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Physics

Locality in the Schrödinger Picture of Quantum Mechanics

Vlatko Vedral

Published May 19, 2024• 1 citation
Publisher

Abstract

This paper explains how the so-called Einstein locality is to be understood in the Schrödinger picture of quantum mechanics. This notion is fully compatible with the Bell non-locality exhibited by entangled states. Contrary to the belief that quantum mechanics is incomplete, it is, As a matter of fact, its overcompleteness, as exemplified by the different pictures of quantum physics, that points to the same underlying reality.

DOI
10.3390/physics6020049

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This paper explains how the so-called Einstein locality is to be understood in the Schrödinger picture of quantum mechanics. This notion is fully compatible with the Bell non-locality exhibited by entangled states. Contrary to the belief that quantum mechanics is incomplete, it is, As a matter of fact, its overcompleteness, as exemplified by the different pictures of quantum physics, that points to the same underlying reality.
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality – locality – completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality – locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
It is known that "quantum non locality", leading to the violation of Bell's inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, which we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing the making of contextual inferences, which can, in turn, explain why quantum non locality does not contradict relativistic causality. An important question remains: if the usual quantum state ψ is predictively incomplete, how do we complete it? We give here a set of new arguments to show that ψ should be completed indeed, not by looking for any "hidden variables", but rather by specifying the measurement context, which is required to define actual probabilities over a set of mutually exclusive physical events.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
In this paper we survey, in an elementary fashion, some of the questions that arise when one considers how entanglement and relativity are related via the notion of non-locality. We begin by reviewing the role of entangled states in Bell inequality violation and question whether the associated notions of non-locality lead to problems with relativity. The use of entanglement and wavefunction collapse in Einstein's famous incompleteness argument is then considered, before we go on to see how the issue of non-locality is transformed if one considers quantum mechanics without collapse to be a complete theory, as in the Everett interpretation. The opportunity is taken to consider whether teleportation and dense coding might constitute a source of non-locality within the Everett interpretation.
Based on a thought experiment the Einstein-Podolsky-Rosen paper’s authors concluded that in quantum mechanics the mathematical objects called wave functions fail to describe the physical reality and consequently quantum theory is incomplete. They left open the question of whether or not a complete description of the physical reality exists, but expressed their belief that such a complete theory is possible. In this paper I show that indeed a theory that gives a complete description of the physical reality exists.