Abstract

One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.

Highlights

  • In spite of having several serious proposals for the quantization of general relativity, a fully consistent quantum theory of gravity is yet unexplored and remains the most important open challenge in modern science

  • It is argued that the fundamental concept of space-time is not wholly compatible with that of the standard version of quantum mechanics, but fits mostly with its noncommutative version [1,2,3,4,5,6]

  • In a recent study [37], the author explored an experiment to test noncommutative theories based on the Aharonov-Bohm effect in nano-scale quantum mechanics

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Summary

INTRODUCTION

In spite of having several serious proposals for the quantization of general relativity, a fully consistent quantum theory of gravity is yet unexplored and remains the most important open challenge in modern science. Astronomical observations have failed to provide any promising evidence to study the quantum gravitational effects It is worth exploring some alternative ways and, noncommutative theories have been very successful so far to circumvent the quantum gravity problem at least theoretically. The purpose of the present manuscript is to propose a fascinating experimental scheme that may provide an alternative way to reach the energy scale near to the Planck length and, probe the noncommutative theories. By utilizing the conventional interferometric techniques, it is possible to provide a high precision measurement of this optical phase shift and, it is viable to shed light on the effects of noncommutative theories at the Planck-scale regime

OPTO-MECHANICAL SCHEME FOR NONCOMMUTATIVE SYSTEMS
EXPERIMENTAL REALIZATION
CONCLUSIONS
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