# Nonlocality Claims are Inconsistent with Hilbert Space Quantum Mechanics

## TL;DR

This paper argues that when properly analyzed within Hilbert space quantum mechanics, quantum theory is inherently local, and violations of Bell inequalities are due to misinterpretations involving classical concepts and non-quantum assumptions.

## Contribution

It demonstrates that quantum mechanics is local under Hilbert space formalism and clarifies misconceptions about nonlocality and Bell inequality violations.

## Key findings

- Quantum mechanics is consistent with locality when analyzed properly.
- Bell inequality violations are explained by noncommuting operators, not nonlocal influences.
- Classical hidden variables are inappropriate for quantum measurement analysis.

## Abstract

It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are shown to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum measurements measure, in terms of quantum properties, is used to identify the basic problem with derivations of Bell inequalities: the use of classical concepts (hidden variables) rather than a probabilistic structure appropriate to the quantum domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics is the use of a counterfactual argument which is not valid if one assumes that Hilbert-space quantum mechanics is complete; locality is not an issue. The quantum correlations that violate Bell inequalities can be understood using local quantum common causes. Wavefunction collapse and Schr\"odinger steering are calculational procedures, not physical processes. A general Principle of Einstein Locality rules out nonlocal influences between noninteracting quantum systems. Some suggestions are made for changes in terminology that could clarify discussions of quantum foundations and be less confusing to students.