Possibility of Classical Entanglement at LIGO

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.