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A Philosopher's View of the Epistemic Interpretation of Quantum Mechanics

Shahar Avin

Published May 1, 2010• 0 citations
OpenAlex

Abstract

There are various reasons for favouring Ψ-epistemic interpretations of quantum mechanics over Ψ-ontic interpretations. One such reason is the correlation between quantum mechanics and Liouville dynamics. Another reason is the success of a specific epistemic model (Spekkens, 2007), in reproducing a wide range of quantum phenomena. The potential criticism, that Spekkens' restricted knowledge principle is counter-intuitive, is rejected using `everyday life' examples. It is argued that the dimensionality of spin favours Spekkens' model over Ψ-ontic models. van Enk's extension of Spekkens' model (2007) can even reproduce Bell Inequality violations, but requires negative probabilities to do so. An epistemic account of negative probabilities is the missing element for deciding the battle between Ψ-epistemic and Ψ-ontic interpretations in favour of the former.

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Abstract Harrigan and Spekkens (Found Phys 40:125–157, 2010) provided a categorization of quantum ontological models classifying them as $$\psi$$ ψ -ontic or $$\psi$$ ψ -epistemic if the quantum state $$\psi$$ ψ describes respectively either a physical reality or mere observers’ knowledge. Moreover, they claimed that Einstein—who was a supporter of the statistical interpretation of quantum mechanics—endorsed an epistemic view of $$\psi .$$ ψ. In this essay we critically assess such a classification and some of its consequences by proposing a twofold argumentation. Firstly, we show that Harrigan and Spekkens’ categorization implicitly assumes that a complete description of a quantum system (its ontic state, $$\lambda$$ λ ) only concernssingle,individualsystems instantiatingabsolute,intrinsicproperties. Secondly, we argue that such assumptions conflict with some current interpretations of quantum mechanics, which employ different ontic states as a complete description of quantum systems. In particular, we will show that, since in the statistical interpretation ontic states describe ensembles rather than individuals, such a view cannot be considered $$\psi$$ ψ -epistemic. As a consequence, the authors misinterpreted Einstein’s view concerning the nature of the quantum state. Next, we will focus onrelational quantum mechanicsandperspectival quantum mechanics, which in virtue of their relational and perspectival metaphysics employ ontic states $$\lambda$$ λ dealing with relational properties. We conclude that Harrigan and Spekkens’ categorization is too narrow and entails an inadequate classification of the mentioned interpretations of quantum theory. Hence, any satisfactory classification of quantum ontological models ought to take into account the variations of $$\lambda$$ λ across different interpretations of quantum mechanics.

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In discussion of the interpretation of quantum mechanics the terms ‘ontic’ and ‘epistemic’ are often used in the sense of pertaining to what exists, and pertaining to cognition or knowledge respectively. The terms are also often associated with the formal definitions given by Harrigan and Spekkens for the wavefunction in quantum mechanics to be �ψ-ontic or �ψ-epistemic in the context of the ontological models framework. The formal definitions are contradictories, so that the wavefunction can be either ψ�-epistemic or ψ �-ontic but not both. However, we argue, nothing about the informal ideas of epistemic and ontic interpretations rules out wavefunctions representing both reality and knowledge. The implications of the Pusey–Barrett–Rudolph theorem and many other issues may be rethought in the light of our analysis.

