## Introduction 

Neyman introduced a formal mathematical theory of counterfactual causation that now has become standard language in many quantitative disciplines, including statistics, epi- demiology, philosophy, economics, sociology, and artificial intelligence, but not in physics. Several researchers in these disciplines (Frangakis et al., 2007; Pearl, 2009) have speculated that there exists a relationship between this counterfactual theory and quantum mechanics, but have not provided any substantive formal relation between the two. In this note, we show that theory concerning causal interaction, grounded in notions of counterfactuals, can be used to give a straightforward proof of a result in quantum physics, namely, Bell’s inequal- ity. Our proof relies on recognizing that results on causal interaction (VanderWeele, 2010) can be used to empirically test for interference between units (VanderWeele et al., 2011). It should be stressed that a number of extremely short and elegant proofs of both Bell’s original inequality (and its generalizations) are already available in the physics literature. In fact some of these proofs are based on reasoning with counterfactuals (Gill et al., 2001). Our contribution is to explicitly show relations to the theory of causal interactions. 

We motivate our proof with an exceedingly short history of the Bell Inequality that is elaborated upon later. A non-intuitive implication of quantum theory is that pairs of spin 1/2 particles (e.g., electrons) can be prepared in an entangled state with the following property. When the spins of both particles are measured along a common (spatial) axis, the measurement of one particle’s spin perfectly predicts the spin of the other; if the first particle’s spin is up, then the spin of the second must be down. One explanation would be that the measurement itself of the first particle determined the spin of the second, even if physically separated, perhaps, by many light years. This would mean that reality was not ”local”; what occurred at one place would affect reality (i.e. the spin of the second electron) at another. However, Einstein believed in ”local realism” and argued that the more plausible explanation was that both particles are carrying with them from their common source ’hidden’ correlated spin outcomes which they will exhibit when measured (Einstein 

