Nonlocality Claims are Inconsistent with Hilbert Space Quantum Mechanics

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 Schrödinger 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.

v3: Minor changes and corrections. This version agrees pretty well with published paper

References in corpus (4)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• What Bell Did
• Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering
• Reply to Werner

Cited by in corpus (22)

• Kochen-Specker Contextuality
• Is the Moon there if nobody looks: Bell Inequalities and Physical Reality
• A Note on Bell's Theorem Logical Consistency
• Contextuality-by-Default description of Bell tests: Contextuality as the rule not as an exception
• Contextuality or nonlocality; what would John Bell choose today?
• Conditional probability framework for entanglement and its decoupling from tensor product structure
• Quantum postulate vs. quantum nonlocality: Is Devil in h?
• Bell inequalities, Counterfactual Definiteness and Falsifiability
• Reply to "Comment on 'Nonlocality claims are inconsistent with Hilbert-space quantum mechanics' '"
• Quantum randomness is chimeric
• Effective interaction force between an electric charge and a magnetic dipole and locality (or nonlocality) in quantum effects of the Aharonov-Bohm type
• Discretisation of the Bloch Sphere, Fractal Invariant Sets and Bell's Theorem
• Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality
• Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations
• Non-Contextual and Local Hidden-Variable Model for the Peres-Mermin and Greenberger-Horne-Zeilinger Systems
• A statistical model for quantum spin and photon number states
• Does locality plus perfect correlation imply determinism?
• A theory of quantum (statistical) measurement
• Comment on "Nonlocality claims are inconsistent with Hilbert-space quantum mechanics"
• Are Bell-tests only about local incompatibility?
• Bell vs Bell: a ding-dong battle over quantum incompleteness
• Violation of Bell Inequalities: Mapping the Conceptual Implications