The nature of the wave function has been a hot topic of debate since the early days of quantum mechanics. The recent PBR theorem proves that the wave function is ontic, representing the ontic state of a physical system or a concrete physical entity. On the other hand, Bohmian mechanics regards the wave function as not ontic but nomological, like a law of nature. This raises an interesting question: does the PBR theorem refute Bohmian mechanics? It seems widely thought that the ontic view and the nomological view are compatible, and thus the PBR theorem has no implications for Bohmian mechanics. In this paper, I argue that this is not the case. First, I point out that the nomological view and the ontic view are two different views of the wave function. This means that the result of the PBR theorem and Bohmian mechanics are incompatible. Next, I argue that the PBR theorem and Bohmian mechanics are nevertheless compatible, and the former does not refute the latter. The reason is that the PBR theorem and Bohmian mechanics are based on different fundamental assumptions, and in particular, Bohmian mechanics rejects one key assumption of the ontological models framework on which the PBR theorem is based. Finally, I argue that the rejection of this assumption will bring to our attention a potential important issue of Bohmian mechanics.
Abstract Harrigan and Spekkens (Found Phys 40:125–157, 2010) provided a categorization of quantum ontological models classifying them as
ψ ψ -ontic or
ψ ψ -epistemic if the quantum state
ψ 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. 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 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 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 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 λ across different interpretations of quantum mechanics.
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.
The Pusey--Barrett--Rudolph (PBR) theorem is commonly taken to establish that a pure quantum state represents a physical property of the system to which it is assigned, rather than merely encoding knowledge. In this work, I distinguish between state-first and dynamics-first physical theories, and argue that this reading presupposes the former. These two types of theories support different approaches to causal explanation, and one of PBR's stated assumptions depends on the state-first approach. Using a recent interpretation of quantum theory as a concrete example, I show how a dynamics-first theory can explain the PBR correlations while maintaining a broadly epistemic reading of quantum states. I conclude that the PBR theorem supports a dilemma: either the quantum state is part of reality, or reality is not fundamentally built out of states.
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 ψ -ontic or
ψ ψ -epistemic in the context of the ontological models framework. The formal definitions are contradictories, so that the wavefunction can be either
ψ ψ -epistemic or
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.
This note contains some initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves generalising and reformulating a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the PBR theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a novel characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to an analogy with Bell locality, and thence to a proposal to weaken it to an assumption of `no-preparation-signalling' in analogy with no-signalling. This amounts to introducing non-local correlations in the joint ontic state, which is, at least, consistent with the Bell and Kochen-Specker theorems. The question of whether the PBR result can be strengthened to hold under this relaxed assumption is therefore posed.