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Journal of Modern Optics

Bell's inequality with times rather than angles

Alexander Afriat

Published Jan 1, 2003• 2 citations
Publisher

Abstract

An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that the property of a system can be changed by the timing of a distant measurement, which could take place in the future.

DOI
10.1080/09500340308234552

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An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that the property of a system can be changed by the timing of a distant measurement, which could take place in the future.
Bipartite temporal Bell inequalities are similar to the usual Bell inequalities except that, instead of changing the direction of the polarizer at each measurement, one changes the time at which the measurement is being performed. By doing so, one is able to test for realism and locality, but relying on position measurements only. This is particularly useful in experimental setups where the momentum direction cannot be probed (such as in cosmology for instance). We study these bipartite temporal Bell inequalities for continuous systems placed in two-mode squeezed states and find some regions in parameter space where they are indeed violated. We highlight the role played by the rotation angle, which is one of the three parameters characterizing a two-mode squeezed state (the other two being the squeezing amplitude and the squeezing angle). In single-time measurements, it only determines the overall phase of the wave function and can therefore be discarded, but in multiple-time measurements, its time dynamics becomes relevant and crucially determines when bipartite temporal Bell inequalities can be violated. Our study provides an opportunity for experimental designs for the observation of Bell inequality violations.