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arXiv:2204.01768

Comment on "Why interference phenomena do not capture the essence of quantum theory"

Jonte R. Hance, Sabine Hossenfelder

Published Apr 4, 2022• 1 citation
arXivHTMLPDF

Abstract

It was recently argued by Catani et al that it is possible to reproduce the phenomenology of quantum interference classically, by the double-slit experiment with a deterministic, local, and classical model (Quantum 7, 1119 (2023)). The stated aim of their argument is to falsify the claim made by Feynman (in his third book of Lectures on Physics) that quantum interference is ``impossible, absolutely impossible, to explain in any classical way'' and that it ``contains the only mystery'' of quantum mechanics. We here want to point out some problems with their argument.

DOI
10.48550/arxiv.2204.01768

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Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that reproduces this phenomenology but which does not sacrifice the classical worldview. In their Comment [arXiv:2204.01768(2022)], Hance and Hossenfelder dispute our claim. Correcting mistaken claims found therein and responding to their criticisms provides us with an opportunity to further clarify some of the ideas in our article.

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It was recently argued by Catani et al that it is possible to reproduce the phenomenology of quantum interference classically, by the double-slit experiment with a deterministic, local, and classical model (Quantum 7, 1119 (2023)). The stated aim of their argument is to falsify the claim made by Feynman (in his third book of Lectures on Physics) that quantum interference is impossible, absolutely impossible, to explain in any classical way'' and that it contains the only mystery'' of quantum mechanics. We here want to point out some problems with their argument.
Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that reproduces this phenomenology but which does not sacrifice the classical worldview. In their Comment [arXiv:2204.01768(2022)], Hance and Hossenfelder dispute our claim. Correcting mistaken claims found therein and responding to their criticisms provides us with an opportunity to further clarify some of the ideas in our article.
Feynman famously said that single-particle interference is ``a phenomenon which is impossible to explain in any classical way, and which has in it the heart of quantum mechanics.'' In this paper we show that some of the phenomenology of interference can be reproduced in a ``classical'' way, by reproducing the Elitzur-Vaidman Bomb Tester (including their improved version) using an extension of the quantum simulation logic (QSL) formalism. Our result improves and simplifies a previous result by Catani \emph{et al}, which relies on a much more complicated extension involving a ``toy field theory.'' We also show that not all single-particle interference can be explained by such a simple extension (including that of Catani et al), by showing that Hofmann's three-path interferometer is ``nonclassical'' in a very specific sense: it violates a Kochen-Specker-noncontextual inequality. Given that both our extension of QSL and Catani et al's extension are \emph{noncontextual} -- so do not reproduce the contextual behaviour of Hofmann's three-path interferometer -- the behaviour of that interferometer is a proper example of a phenomenon that has in it the heart of quantum mechanics, according to Feynman.
Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the `toy field theory') that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler's delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known . The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer's knowledge of reality, not reality itself.
What is the most beautiful experiment in physics? More than 200 readers replied when Robert Crease asked this question in May, and their top five choices include classic experiments by Galileo, Millikan, Newton and Thomas Young (see pp19–20). But uniquely among the top 10, the most beautiful experiment in physics – the double-slit interference experiment with electrons – does not have the name of an individual associated with it. Most discussions of double-slit experiments with particles refer to Feynman's quote in his 1963 lectures: "[It] is absolutely impossible to explain in any classical way and has in it the heart of quantum mechanics. In reality, it contains the only mystery." But who actually carried out the experiment? Standard reference books offer no answer to this question but a search through the literature does reveal several unsung experimental heroes.