Quantum physics in inertial and gravitational fields (original) (raw)

Quantum Mechanics and General Relativity

Fundamental subjects of quantum mechanics and general relativity are presented in a unitary framework. A quantum particle is described by wave packets in the two conjugate spaces of the coordinates and momentum. With the time dependent phases proportional to the Lagrangian, the group velocities of these wave packets are in agreement with the fundamental Hamilton equations. When the relativistic Lagrangian, as a function of the metric tensor and the matter velocity field, is considered, the wave velocities are equal to the matter velocity. This means that these waves describe the matter propagation, and that the equality of the integrals of the matter densities over the spatial and the momentum spaces, with the mass in the Lagrangian of the time dependent phases, which describes the particle dynamics, represent a mass quantization rule. Describing the interaction of a quantum particle with the electromagnetic field by a modification of the particle dynamics, induced by additional terms in the time dependent phases, with an electric potential conjugated to time, and a vector potential conjugated to the coordinates, Lorentz’s force and Maxwell’s equations are obtained. With Dirac’s Hamiltonian, and operators satisfying the Clifford algebra, dynamic equations similar to those used in the quantum field theory and particle physics are obtained, but with an additional relativistic function, depending on the velocity, and the matter-field momentum. For particles and antiparticles, wavefunctions for finite matter distributions are obtained. The particle transitions, and Fermi’s golden rule, are described by the Lagrangian matrix elements over the Lagrangian eigenstates and densities of these states. Transition rates are obtained for the two possible processes, with the spin conservation or with the spin inversion. Dirac’s formalism of general relativity, with basic concepts of Christoffel symbols, covariant derivative, scalar density and matter conservation, the geodesic dynamics, curvature tensor, Bianci equations, Ricci tensor, Einstein’s gravitation law and the Schwarzschild matric elements, are presented in detail. From the action integrals for the gravitational field, matter, electromagnetic field, and electric charge, Lorentz’s force and Maxwell’s equations in the general relativity are obtained. It is also shown that the gravitational field is not modified by the electromagnetic field. For a black hole, the velocity and the acceleration of a particle are obtained. It is shown that, in the perfect spherical symmetry hypothesis, an outside particle is attracted only up to three times the Schwarzschild radius, between this distance and the Schwarzschild radius the particle being repelled, so that it reaches this boundary only in an infinite time, with null velocity and null acceleration. At the formation of a black hole, as a perfectly spherical object of matter gravitationally concentrated inside the Schwarzschild boundary, the central matter explodes, the inside matter being carried out towards this boundary, but reaching there only in an infinite time, with null velocity and null acceleration. In this way, our universe is conceived as a huge black hole. Based on this model, the essential properties, as big bang, inflation, the low large-scale density, the quasi-inertial behavior of the distant bodies, redshift, the dark matter and the dark energy, are unitarily explained. From the description of a gravitational wave by harmonically oscillating coordinates, the wave equation for the metric tensor is obtained, the propagation direction of such a wave being taken for reference. For a quantum particle as a distribution of matter interacting with a gravitational field, according to the proposed model, it is obtained that this field rotates with the angular momentum 2, called the graviton spin, as a rotation of the metric tensor which is correlated to the matter velocity, as the particle matter rotates with a half-integer spin for Fermions, and an integer spin for Bosons.

Quantum Gravitation and Inertia

Quantum Gravitation and Inertia, 2021

Newton's Law of Universal Gravitation provides the basis for calculating the attraction force between two bodies, which is called the "gravitational force" [1]. This Law uses the "mass" of bodies. Einstein General Relativity Theory proposes to calculate this gravitational force by using the curvature of space-time. This space-time curvature is supposedly due to the same "mass" [2]. Stephan Hawkings in his book (A Brief History of Time)[3] supposes that gravitons particles of quantum mechanics are the intermediaries that "give mass" to the bodies. However, there is no explanation about the nature of the gravitons or how their interaction with bodies could "give them mass". This paper presents a new way of explaining how the "mass" can be given to bodies. The starting point is an idea proposed in 1690 by Nicolas Fatio de Duillier and revisited here with new hypotheses, and then further developped with the use of the Bohmian quantum mechanics. It is shown, by means of reasoning and equations reflecting these reasoning, that the gravitational force between two bodies comes from the interaction between the revisited Nicolas Fatio's aether and matter atomic nuclei. It is also shown that the "mass" of a body is not a real entity, but is an emerging phenomenon. This idea has already been suggested by Erick Verlinde in another context [4]. Here, the emergence of "mass" is given by the interaction of the aether particles with matter atomic nuclei. The interesting point of Nicolas Fatio's theory is that it is able to solve not only the origin of gravitational force, but also the origin of inertial force. The origin of inertia comes from an induction phenomena between Nicolas Fatio's aether and matter atomic nuclei. This paper uses Nicolas Fatio's medium own word, aether, to describe gravitation and inertia. It has nothing to do with Lorentz or Maxwell luminiferous aether that has been disproved by the scientific community after the Michelson and Morley experiment.

Applied Physics B manuscript Inertial and gravitational mass in quantum mechanics

2016

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.

Gravity and the Quantum Vacuum Inertia Hypothesis. I. Formalized Groundwork for Extension to Gravity

Arxiv preprint gr-qc/0108026, 2001

Abstract: It has been shown [1, 2] that the electromagnetic quantum vacuum makes a contribution to the inertial mass, $ m_i $, in the sense that at least part of the inertial force of opposition to acceleration, or inertia reaction force, springs from the electromagnetic quantum vacuum. As experienced in a Rindler constant acceleration frame the electromagnetic quantum vacuum mainfests an energy-momentum flux which we call the Rindler flux (RF). The RF, and its relative, Unruh-Davies radiation, both stem from event- ...

Inertial and gravitational mass in quantum mechanics

2010

Unitary theory of quantum mechanics and general relativity

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 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 Unified Equation of Gravity and QM: The Case of Non-Relativistic Motion

We propose to simplify the problem of the unified theory of Quantum-Gravity through dealing first with the simple case of non-relativistic equations of Gravity and Quantum Mechanics. We show that unification of the two non-relativistic formalisms can be achieved through the joined classical and Quantum postulate that every natural body is composed of N identical final particles. This includes the current 'elementary' particles of the standard model such as quarks, photons, gluons, etc. Furthermore, we show that this opens a new route toward a Generalized Equation of Quantum-Gravity that takes the effects of both of velocity and acceleration into account.

Gravity and the quantum vacuum inertia hypothesis

Annalen der Physik, 2005

In previous work it has been shown that the electromagnetic quantum vacuum, or electromagnetic zero-point field, makes a contribution to the inertial reaction force on an accelerated object. We show that the result for inertial mass can be extended to passive gravitational mass. As a consequence the weak equivalence principle, which equates inertial to passive gravitational mass, appears to be explainable. This in turn leads to a straightforward derivation of the classical Newtonian gravitational force. We call the inertia and gravitation connection with the vacuum fields the quantum vacuum inertia hypothesis. To date only the electromagnetic field has been considered. It remains to extend the hypothesis to the effects of the vacuum fields of the other interactions. We propose an idealized experiment involving a cavity resonator which, in principle, would test the hypothesis for the simple case in which only electromagnetic interactions are involved. This test also suggests a basis for the free parameter η(ν) which we have previously defined to parametrize the interaction between charge and the electromagnetic zero-point field contributing to the inertial mass of a particle or object.

Quantum physics in inertial and gravitational fields (original) (raw)

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