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arXiv:gr-qc/0005112 · International Journal of Modern Physics A

QUANTUM-MECHANICAL DETECTION OF NON-NEWTONIAN GRAVITY

Abel Camacho

Published Jan 10, 2001• 4 citations
arXivHTMLPDF

Abstract

In this work the possibility of detecting the presence of a Yukawa term, as an additional contribution to the usual Newtonian gravitational potential, is introduced. The central idea is to analyze the effects at quantum level employing interference patterns (at this respect the present proposal resembles the Colella, Overhauser and Werner experiment), and deduce from it the possible effects that this Yukawa term could have. We will prove that the corresponding interference pattern depends on the phenomenological parameters that define this kind of terms. Afterwards, using the so-called restricted path integral formalism, the case of a particle whose position is being continuously monitored, is analyzed, and the effects that this Yukawa potential could have on the measurement outputs are obtained. This allows us to obtain another scheme that could lead to the detection of these terms. This last part also renders new theoretical predictions that could enable us to confront the restricted path integral formalism against some future experiments.

DOI
10.1142/s0217751x01002105

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In this work the possibility of detecting the presence of a Yukawa term, as an additional contribution to the usual Newtonian gravitational potential, is introduced. The central idea is to analyze the effects at quantum level employing interference patterns (at this respect the present proposal resembles the Colella, Overhauser and Werner experiment), and deduce from it the possible effects that this Yukawa term could have. We will prove that the corresponding interference pattern depends on the phenomenological parameters that define this kind of terms. Afterwards, using the so-called restricted path integral formalism, the case of a particle whose position is being continuously monitored, is analyzed, and the effects that this Yukawa potential could have on the measurement outputs are obtained. This allows us to obtain another scheme that could lead to the detection of these terms. This last part also renders new theoretical predictions that could enable us to confront the restricted path integral formalism against some future experiments.
In the present work the detection, by means of a nondemolition measurement, of a Yukawa term, coexisting simultaneously with gravity, has been considered. In other words, a nondemolition variable for the case of a particle immersed in a gravitational field containing a Yukawa term is obtained. Afterwards the continuous monitoring of this nondemolition parameter is analyzed, the corresponding propagator is evaluated, and the probabilities associated with the possible measurement outputs are found. The relevance of these kind proposals in connection with some unified theories of elementary particles has also been underlined.
A very interesting quantum mechanical effect is the emergence of gravity-induced interference, which has already been detected. This effect also shows us that gravity is at the quantum level not a purely geometric effect, the mass of the employed particles appears explicitly in the interference expression. In this work we will generalize some previous results. It will be shown that the introduction of a second order approximation in the propagator of a particle, immersed in the Earth's gravitational field, and whose coordinates are being continuously monitored, allows us to include, in the corresponding complex oscillator, a frequency which now depends on the geometry of the source of the gravitational field, a fact that is absent in the case of a homogeneous field. Using this propagator we will analyze the interference pattern of two particle beams whose coordinates are being continuously monitored. We will compare our results against the case of a homogeneous field, and also against the measurement outputs of the Colella, Overhauser, and Werner experiment, and find that the difference in the dependence upon the geometry of the source of the gravitational field could render detectable differences in their respective measurement outputs. (orig.)
In the present work we solve the motion equations of a particle in a Paul trap embedded in the gravitational field of a spherically symmetric mass. One of the ideas behind this work concerns the analysis of the effects that the gravity-induced quantum noise, stemming from the bodies in the neighborhood of the Paul trap, could have upon the enhancement of the quantum behavior of this system. This will be done considering a series expansion for the gravitational field of the source, and including in the Hamiltonian of the Paul trap only the first two terms. Higher-order contributions will be introduced as part of the environment of the system, and in consequence will not appear in the Hamiltonian. In other words, we put forward an argument that allows us to differentiate those gravitational degrees of freedom that will appear as an uncontrollable influence on the Paul trap. Along the ideas of the so-called restricted path integral formalism, we take into account the continuous monitoring of the position of our particle, and in consequence the corresponding propagators and probabilities, associated with the different measurements outputs, are obtained. Afterwards, the differential equation related to a quantum nondemolition variable is posed and solved, i.e., a family of quantum nondemolition parameters is obtained. Finally, a qualitative analysis of the effects on the system, of the gravity-induced environment, will be done.
Abstract In this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.