Statistics, Causality and Bell’s theorem

Bell’s (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell’s inequality in experiments such as that of Aspect and coworkers (1982) is popularly supposed to provide empirical proof of non-locality in the real world. This paper reviews recent work on Bell’s theorem, linking it to issues in causality as understood by statisticians. The paper starts with a new proof of a strong (finite sample) version of Bell’s theorem which relies only on elementary arithmetic and (counting) probability. This proof underscores the fact that Bell’s theorem tells us that quantum theory is incompatible with the conjunction of three cherished and formerly uncontroversial physical principles, nicknamed here locality, realism, and freedom. The first, locality, is obviously connected to causality: causal influences need time to propagate spatially. Less obviously, the other two principles, realism and freedom, are also founded on two ideas central to modern statistical thinking on causality: counterfactual reasoning, and the distinction between do-ing X = x and selecting on X = x, respectively. I will argue that (accepting quantum theory) Bell’s theorem should lead us to seriously consider relinquishing not locality, but realism, as a fundamental physical principle. The paper goes on to discuss statistical issues, in the interpretation of state-of-the-art Bell type experiments, related to post-selection in observational studies. Finally I state an open problem concerning the design of a quantum Randi challenge: a computer challenge to Bell-deniers.