Quantum physics in inertial and gravitational fields (original) (raw)
Inertial and gravitational mass in quantum mechanics
2010
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.
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.
On some classical and quantum effects due to gravitational fields
Brazilian Journal of Physics, 2006
We consider the gravitational fields generated by a cosmic string, a global monopole and a tubular matter with interior magnetic field (Safko-Witten space-time), and examine some classical and quantum effects due to these fields. We investigate the Aharonov-Bohm effect in the space-time of a cosmic string, using the loop variables. In the space-time of a global monopole, we calculate the total energy radiated by a uniformly moving charged scalar particle, for small solid angle deficit. We show that the radiated energy is proportional to the cube of the velocity of the particle and to the cube of the Lorenz factor, in the non-relativistic and ultra-relativistic cases, respectively. In the Safko-Witten space-time, we investigate the existence of an electrostatic self-force on a charged particle. We also consider a hydrogen atom in the background space-time generated by a cosmic string and we find the solutions of the corresponding Dirac equation and we determine the energy levels of the atom. We investigate how the topological features of this space-time lead to shifts in the energy levels as compared with the flat Minkowski space-time. We study the behavior of non-relativistic quantum particles interacting with a Kratzer potential in the space-time generated by a global monopole and we find the energy spectrum in the presence of this topological defect. In the Safko-Witten space-time, an investigation is also made concerning the interaction of an harmonic oscillator with this background gravitational field.
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.
Remarkable aspects and and unsolved problems in quantum gravity theory
Academia Letters, 2022
The search of a theory of quantum gravity (QG) which is consistent both with the principles of quantum mechanics as well as with the postulates of the classical Einstein theory of General Relativity (GR) has represented until recently one of the most challenging, long-standing debated and hard-to-solve conceptual problems of mathematical and theoretical physics alike. In fact, a basic crucial issue is about the possibility of achieving in the context of either classical or quantum relativistic theories, and in particular for a quantum theory of gravity, a truly coordinate-(i.e., frame-) independent representation, realized by 4-tensor notation of physical laws. This means that the latter theory must satisfy both the principles of general covariance and of manifest covariance with respect to the group of local point transformations (LPT-group), i.e., coordinate diffeomorphisms mutually mapping in each other different GR frames. These principles lie at the foundation of all relativistic theories and of the related physical laws. In fact, although the choice of special coordinate systems is always legitimate for all physical systems either discrete or continuous, including in particular classical and quantum gravity, the intrinsic objective nature of physical laws makes them frame-independent. For the same reason, since LPTs preserve the differential-manifold structure of space-time, these principles represent also a cornerstone of the standard formulation of GR, namely the Einstein field equations and the corresponding classical treatment of the gravitational field. The same principles should apply as well to the very foundations of quantum field theory
Quantum fields as gravitational sources
2008
The practice of setting quantum fields as sources for classical general relativity is examined. Several conceptual problems are identified which invalidate apparently innocuous equations. Alternative ways to links classical general relativity with quantum theory using Bohm's theory are proposed.
Gravitational effects in macroscopic quantum systems: a first-principles analysis
Classical and Quantum Gravity
We analyze the weak-field limit of General Relativity with matter and its possible quantisations. This analysis aims towards a predictive quantum theory to provide a first-principles description of gravitational effects in macroscopic quantum systems. This includes recently proposed experiments on the generation of (Newtonian) gravitational forces from quantum distributions of matter, and phenomena like gravity-induced entanglement, gravitational cat states, gravity-induced Rabi oscillations, and quantum causal orderings of events. Our main results include: (i) The demonstration that these phenomena do not involve true gravitational degrees of freedom. (ii) We show that, unlike full general relativity, weak gravity with matter is a parameterised field theory, i.e., a theory obtained by promoting spacetime coordinates to 'dynamical' variables. (iii) Quantisation via gauge-fixing leads to an effective field theory that account for some phenomena, but at the price of gauge dependence that manifests more strongly on spacetime observables. This ambiguity is a manifestation of the problem of time that persists even in weak gravity. (iv) A consistent quantisation of parameterised field theories is essential for a predictive and spacetime covariant theory of weak gravity that describes gravitational effects in macroscopic quantum systems. We also discuss the implication of our results to gravitational decoherence theories, the notion of locality in gravity visa -vis quantum information theory, and the intriguing possibility that proposed solutions to the problem of time can be tested in weak-gravity quantum experiments.