Examining a Hidden Assumption of Bell's Theorem and Counterexamples to Bell's Theorem in the Space of All Paths for a Quantum System

TL;DR

This paper introduces a 'space of all paths' model for quantum systems, providing counterexamples to Bell's theorem and constraining interpretations of quantum mechanics to either include all paths or accept action-at-a-distance.

Contribution

It presents a rigorous all-paths model that offers counterexamples to Bell's theorem and challenges existing interpretations of quantum mechanics.

Findings

Counterexamples to Bell's theorem using the all-paths model

Constraints on quantum interpretations requiring all paths or action-at-a-distance

Rejection of action-at-a-distance as physically plausible

Abstract

This paper implements in a simple but rigorous fashion a model of particle interaction involving all paths within a quantum system, both for configuration space and for spin. The model, which we call the space of all paths, leads to a locally explicable conceptual framework for quantum mechanics. Using it we present two counterexamples to Bell's theorem. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all paths within the system or, alternatively, the interpretation must harbor "action at a distance." We take action-at-a-distance as a reductio ad absurdum argument for our framework for quantum foundations, since any mechanism in which causal effects can operate instantaneously across vast distances would be completely unknown and magical, a near absurdity.