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CRC Press eBooks

Interpretations

Jonathan Allday

Published Sep 21, 2022• 0 citations
Publisher

Abstract

Every physical theory needs a form of interpretation. When the mathematicians write down a string of mathematical formulas, there has to be some link between the symbols on the page and the measurements that they make if the formulas are to be physically relevant. This is one of the jobs an interpretation is designed for. Many physicists and philosophers look to an interpretation to enshrine some physical picture of the world. Some physicists deny that quantum states refer to individual examples of a system. They regard the state as a description of the ensemble, not the individuals within it. Bell’s inequality already deals with the inability to reproduce quantum correlations using local hidden variables. The Kochen-Specker theorem speaks to the contextuality of quantum theory.

DOI
10.1201/9781003225997-30

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Every physical theory needs a form of interpretation. When the mathematicians write down a string of mathematical formulas, there has to be some link between the symbols on the page and the measurements that they make if the formulas are to be physically relevant. This is one of the jobs an interpretation is designed for. Many physicists and philosophers look to an interpretation to enshrine some physical picture of the world. Some physicists deny that quantum states refer to individual examples of a system. They regard the state as a description of the ensemble, not the individuals within it. Bell’s inequality already deals with the inability to reproduce quantum correlations using local hidden variables. The Kochen-Specker theorem speaks to the contextuality of quantum theory.
The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems.
Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.
There are two powerful arguments against the possibility of extending quantum mechanics (QM) into a more fundamental theory yielding a deterministic description of nature. One is the experimental violation of Bell inequalities, which discards local hidden‐variable theories as a possible extension to QM. The other is the Kochen‐Specker (KS) theorem, which stresses the incompatibility of QM with a larger class of hidden‐variable theories, known as noncontextual hidden‐variable theories. We performed experiments with neutron interferometer, which exploits spin‐path entanglements in single neutrons. A Bell‐like state is generated to demonstrate a violation of the Bell‐like inequality and phenomena in accordance with KS theorem: both experiments study quantum contextuality and show clear evidence of the incompatibility of noncontextual hidden variable theories with QM. The value S = 2.202±0.007≰2 is obtained in the new measurement of the Bell‐like inequality, which shows a larger violation than the previous measurement. For the study of KS theorem, the obtained violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
The interpretation of quantum mechanics in the context of measurements, and concepts such as state “collapse,” have troubled physicists since the inception of quantum theory. Pushed to their logical extreme, such issues become entangled (in the colloquial sense) with questions of consciousness, reality, etc. Bell’s theorem eliminated possible ways out of this tangle via any (halfway reasonable) classical underlying theory, and the success of quantum mechanics forces us to adopt it as a fundamental theory and face the logical consequences.