A mathematical model for the Einstein-Podolsky-Rosen argument

TL;DR

This paper presents a rigorous mathematical model demonstrating how entanglement and interactions in a two-particle quantum system lead to observable correlations, specifically linking spin flips to momentum changes in a distant particle.

Contribution

It introduces a novel nonrelativistic quantum model analyzing entanglement dynamics and correlations between particles and a fixed spin, with rigorous proofs of the resulting quantum correlations.

Findings

Correlation between spin state and second particle's momentum established

In a scaling limit, spin flip correlates with opposite momentum in the second particle

Rigorous mathematical proof of entanglement-induced correlations

Abstract

We study a nonrelativistic system made of two quantum particles constrained to move on a line and a spin located at a fixed point of the line. Initially the two particles are in a maximally entangled state and the spin is down. The first particle interacts with the spin while the second particle is free, i.e., it does not interact neither with the first particle nor with the spin. We rigorously prove that there is a correlation between the state of the spin and the state of the second particle. More precisely, we show that, in a suitable scaling limit, if the first particle flips the spin, then the second particle possesses a definite momentum in the direction opposite to the spin.