Heisenberg (and Schrödinger, and Pauli) on hidden variables

Bacciagaluppi, Guido; Crull, Elise

doi:10.1016/j.shpsb.2009.08.004

Cited by 38 publications

(29 citation statements)

References 21 publications

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“…52 For more detailed accounts, see Bacciagaluppi and Valentini (2009), Bacciagaluppi (2008), Bacciagaluppi and Crull (2009), and Bacciagaluppi, Crull and Maroney (2017).…”

Section: Further Remarks On the Quantum Statementioning

confidence: 99%

Unscrambling Subjective and Epistemic Probabilities

Bacciagaluppi

2020

Jerusalem Studies in Philosophy and History of Science

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There are two notions in the philosophy of probability that are often used interchangeably: that of subjective probabilities and that of epistemic probabilities. This paper suggests they should be kept apart. Specifically, it suggests that the distinction between subjective and objective probabilities refers to what probabilities are, while the distinction between epistemic and ontic probabilities refers to what probabilities are about. After arguing that there are bona fide examples of subjective ontic probabilities and of epistemic objective probabilities, I propose a systematic way of drawing these distinctions in order to take this into account. In doing so, I modify Lewis's notion of chances, and extend his Principal Principle in what I argue is a very natural way (which in fact makes chances fundamentally conditional). I conclude with some remarks on time symmetry, on the quantum state, and with some more general remarks about how this proposal fits into an overall Humean (but not quite neo-Humean) framework. This second notion of 'epistemic probabilities', which is perhaps most common in the philosophy of probability, belongs somewhere along the axis between subjective and objective probabilities. It is often contrasted with subjective probabilities when these are understood as merely 'prudential' or 'pragmatic' or 'instrumental'. This distinction is challenged by Berkovitz (2019), who convincingly argues that de Finetti's instrumental probabilities are also epistemic in this sense. Indeed, when talking about subjective probabilities in Sections 4, 6 and 10, I shall always implicitly take them to be so. This second sense of 'epistemic probabilities' is not the topic of this paper, and will be discussed no further. Epistemic probabilities in the sense of ignorance-interpretable ones instead are liable to be assimilated to subjective probabilities, but, as I shall argue, they ought not to, because the distinction between probabilities that are epistemic in this sense and those that are not (we shall call them 'ontic') is conceptually orthogonal to the subjective-objective distinction.

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“…52 For more detailed accounts, see Bacciagaluppi and Valentini (2009), Bacciagaluppi (2008), Bacciagaluppi and Crull (2009), and Bacciagaluppi, Crull and Maroney (2017).…”

Section: Further Remarks On the Quantum Statementioning

confidence: 99%

Unscrambling Subjective and Epistemic Probabilities

Bacciagaluppi

2020

Jerusalem Studies in Philosophy and History of Science

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“…Admittedly, the assumptions needed for this result are not as innocuous as they look at first sight. They are essentially the same as those that go into von Neumann's infamous no-hidden-variable proof (Bell, 1966;Bacciagaluppi and Crull, 2009;Bub, 2010).…”

Section: Von Neumann's Alternative To the Dirac-jordan Theorymentioning

confidence: 85%

(Never) Mind your p’s and q’s: Von Neumann versus Jordan on the foundations of quantum theory

Duncan

Janssen

2012

EPJ H

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In two papers entitled "On a new foundation [Neue Begründung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formalism of quantum mechanics. In this paper, we focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan (1927b) was the first to state those rules in full generality. Von Neumann (1927a) rephrased them and, in a subsequent paper , sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics.

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“…3.2]. Thus, Heisenberg clearly 'recognises as a separate assumption that hidden variables are to be considered independently of the means of observation' ( [27], emphasis mine), that is to be non-contextual versus the more non-trivial case wherein context must be taken into account.…”

Section: Completeness and Contextualitymentioning

confidence: 99%

Quantum contextuality in the Copenhagen approach

Jaeger

2019

Phil. Trans. R. Soc. A.

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The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

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Heisenberg (and Schrödinger, and Pauli) on hidden variables

Cited by 38 publications

References 21 publications

Unscrambling Subjective and Epistemic Probabilities

Unscrambling Subjective and Epistemic Probabilities

(Never) Mind your p’s and q’s: Von Neumann versus Jordan on the foundations of quantum theory

Quantum contextuality in the Copenhagen approach

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