Inertial and gravitational mass in quantum mechanics (original) (raw)
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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.
Quantum physics in inertial and gravitational fields
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise in models that incorporate Born reciprocity principle and the notion of a maximal acceleration. Some specific examples are discussed in detail.
Some aspects of gravitational quantum mechanics
General Relativity and Gravitation, 2006
String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions. PACS: 03.65.-w, 04.60.-m , 42.50.Nn
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.
A Gravitational Explanation for Quantum Mechanics
1996
It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution. The measurement apparatus itself can impose non-redundant boundary conditions. Measurements of such an object would fail to satisfy the distributive law of classical physics. This model reconciles General Relativity and Quantum Mechanics without the need for Quantum Gravity. The equations of Quantum Mechanics are unmodified but it is not universal; classical particles and waves could exist and there is no graviton.
The quantum-mechanical wavefunction as a gravitational wave
The geometry of the elementary quantum-mechanical wavefunction (a·cosθ − i•a·sinθ) and a linearly polarized electromagnetic wave (E + B) consist of two plane waves that are perpendicular to the direction of propagation: their components only differ in magnitude and-more importantly-in their relative phase (0 and 90° respectively). The physical dimension of the electric field vector is force per unit charge (N/C). It is, therefore, tempting to associate the real and imaginary component of the wavefunction with a similar physical dimension: force per unit mass (N/kg). This is, of course, the dimension of the gravitational field, which reduces to the dimension of acceleration (1 N/kg = 1 m/s 2). The results and implications are remarkably elegant and intuitive: Schrödinger's wave equation, for example, can now be interpreted as an energy diffusion equation, and the wavefunction itself can be interpreted as a propagating gravitational wave. The energy conservation principle then gives us a physical normalization condition, as probabilities (P = |ψ| 2) are then, effectively, proportional to energy densities (u). We also get a more intuitive explanation of spin angular momentum, the boson-fermion dichotomy, and the Compton scattering radius for a particle. Finally, this physical interpretation of the wavefunction may also give us some clues in regard to the mechanism of relativistic length contraction. The interpretation does not challenge the Copenhagen interpretation of quantum mechanics: interpreting probability amplitudes as traveling field disturbances does not explain why a particle hits a detector as a particle (not as a wave). As such, this interpretation respects the complementarity principle. Contents :
Quantum and classical divide: the gravitational case
Physics Letters B, 2006
We study the transition between quantum and classical behaviour of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of view. We also discuss the way these effects could be tested by conducting experiments with atoms and fullerene-type molecules.
International Letters of Chemistry, Physics and Astronomy, 2013
In the paper, the outline of a new quantum theory of gravitation is presented. The energetic states of a material body, stable and unstable, are described. Characteristics of a body motion in a gravitation-inertia space-time has been given. It has been proved that all the time both gravitation and inertia are co-existent, independent on the position of a moving object. This is the reason of that twolink name of the space-time. A thorough in-depth analysis of the problem made it possible to state that so called the law of common gravity is a hyperbolic approximation of a proper course of inertia force. Therefore the mentioned courses have only two common points. One of them, the initial point belongs also to the course line of the gravity force, constant on the whole length of space-time. This theory is adequate in character and thus generally does not corresponds with the existent classical theory of gravitation.
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- ...