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International Journal of Astronomy and Astrophysics

Possibility of Classical Entanglement at LIGO

Partha Ghose, A. K. Rajagopal

Published Jan 1, 2018• 0 citations
Publisher

Abstract

It is now established that entanglement in the sense of local non-factorizability of two or more degrees of freedom of a system occurs in classical polarization optics. We extend the idea to weak gravitational waves which are strikingly similar to optical waves. It is shown that a linearized classical gravity wave can in principle get entangled in the sense mentioned with the vibrational modes of an array of test masses in a plane perpendicular to its direction of propagation. A Bell-CHSH inequality based on the requirement of noncontextuality for classical realism is derived, and it is shown that the putative nonfactorizable state violates this inequality. The idea is therefore empirically falsifiable.

DOI
10.4236/ijaa.2018.83019

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It is now established that entanglement in the sense of local non-factorizability of two or more degrees of freedom of a system occurs in classical polarization optics. We extend the idea to weak gravitational waves which are strikingly similar to optical waves. It is shown that a linearized classical gravity wave can in principle get entangled in the sense mentioned with the vibrational modes of an array of test masses in a plane perpendicular to its direction of propagation. A Bell-CHSH inequality based on the requirement of noncontextuality for classical realism is derived, and it is shown that the putative nonfactorizable state violates this inequality. The idea is therefore empirically falsifiable.
It is shown that a linearized classical gravity wave a^\hat{a}a^ {\em la} Einstein can get entangled with an array of test masses in a plane perpendicular to its direction of propagation. A Bell-CHSH inequality based on the requirement of noncontextuality for classical realism is derived, and it is shown that the entangled state produced violates this inequality.
When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction. However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances. This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses.
A method is proposed to produce a classical optical state that is `intersystem nonseparable' and a close analog of the ϕ+ϕ^+ϕ+ Bell state. A derivation of the CHSH-Bell inequality is sketched within the framework of classical polarization optics, using non-contextuality for factorizable states as an axiom rather than any hidden variable theory. It is shown that the classical state violates this inequality.
In recent work, Arora and Asadian have proposed a sophisticated physical structure for testing the macroscopic Clauser-Horne-Shimony-Holt (CHSH) inequality of two entangled particles using a multislit Young experiment that employs classical-like modular variables and measurements. By imposing the algebraic CHSH constraint on the Wigner representations of these observables, they found that a strong connection exists between the non-negative Wigner function of a quantum state and having the macroscopic CHSH inequality hold. The entangled states with negative Wigner functions violate the macroscopic CHSH inequality when the number of slits is $N\ensuremath{\ge}8$ and the maximum violation, in principle, requires $N\ensuremath{\rightarrow}+\ensuremath{\infty}$. In this paper, we further study this macroscopic local-realism test by analyzing the eigenvalues of the classical-like modular variables when NNN is finite. Through this analysis, we find that one can modify the classical boundary for the macroscopic CHSH inequality when NNN is finite, which makes it possible to demonstrate macroscopic Bell nonlocality for entangled states with N<8N<8N<8. More interestingly, we find another form of an entangled state that violates the macroscopic CHSH inequality under the modified boundaries when the number of slits is N=2N=2N=2. But the violation of the macroscopic CHSH inequality under the modified classical boundaries with a finite NNN does not necessarily correspond to states with a non-positive-definite Wigner function.