# EPR-Bell-Schr\"odinger proof of nonlocality using position and momentum

## TL;DR

This paper presents a nonlocality proof using position and momentum observables, extending Schrödinger's EPR argument and avoiding Bell inequalities, to demonstrate quantum nonlocality in continuous variables.

## Contribution

It introduces a Schrödinger-based nonlocality proof using position and momentum, expanding previous spin-based approaches to continuous variables.

## Key findings

- Demonstrates nonlocality with position and momentum observables.
- Provides a contradiction to locality without Bell inequalities.
- Extends EPR-based nonlocality proofs to continuous variables.

## Abstract

Based on his extension of the classical argument of Einstein, Podolsky and Rosen, Schr\"odinger observed that, in certain quantum states associated with pairs of particles that can be far away from one another, the result of the measurement of an observable associated with one particle is perfectly correlated with the result of the measurement of another observable associated with the other particle. Combining this with the assumption of locality and some "no hidden variables" theorems, we showed in a previous paper [11] that this yields a contradiction. This means that the assumption of locality is false, and thus provides us with another demonstration of quantum nonlocality that does not involve Bell's (or any other) inequalities. In [11] we introduced only "spin-like" observables acting on finite dimensional Hilbert spaces. Here we will give a similar argument using the variables originally used by Einstein, Podolsky and Rosen, namely position and momentum.

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Source: https://tomesphere.com/paper/1906.06687