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arXiv:1706.01819

On the Reality of the Wavefunction

Omid Charrakh

Published Jun 5, 2017• 1 citation
arXivHTMLPDF

Abstract

Within the Ontological Models Framework (OMF), Pusey, Barrett, and Rudolph (PBR) have given an argument by which they claimed that the epistemic view on the wavefunction should be ruled out. This study highlights an incorrect conclusion in PBR's arguments, which was made due to inadequacies in the definitions of OMF. To be precise, OMF models the ontology of the preparation procedure, but it does not model the ontology of the measurement device. Such an asymmetric treatment becomes problematic, in scenarios in which measurement devices have a quantum nature. Modifying the OMF's definition such that the ontology of the measurement device becomes included, we will see how PBR's result disappears.

DOI
10.48550/arxiv.1706.01819

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Within the Ontological Models Framework (OMF), Pusey, Barrett, and Rudolph (PBR) have given an argument by which they claimed that the epistemic view on the wavefunction should be ruled out. This study highlights an incorrect conclusion in PBR's arguments, which was made due to inadequacies in the definitions of OMF. To be precise, OMF models the ontology of the preparation procedure, but it does not model the ontology of the measurement device. Such an asymmetric treatment becomes problematic, in scenarios in which measurement devices have a quantum nature. Modifying the OMF's definition such that the ontology of the measurement device becomes included, we will see how PBR's result disappears.
Harrigan and Spekkens give formal definitions for the wavefunction in quantum mechanics to be ψ\psiψ-ontic or ψ\psiψ-epistemic, such that the wavefunction can only be one or the other. We argue that 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 need to be rethought in the light of our analysis.
The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out $\ensuremath{\psi}$-epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an assumption of preparation independence, the validity of which has been subject to debate. We propose two plausible and less restrictive alternatives: a weaker notion allowing for classical correlations, and an even weaker, physically motivated notion of independence, which merely prohibits the possibility of superluminal causal influences in the preparation process. The latter is a minimal requirement for enabling a reasonable treatment of subsystems in any theory. It is demonstrated by means of an explicit $\ensuremath{\psi}$-epistemic ontological model that the argument of PBR becomes invalid under the alternative notions of independence. As an intermediate step, we recover a result which is valid in the presence of classical correlations. Finally, we obtain a theorem which holds under the minimal requirement, approximating the result of PBR. For this, we consider experiments involving randomly sampled preparations and derive bounds on the degree of $\ensuremath{\psi}$ epistemicity that is consistent with the quantum-mechanical predictions. The approximation is exact in the limit as the sample space of preparations becomes infinite.
The Pusey-Barrett-Rudolph (PBR) theorem establishes ψψψ-onticity for individual quantum systems, but its standard formulation relies on the Preparation Independence Postulate (PIP). This has led to a prevalent view that rejecting PIP leaves open the possibility of ψψψ-epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes ψψψ-onticity for composite systems prepared in product states, the ψψψ-onticity of the individual subsystems follows directly from the tensor-product structure of quantum mechanics, without invoking PIP or any further auxiliary assumptions. This result removes a key auxiliary assumption from the PBR theorem, closes a persistent loophole for preserving ψψψ-epistemic models, and strengthens the conceptual foundations of ψψψ-ontology.
In this paper we consider time as a property of a preparation or a quantum system and investigate whether it is an epistemic property according to Harrigan and Spekkens’ criterion [Found Phys 40, 125–157 (2010)]. To be precise, using a tabletop setup where the predictions of quantum mechanics and general relativity can be combined, we prepare a quantum state such that it is a quantum superposition of the different durations ticked by a quantum mechanical clock moving in spacetime. Such a preparation provides a quantum system that includes time as an intrinsic property. Indeed, changing the weights in the superposition changes the time as an expectation value as well as the possible different clock readings and histories. With a proof similar to the Pusey-Barrett-Rudolph (PBR) theorem [Nature Phys 8, 475–478 (2012)], it is shown that time in quantum theory is not an epistemic notion, but has ontological reality. In fact, the PBR theorem implies an ontic notion of time. Indeed, by proving that the quantum state is a physical property, the PBR theorem requires quantum state reduction to be a physical process. In this case, quantum probabilities are intrinsic probabilities without epistemic origin, and they generate a genuinely new sequence of events. This novelty introduced by quantum probabilities can be interpreted as time. However, although the PBR theorem implies this result, it does not prove it. First, an additional assumption is required to ensure the intrinsic character of quantum probabilities. Second, the PBR theorem is not constructed to prove that time is ontic, but to prove that ψ is ontic. All these issues are discussed in detail in the paper.