Understanding of Quantum Mechanics as a Theory Based on General Relativity | Chapter 8 | Current Research Progress in Physical Science Vol. 4

In this paper, the quantum dynamics was obtained in the framework of the general theory of relativity, where a quantum particle is described by a distribution of matter, with amplitude functions of the matter density, in the two conjugate spaces of the spatial coordinates and of the momentum, called wave functions. For a free particle, these wave functions are conjugate wave packets in the coordinate and momentum spaces, with time-dependent phases proportional to the relativistic Lagrangian, as the wave velocities in the coordinate space are equal to the distribution velocity described by the wave packet in this space. From the wave velocities of the particle wave functions, Lorentz’s force and the Maxwell equations were obtained. From the wave/group equation in the momentum space describing the Lorentz force, the expressions of the electric and magnetic fields as functions of the electric potential conjugated to time and of the vector potential conjugated to the coordinates in the particle-field Lagrangian were obtained. With these expressions, the electric and magnetic fields that satisfy the Faraday-Maxwell law of electromagnetic induction and the two Gauss-Maxwell laws of these fields were obtained. The Ampère-Maxwell law is obtained only by taking into account the physical consistency of the matter-field interaction of the equality of the propagation field velocity with the maximum relativistic velocity c. For a quantum particle in the electromagnetic field, dynamic equations in the coordinate and momentum spaces and the particle and antiparticle wave functions were obtained. It was shown that the electromagnetic potentials as functions of the coordinates describing the matter distribution of the quantum particle do not alter this distribution – under the action of an electromagnetic a quantum particle moves as a whole. The scattering or tunneling rate in an electromagnetic field, for the two possible cases, with the spin conservation, or inversion, were obtained. This description of a quantum particle as a distribution of matter with a density amplitude/wavefunction of the form of a wave packet, with the time-dependent phase proportional to the relativistic Lagrangian as a function of the metric tensor including also the gravitational field, enables the application of this theory in quantum gravity and quantum field theory in agreement with general relativity.

 

Author (s) Details

Eliade Stefanescu
Advanced Studies in Physics Centre of the Romanian Academy, Academy of Romanian Scientists, Bucharest, Romania.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v4/2925

Dynamics of Matter in a Unitary Relativistic Quantum Framework | Chapter 8 | Current Research Progress in Physical Science Vol. 7

The matter dynamics as a positively defined density P (xⁱ,t)= M|y (xⁱ,t )|² was described and showed that, according to the general theory of relativity, such a distribution can be conceived only as a fragment of matter with a finite mass M equal to a mass  M₀ , as a characteristic of the matter dynamics, M= M₀  – the matter quantization. The group velocities of the Fourier conjugate representations in the coordinate and momentum spaces describe the dynamics of a quantum particle in agreement with the Hamiltonian equations, unlike the Schrodinger representation which is in disagreement with these equations. Under the action of an external (nongravitational) field, the acceleration of the quantum matter has two components: 1) A component perpendicular to the velocity, given by the relativistic mechanical component of the time-dependent phase, and 2) A component given by the additional field terms of this phase. A free quantum particle is described by a non-dispersing wave function  y(xⁱ,t), contrary to the solution of the Schrödinger equation. A coherent electromagnetic field, in resonance with a system of active quantum particles in a Fabry-Perot cavity, has a wave vector approximately proportional to the metric elements, as the resonance frequency is approximately constant – a gravitational wave can be detected by the transmission characteristics of an active Fabry-Perot cavity. In a constant gravitational field, a quantum particle undertakes a velocity and an acceleration, which, at the boundary of a black hole are null – absorption and evaporation processes at the boundary of a black hole arise only by gravitational perturbations. Important perturbations, significantly deforming the gravitational spherical symmetry of a black hole, are produced by strong nuclear and electromagnetic forces leading to the big matter concentrations of the celestial bodies. Generally, a quantum particle is described by a time-space volume, called a graviton, with a spin of 2, and a distribution of a specific matter in this volume, with a half-integer spin for Fermions and an integer spin for Bosons. A graviton Lagrangian is obtained as a curvature integral on a graviton volume, and a Hamiltonian tensor is obtained for the gravitational coordinates and velocities.

 

Author (s) Details

 

Eliade Stefanescu
Advanced Studies in Physics Centre of the Romanian Academy, Academy of Romanian Scientists, Bucharest, Romania.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v7/4094