A proof of Bells inequality in quantum mechanics using causal interactions

We give a simple proof of Bell’s inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between particles.

💡 Research Summary

The paper presents a streamlined proof of Bell’s inequality that leverages the modern statistical concept of causal interaction. After a brief historical overview of Bell’s theorem and its traditional derivations—typically rooted in probabilistic inequalities and the assumption of statistical independence—the authors introduce a causal‑interaction framework borrowed from epidemiology and causal inference. In this framework, a set of potential outcome variables (Y_{ij}) (i = 1,2 for Alice’s settings, j = 1,2 for Bob’s settings) is defined, each representing the measurement result that would be observed if the corresponding pair of settings were chosen. The key causal‑interaction assumption is that no single hidden cause (often denoted λ) can simultaneously flip the outcomes for more than one setting pair; in other words, the joint potential outcomes cannot all be +1 at the same time. This logical restriction translates directly into a probability constraint:
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