Finite-Speed Hidden Influences

Abstract

The violation of a Bell inequality with space-like separated measurements precludes the explaination of nonlocal correlations in terms of causal influences propagating slower than light. Yet, these correlations can still be explained in a causal manner if one gives up Bell’s locality condition. Indeed, this is the explanation followed when one says something like “A measurement on the singlet state $|\psi ^-\rangle =\frac{1}{\sqrt{2}}(|01\rangle -|10\rangle )$ yielding result ‘0’ in the computational basis of Alice prepares the state $|1\rangle$ for Bob”. With a slightly different taste, Bohmian mechanics also provides a causal explanation for quantum correlations, which does not rely on quantum steering or collapse of the wavefunction. However, both of these explanations are much more nonlocal than a simple violation of Bell’s local causality condition implies: not only do they involve faster-than-light influences at a distance, but these influences also have immediate effects on distant particles no matter how far away they are from each other. Here we question whether such a strong violation of the notion of locality is necessary or not.