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There are various reasons for favouring Ψ-epistemic interpretations of quantum mechanics over Ψ-ontic interpretations. One such reason is the correlation between quantum mechanics and Liouville dynamics. Another reason is the success of a specific epistemic model (Spekkens, 2007), in reproducing a wide range of quantum phenomena. The potential criticism, that Spekkens' restricted knowledge principle is counter-intuitive, is rejected using `everyday life' examples. It is argued that the dimensionality of spin favours Spekkens' model over Ψ-ontic models. van Enk's extension of Spekkens' model (2007) can even reproduce Bell Inequality violations, but requires negative probabilities to do so. An epistemic account of negative probabilities is the missing element for deciding the battle between Ψ-epistemic and Ψ-ontic interpretations in favour of the former.
On the Classification Between ψ\psiψ-Ontic and ψ\psiψ-Epistemic Ontological Models
Abstract Harrigan and Spekkens (Found Phys 40:125–157, 2010) provided a categorization of quantum ontological models classifying them as ψ\psiψ ψ -ontic or ψ\psiψ ψ -epistemic if the quantum state ψ\psiψ ψ describes respectively either a physical reality or mere observers’ knowledge. Moreover, they claimed that Einstein—who was a supporter of the statistical interpretation of quantum mechanics—endorsed an epistemic view of ψ.\psi .ψ. ψ. In this essay we critically assess such a classification and some of its consequences by proposing a twofold argumentation. Firstly, we show that Harrigan and Spekkens’ categorization implicitly assumes that a complete description of a quantum system (its ontic state, λ\lambdaλ λ ) only concernssingle,individualsystems instantiatingabsolute,intrinsicproperties. Secondly, we argue that such assumptions conflict with some current interpretations of quantum mechanics, which employ different ontic states as a complete description of quantum systems. In particular, we will show that, since in the statistical interpretation ontic states describe ensembles rather than individuals, such a view cannot be considered ψ\psiψ ψ -epistemic. As a consequence, the authors misinterpreted Einstein’s view concerning the nature of the quantum state. Next, we will focus onrelational quantum mechanicsandperspectival quantum mechanics, which in virtue of their relational and perspectival metaphysics employ ontic states λ\lambdaλ λ dealing with relational properties. We conclude that Harrigan and Spekkens’ categorization is too narrow and entails an inadequate classification of the mentioned interpretations of quantum theory. Hence, any satisfactory classification of quantum ontological models ought to take into account the variations of λ\lambdaλ λ across different interpretations of quantum mechanics.
Generally, there are two interpretative approaches to quantum theory: psi-ontic and psi-epistemic. According to the psi-ontic interpretations, quantum theory does/should describe or represent what the world is like. In contrast, according to the psi-epistemic interpretations, rather than representing the way the world is, quantum theory advises us on what to expect from the world and so helps us better navigate our surrounding world. In this paper, we will argue that Edmund Husserl’s philosophy of science especially his notion of lifeworld provides an appropriate framework for better understanding this shift from the psi-ontic to psi-epistemic interpretations of quantum theory. In particular, we analyse Richard Healey’s pragmatic approach to quantum mechanics from a phenomenological point of view.
In discussion of the interpretation of quantum mechanics the terms ‘ontic’ and ‘epistemic’ are often used in the sense of pertaining to what exists, and pertaining to cognition or knowledge respectively. The terms are also often associated with the formal definitions given by Harrigan and Spekkens for the wavefunction in quantum mechanics to be �ψ-ontic or �ψ-epistemic in the context of the ontological models framework. The formal definitions are contradictories, so that the wavefunction can be either ψ�-epistemic or ψ �-ontic but not both. However, we argue, nothing about the informal ideas of epistemic and ontic interpretations rules out wavefunctions representing both reality and knowledge. The implications of the Pusey–Barrett–Rudolph theorem and many other issues may be rethought in the light of our analysis.
Abstract The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave-functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave-function in this interpretation is best regarded as ψ-ontic and incomplete.
Abstract In discussion of the interpretation of quantum mechanics the terms ‘ontic’ and ‘epistemic’ are often used in the sense of pertaining to what exists, and pertaining to cognition or knowledge respectively. The terms are also often associated with the formal definitions given by Harrigan and Spekkens for the wavefunction in quantum mechanics to be ψ\psi ψ ψ -ontic or ψ\psi ψ ψ -epistemic in the context of the ontological models framework. The formal definitions are contradictories, so that the wavefunction can be either ψ\psi ψ ψ -epistemic or ψ\psi ψ ψ -ontic but not both. However, we argue, nothing about the informal ideas of epistemic and ontic interpretations rules out wavefunctions representing both reality and knowledge. The implications of the Pusey–Barrett–Rudolph theorem and many other issues may be rethought in the light of our analysis.
Formalizing an old desire of Einstein, ``$\ensuremath{\psi}$-epistemic theories'' try to reproduce the predictions of quantum mechanics, while viewing quantum states as ordinary probability distributions over underlying objects called ``ontic states.'' Regardless of one's philosophical views about such theories, the question arises of whether one can cleanly rule them out by proving no-go theorems analogous to the Bell inequality. In the 1960s, Kochen and Specker (who first studied these theories) constructed an elegant $\ensuremath{\psi}$-epistemic theory for Hilbert space dimension d=2d=2d=2, but also showed that any deterministic $\ensuremath{\psi}$-epistemic theory must be ``measurement contextual'' in dimensions 3 and higher. Last year, the topic attracted renewed attention, when Pusey, Barrett, and Rudolph (PBR) showed that any $\ensuremath{\psi}$-epistemic theory must ``behave badly under tensor product.'' In this paper, we prove that even without the Kochen-Specker or PBR assumptions, there are no $\ensuremath{\psi}$-epistemic theories in dimensions $d\ensuremath{\ge}3$ that satisfy two reasonable conditions: (1) symmetry under unitary transformations and (2) ``maximum nontriviality'' (meaning that the probability distributions corresponding to any two nonorthogonal states overlap). This no-go theorem holds if the ontic space is either the set of quantum states or the set of unitaries. The proof of this result, in the general case, uses some measure theory and differential geometry. On the other hand, we also show the surprising result that without the symmetry restriction, one can construct maximally nontrivial $\ensuremath{\psi}$-epistemic theories in every finite dimension ddd.