We present the exact relativistic solution of this exact equation in the circular case. We prove that the Schrödinger equation is such a non-relativistic approximation, that is, is a particular case of the ether elasticity theory. One recalls that the Schrödinger equation was obtained by the use of operators and not from the theory of elasticity. It follows that this manner of obtaining this equation from operators is arbitrary and does not permit to obtain its complete relativistic form, but permits to reach absurd conclusions as, e.g., the cat that, at the same moment, is alive and dead. One shows then that other results ensuing from the Schrödinger equation are particular cases of the non-relativistic equation that governs the elastic ether, like for example: the Bohr-Sommerfeld condition, and the eigenstates function equation.
The theory of Quantum Electromagnetics presents a wave equation which is constructed, in compliance with Galilean transformations, for electromagnetic and matter waves. A fundamental feature entirely different from the principle of relativity is that the wave equation is referred specifically to the proposed local-ether frame. For electromagnetic wave, the local-ether wave equation accounts for a wide variety of experiments on propagation and interference. For matter wave, the wave equation leads to modifications of Schrodinger’s equation which in turn lead to a unified quantum theory of electromagnetic and gravitational forces in conjunction with the origin and the identity of inertial and gravitational mass. Further, it leads to modifications of the Lorentz force law and of Maxwell’s equations. Moreover, the wave equation leads to the dispersion of matter wave, from which the speed-dependence in the mass of a particle and in the wavelength, angular frequency, and quantum energy of a matter wave can be derived. The consequences of the wave equation are in accord with a wide variety of experiments that are commonly ascribed to the special relativity, the general relativity, the Lorentz mass-variation law, or to the de Broglie matter wave. Thereby, the local-ether wave equation unifies quantum mechanics, electromagnetics, and gravitation.
A wave equation complying with Galilean transformations is proposed for electromagnetic and matter waves. A fundamental feature entirely different from the principle of relativity is that the wave equation is referred specifically to the proposed local-ether frame. For electromagnetic wave, the local-ether wave equation accounts for a wide variety of experiments of propagation or interference. For matter wave, the wave equation leads to modifications of Schrodinger's equation which in turn lead to a unified quantum theory of electromagnetic and gravitational forces in conjunction with the identity of inertial and gravitational mass. Further, it leads to modifications of the Lorentz force law and of Maxwell's equations. Moreover, the wave equation leads to dispersion of matter wave, from which the speed-dependences in the mass of a particle and in the wavelength, angular frequency, and quantum energy of a matter wave are derived. The consequences of the wave equation are in accord with a wide variety of experiments which are commonly ascribed to the special relativity, the general relativity, the Lorentz mass-variation law, or to the de Broglie matter wavelength. Thereby, the local-ether wave equation unifies quantum mechanics, electromagnetics, and gravitation.
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work undertakes to investigate the issue of reality, treading a more fundamental route from the Hamilton-Jacobi equation of classical mechanics to the Schrodinger equation of quantum mechanics. Motivation for this is a similar approach from the eikonal equation in geometrical optics to the wave equation in electromagnetic theory. We rewrite the classical Hamilton-Jacobi equation as a wave equation and seek to generalise de Broglie's wave particle duality by demanding that both particle and light waves have the freedom of being described by any square-integrable function. This generalisation, which allows superposition also for matter wave functions, helps us to obtain the Schrodinger equation, whose solution can be seen to be as much objective as the classical mechanics wave function. Several other equations which one writes in quantum mechanics, including the eigenvalue equations for observables, series expansion of energy states in terms of eigenstates of observables other than energy, etc., can be written in the classical case too. Absence of any collapse of the wave function, entanglement, etc. in the classical realm have their origin in the nonlinearity of the classical wave equation. These considerations indicate that many of the puzzles in quantum mechanics are present also in classical mechanics in a dormant form, which fact shall help to demystify quantum mechanics to a great extent.
New insight on the principles of the quantum physics development is given. The quite different behavior of quantum microworld mechanical systems in comparison with classical mechanical macroworld systems is attributed to the drastical change of the role of the gravitation field on the dynamics of microworld mechanical systems, for which it seems to be vanishing in com- parison with the role of the gravitation field on the dynamics of macroworld mechanical systems, for which it is decisive. The conclusion on the status of the second main postulate of quantum mechanics is given. Its formulation in all textbooks has to be represented in the form of the proved statement, since the hypothesis of Schrödinger on the existence of the field scalar function, being to be observable quantity, just charge density, is strictly mathematically proved. It is shown, that the field scalar function, being to be the solution of the corresponding nonstationary in general case Schrödinger equation and being to be the function the only of coordinates and time, actually describes the state of the atomic system, more strictly its corpuscular aspect. The atomic system is considered from the positions of the field theory, that is, it is the association of elementary particles with corresponding fields. The given fields being to be the media for the particles’ propagation are responsible for the wave aspect in the characteristic of atomic systems. The wave aspect is described by the independent scalar wave-function which was also introduced in quantum physics by Schrödinger, althogh the given fact seems to be unknown to the wide circle of the readers. The second main postulate being to be mathematically strictly grounded in Schrödinger formulation of quantum nechanics, in the popular probabilistic form of quantum nechanics cannot be proved for the general case, although the probabilistic theatise, proposed by Born is true in a number of special cases, quite correctly indicated by Dirac. The possible ways of the development of quantum theory, based on clear understanding of the origin of corpuscular-wave dualism and based on the fundamental both now mathemtically grounded main postulates are analysed.
Striking parallelism between classical mechanics and quantum mechanics is evidenced for several bound system in a rather general form by introducing reasonably “quantum-mechanical momentum” from the Schrödinger equation. The following are proved: The “quantum-mechanical momentum” which is nearly equal to the corresponding classical momentum in “classical region” can be defined in the whole range of validity of the coordinate for the bound systems. In the same way as in classical mechanics, in quantum mechanics one can construct an associated wave accompanying a motion of a quantum particle and obeying the Schrödinger equation. The uniqueness condition on the associated wave throughout an orbit leads to the boundary condition on the wave function which is composed of the associated wave and to “quantum-mechanical quantization condition”, equivalently. In addition, all these quantum-mechanical quantities are approximately equal to the corresponding classical ones in the “classical region” of the coordinate. In particular it is demonstrated that even for a bound system of a singular (central) potential exists the ground state with the lowest energy eigenvalue. It is proved in one dimension that to any physical system obeying the Schrödinger equation always exists the corresponding classical system.