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arXiv:1906.00956

Do psi-ontology theorems prove that the wave function is not epistemic?

I. Schmelzer

Published Jun 2, 2019• 0 citations
arXivHTMLPDF

Abstract

As a counterexample to $ψ$-ontology theorems we consider a $ψ$-epistemic interpretation of the wave function in the configuration space representation with a configuration space trajectory defining the ontology. This shows that $ψ$-ontology theorems appear unable to prove that the wave function cannot be interpreted as epistemic. We identify the criterion used to decide if $ψ$ is epistemic or ontological as the misleading part. Different states having overlaps is only sufficient for being epistemic. In an epistemic interpretation the information which completely identifies the wave function also has an objective base in reality - the preparation procedure, which has to be really executed to prepare a state. Naming the $λ\in Λ$ "hidden variables" and considering them as part of the state of the system we also identify as misleading, because it hides the possibility that they may be visible and external to the system. This leads to further misconceptions about the consequences of the theorems.

DOI
10.48550/arxiv.1906.00956

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As a counterexample to ψψψ-ontology theorems we consider a ψψψ-epistemic interpretation of the wave function in the configuration space representation with a configuration space trajectory defining the ontology. This shows that ψψψ-ontology theorems appear unable to prove that the wave function cannot be interpreted as epistemic. We identify the criterion used to decide if ψψψ is epistemic or ontological as the misleading part. Different states having overlaps is only sufficient for being epistemic. In an epistemic interpretation the information which completely identifies the wave function also has an objective base in reality - the preparation procedure, which has to be really executed to prepare a state. Naming the λ∈Λλ\in Λλ∈Λ "hidden variables" and considering them as part of the state of the system we also identify as misleading, because it hides the possibility that they may be visible and external to the system. This leads to further misconceptions about the consequences of the theorems.
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.
The consequences of the theorems about ontological models are studied. "Maximally ψψψ-epistemic" is shown to be equivalent to the conjunction of two other conditions, each of which can be realized in Hilbert spaces of arbitrary dimension, but which cannot occur together for d>2. I argue that current theorems do not invalidate an epistemic interpretation of quantum states. A new condition, called "functionally ψψψ-epistemic", is introduced, which, were it to be excluded, would signal the exclusion of epistemic interpretations.
What does quantum physics tell us about the nature of reality, specifically the parts of reality we do not directly perceive called hidden variables? One may think it could tell us a lot because of our enhanced technological sensing abilities that delve into the realms that quantum physics covers so well. Surprisingly, it seems to surround us in a deeper mystery rather than reveal more of nature's secrets. It seems that we cannot escape from philosophical consideration when dealing with what is hidden in quantum physics. In Part I we will look at how Epistemology and Ontology bear upon Hidden Variables. In Part II we will consider Hidden Variables in the light of Contextuality, and Non-Classicality. Inevitably questions of subjectivity and objectivity arise in dealing with states of observation. How should we think about these states? Perhaps it is a question of the meaning associated with our knowledge of a state-that is, a question of ontology or epistemology. The issue of ontic and epistemic states is particularly important when considering hidden variables in quantum physics because, as one may argue, the interpretation of quantum states as either ontic or epistemic will naturally lead to different assumptions about how reality is constructed; if it is constructed or not. It also raises the question of what attributes we are able to observe simultaneously and that brings contextuality into the discussion. If it turns out that reality is constructed contextually what does that imply about ontological realism? If on the other hand reality is constructed non-contextually what does that imply about ontological realism? Many implications can arise when considering these questions from a quantum physical point of view. In this paper I shall discuss how quantum physics provides some answers to these questions by considering quantum physical states and their measurements.
One of the major concerns of Schr\"odinger, Lorentz, Einstein, and many others about the wave function is that it is defined on the 3N3\mathbf{N}3N-dimensional configuration space, rather than on the three-dimensional (3D) physical space. This gives the impression that quantum mechanics cannot have a 3D3\mathrm{D}3D space or space-time ontology, even in the absence of quantum measurements. In particular, this seems to affect interpretations which take the wave function as a physical entity, in particular, the many-worlds and the spontaneous collapse interpretations, and some versions of the pilot wave theory. Here, a representation of the many-particle states is given, as multilayered fields defined on the three-dimensional physical space. This representation is equivalent to the usual representation on the configuration space, but it makes it explicit that it is possible to interpret the wave functions as defined on the physical space. As long as only unitary evolution is involved, the interactions are local. I intended this representation to capture and formalize the nonexplicit and informal intuition of many working quantum physicists, who, by considering the wave function sometimes to be defined on the configuration space and sometimes on the physical space, may seem to researchers in the foundations of quantum theory as adopting an inconsistent view about its ontology. This representation does not aim to solve the measurement problem, and it allows for Schr\"odinger cats just like the usual one. But, it may help various interpretations to solve these problems, through inclusion of the wave function as (part of) their primitive ontology. In appendices, it is shown how the multilayered field representation can be extended to quantum field theory.
The status of the quantum wave function is one of the most debated issues in quantum foundations---whether it corresponds directly to the reality or just represents knowledge or information about some aspect of reality. We propose a $\ensuremath{\psi}$-ontology theorem that excludes a class of ontological explanations where the quantum wave function is treated as mere information. Our result, unlike the acclaimed Pusey-Barrett-Rudolph's theorem, does not presume the absence of holistic ontological properties for product quantum preparations. At the core of our derivation, we utilize the seminal no-go result by Bell that rules out any local realistic world view for quantum theory. We show that the observed phenomenon of quantum nonlocality cannot be incorporated in a class of $\ensuremath{\psi}$-epistemic models. Using the well-known Clauser-Horne-Shimony-Holt inequality, we obtain a threshold bound on the degree of epistemicity above which the ontological models are not compatible with quantum statistics.