The shadow system in coordinate space: The shadow system in coordinate space: A locally explicable system that violates Bell's inequality

Abstract

We explore the consequences of denying the "emptiness of paths not taken," EPNT, a premise of Bernstein, Greenberger, Horne, and Zeilinger in their paper titled, Bell theorem without inequalities. Carrying out the negation of EPNT leads to the concept of a "shadow stream." Streams are essentially particle implementations of the path amplitudes in Feynman's formulation of quantum mechanics, resulting in a simple and consistent extension of the standard postulates for quantum mechanics. Following up on the negation of EPNT using shadow streams, we analyze the experimental outcomes in a standard two-particle interferometer. The result is a simple counterexample to Bell's theorem in position/momentum space.