The Problem of Hidden Variables in Quantum Mechanics

Kochen, Simon; Specker, Ernst

doi:10.1007/978-3-0348-9259-9_21

Cited by 904 publications

(1,670 citation statements)

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“…33 We argue in this subsection that this is not the case. The reason why Prism Models are successful is our actual failure of detection of all quantum systems.…”

Section: Prism Models the Experiments And Quantum Mechanicsmentioning

confidence: 91%

Fine ways to fail to secure local realism

Bihan¹

2009

Studies in History and Philosophy of Science Part B: Studies in

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For more than twenty five years, Fine has been challenging the traditional interpretation of the violations of Bell inequalities (BI) by experiment. A natural interpretation of Fine's theorem is that it provides us with an alternative set of assumptions on which to put the blame for the failure of the BI, and a new interpretation of the violation of the BI by experiment should follow. This is not, however, how Fine interprets his theorem. Indeed, Fine claims that his result undermines other interpretations, including the traditional interpretation in terms of local realism. The aim of this paper is to understand and to assess Fine's claims. We distinguish three different strategies that Fine uses in order to support his interpretation of his result.We show that none of these strategies is successful. Fine fails to prove that local realism is not at stake in the violation of the BI by quantum phenomena.

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“…33 We argue in this subsection that this is not the case. The reason why Prism Models are successful is our actual failure of detection of all quantum systems.…”

Section: Prism Models the Experiments And Quantum Mechanicsmentioning

confidence: 91%

Fine ways to fail to secure local realism

Bihan¹

2009

Studies in History and Philosophy of Science Part B: Studies in

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“…There are more sophisticated ways to understand the difficulty with a probabilistic reading, and to rule out subtler variants (ranging from the classic Kochen-Specker theorem (Kochen and Specker 1967)) to the recent, celebrated result of Pusey, Barrett, and Rudolph (2011)) but ultimately they turn on the same feature of quantum dynamics: interference rules out a probabilistic interpretation of the amplitudes. Essentially the only way around this problem is to abandon any attempt at a realist understanding of quantum theory and fall back on the idea that the theory is simply a black-box device to make empirical predictions; I will ignore such instrumentalism for the purposes of this paper.…”

Section: Quantum Theorymentioning

confidence: 99%

Probability in Physics: Stochastic, Statistical, Quantum

Wilson¹

2014

Chance and Temporal Asymmetry

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I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case (both stochastic mechanics and classical statistical mechanics) but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of probabilistic asymmetry in time, is dependent on the correct resolution of the quantum measurement problem.

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“…Kochen and Specker's celebrated theorem (Specker, 1960;Kochen & Specker, 1967) states that if n > 2 there are KS-uncolourable sets, i.e., sets K for which no KS-colouring exists. It follows trivially that the set of all Hermitian operators acting on a Hilbert space of dimension > 2 is KS-uncolourable.…”

Section: The Kochen-specker Theoremmentioning

confidence: 99%

“…The argument of Kochen & Specker (1967), and most later discussions until recently, including Meyer (1999), assume that the quantum theory of measurement can be framed entirely in terms of projective measurements. This remains a tenable view, so long as one is willing to accept that the experimental configuration defines the quantum system being measured.…”

Section: Projective Measurementsmentioning

confidence: 99%

Non-contextuality, finite precision measurement and the Kochen–Specker theorem

Barrett

Kent

2004

Studies in History and Philosophy of Science Part B: Studies in

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Meyer originally raised the question of whether non-contextual hidden variable models can, despite the Kochen-Specker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental precision (Meyer, D. 1999. Phys. Rev. Lett., 83, 3751-3754). Meyer's result was extended by Kent (Kent, A. 1999. Phys. Rev. Lett., 83, 3755-3757). Clifton and Kent later presented constructions of non-contextual hidden variable theories which, they argued, indeed simulate quantum mechanics in this way (Clifton, R and Kent, A. 2000. Proc. Roy. Soc. Lond. A, 456, 2101-2114.These arguments have evoked some controversy. Among other things, it has been suggested that the Clifton-Kent models do not in fact reproduce correctly the predictions of quantum mechanics, even when finite precision is taken into account. It has also been suggested that careful analysis of the notion of contextuality in the context of finite precision measurement motivates definitions which imply that the Clifton-Kent 1 models are in fact contextual. Several critics have also argued that the issue can be definitively resolved by experimental tests of the KochenSpecker theorem or experimental demonstrations of the contextuality of Nature.One aim of this paper is to respond to and rebut criticisms of the Meyer-Clifton-Kent papers. We thus elaborate in a little more detail how the Clifton-Kent models can reproduce the predictions of quantum mechanics to arbitrary precision. We analyse in more detail the relationship between classicality, finite precision measurement and contextuality, and defend the claims that the Clifton-Kent models are both essentially classical and non-contextual. We also examine in more detail the senses in which a theory can be said to be contextual or non-contextual, and in which an experiment can be said to provide evidence on the point. In particular, we criticise the suggestion that a decisive experimental verification of contextuality is possible, arguing that the idea rests on a conceptual confusion.

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The Problem of Hidden Variables in Quantum Mechanics

Cited by 904 publications

References 9 publications

Fine ways to fail to secure local realism

Fine ways to fail to secure local realism

Probability in Physics: Stochastic, Statistical, Quantum

Non-contextuality, finite precision measurement and the Kochen–Specker theorem

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