Bell’s Theorem and Spacetime-Based Reformulations of Quantum Mechanics

In this critical review of Bell’s Theorem, its implications for reformulations of quantum theory are considered. The assumptions of the theorem are set out explicitly, within a framework of mathematical models with well-defined inputs and outputs. Attention is drawn to the assumption that the mathematical quantities associated with a certain time and place can depend on past model inputs (such as preparation settings) but not on future inputs (such as measurement settings at later times). Keeping this time- asymmetric assumption leads to a substantial tension between quantum mechanics and relativity.

Relaxing it, as should be considered for such no-go theorems, opens a category of Future-Input Dependent (FID) models, for which this tension need not occur. This option (often called “retrocausal”) has been repeatedly pointed out in the literature, but the exploration of explicit FID models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. Unlike conventional quantum models, the FID model parameters needed to specify the state of a system do not grow exponentially with the number of entangled particles. The promise of generalizing FID models into a Lorentz-covariant account of all quantum phenomena is identified as a grand challenge.