The Scope and Generality of Bells Theorem

I present what might seem to be a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here.

💡 Research Summary

The paper titled “The Scope and Generality of Bell’s Theorem” revisits the celebrated Bell‑type no‑go theorems by scrutinizing a recent proposal that claims to reproduce the EPR‑Bohm correlations with a local, deterministic hidden‑variable model. The model under consideration is inspired by Joy Christian’s work, which replaces the usual real‑valued hidden variable λ with an element of a Clifford (or quaternionic) algebra. In the construction, each particle and each measurement device is associated with a bivector (or unit quaternion) that lives in the double cover of the rotation group SU(2). The measurement outcomes are defined as algebraic functions A(a, λ) and B(b, λ) of the detector orientations a, b and the hidden algebraic variable λ. Because these functions output bivectors rather than ordinary numbers, the model’s expectation value is written as

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