John Bell, relativistic causality, and the arrow of time

Reinhold Bertlmann’s reminiscences of John Bell (Physics Today, July 2015, page 40 ) are a pleasure to read and faithfully summarize the generally accepted wisdom on the topic. However, the article ends at a seemingly insurmountable theoretical impasse: the conclusions of Bell’s 1980 review describing the apparent incompatibility of quantum correlations with Lorentz invariance. It would perhaps be preferable to conclude on a more optimistic note, by emphasizing the tacit underlying assumption—the causal arrow of time. After all, the quantum correlations are incompatible not with Lorentz invariance per se but with relativistic causality, a time-asymmetric notion. The culprit, apparently, is in the manner that time asymmetry is introduced into the context of a microscopic theory.

Bell himself fully acknowledged the relevance of causality in his 1990 review of the topic, ¹ though he remained unwilling to consider the alternative of retrocausation. He clarified that the “locality” of local realism is merely shorthand for “local causality.” In his concluding paragraph he wrote, “The more closely one looks at the fundamental laws of physics the less one sees of the laws of thermodynamics. The increase of entropy emerges only for large complicated systems, in an approximation depending on ‘largeness’ and ‘complexity.’ Could it be that causal structure emerges only in something like a ‘thermodynamic’ approximation, where the notions ‘measurement’ and ‘external field’ become legitimate approximations?” That is the question Bell left us with.

Is there hope for a more palatable theoretical description? ¹ Bell’s theorem tells us that it would require either abandoning local causality or abandoning the causal arrow of time altogether, perhaps replacing it with a weaker temporal arrow, an arrow of information or entropy. At the level of a simplistic toy model, an explicit retrocausal (but otherwise local) formulation can reproduce Bell-type correlations. ² The challenge remains to formulate a general retrocausal and spacetime-local description of quantum phenomena. Such a reformulation of quantum theory, if achieved, is likely to have important ramifications, perhaps comparable to those following from Feynman’s development of path integrals.