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arXiv:1904.10991

No-Go Theorems and the Foundations of Quantum Physics

Andréa Oldofredi

Published Apr 24, 2019• 0 citations
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Abstract

In the history of quantum physics several no-go theorems have been proved, and many of them have played a central role in the development of the theory, such as Bell's or the Kochen-Specker theorem. A recent paper by F. Laudisa has raised reasonable doubts concerning the strategy followed in proving some of these results, since they rely on the standard framework of quantum mechanics, a theory that presents several ontological problems. The aim of this paper is twofold: on the one hand, I intend to reinforce Laudisa's methodological point by critically discussing Malament's theorem in the context of the philosophical foundation of Quantum Field Theory; secondly, I rehabilitate Gisin's theorem showing that Laudisa's concerns do not apply to it.

DOI
10.48550/arxiv.1904.10991

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In the history of quantum physics several no-go theorems have been proved, and many of them have played a central role in the development of the theory, such as Bell's or the Kochen-Specker theorem. A recent paper by F. Laudisa has raised reasonable doubts concerning the strategy followed in proving some of these results, since they rely on the standard framework of quantum mechanics, a theory that presents several ontological problems. The aim of this paper is twofold: on the one hand, I intend to reinforce Laudisa's methodological point by critically discussing Malament's theorem in the context of the philosophical foundation of Quantum Field Theory; secondly, I rehabilitate Gisin's theorem showing that Laudisa's concerns do not apply to it.
In the area of the foundations of quantummechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the significance of proving ‘no-go’ results should consist in clarifying the fundamental structure of the theory, by pointing out a class of basic constraints that the theory itself is supposed to satisfy. In the present paper I will discuss some more recent no-go claims and I will argue against the deep significance of these results, with a two-fold strategy. First, I will consider three results concerning respectively local realism, quantum covariance and predictive power in quantum mechanics, and I will try to show how controversial the main conditions of the negative theorem turn out to be—something that strongly undermines the general relevance of these theorems. Second, I will try to discuss what I take to be a common feature of these theoretical enterprises, namely that of aiming at establishing negative results for quantum mechanics in absence of a deeper understanding of the overall ontological content and structure of the theory. I will argue that the only way toward such an understanding may be to cast in advance the problems in a clear and well-defined interpretational framework—which in my viewmeans primarily to specify the ontology that quantum theory is supposed to be about—and after to wonder whether problems that seemed worth pursuing still are so in the framework.
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.
One of the recent no-go theorems on Ψ-epistemic interpretations of quantum proves that there are no 'maximally epistemic' interpretations of quantum theory. The proof utilises similar arrangements to Clifton's quantum contextuality proof and has parallels to Harrigan and Rudolph's quantum deficiency no-go theorem, itself based on the Kochen-Specker quantum contextuality proof. This paper shows how the Kochen-Specker theorem can also be turned into a no 'maximally epistemic' theorem, but of a more limited kind.
This thesis explores the exact differences between the two most well-known no-hidden variable theories: the Bell theorem and the Kochen-Specker theorem. Furthermore, it tries to place a newer result called `the free will theorem', as developed by John Conway and Simon Kochen, in this context. To compare the Bell and Kochen-Specker theorems a reformulation of the two theorems by David Mermin will be discussed, which turns out to lead to an even stronger no-hidden variable theory. From the discussion of the free will theorem and the critical reactions it has elicited, it will become clear that the free will theorem is actually very similar to this stronger no-hidden variable theory.