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arXiv:1409.3478

The PBR theorem seen from the eyes of a Bohmian

Aurélien Drezet

Published Sep 11, 2014• 6 citations
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Abstract

The aim of this paper is to present an analysis of the new theorem by Pusey, Barrett and Rudolph (PBR) concerning ontic and epistemic hidden variables in quantum mechanics [Nature Phys. 8, 476 (2012)]. This is a kind of review and defense of my previous critical analysis done in the context of Bohmian mechanics. This is also the occasion for me to review some of the fundamental aspects of Bohmian theory rarely discussed in the literature. The paper is submitted for the issue PBR theorem and Beyond of IJQF (International Journal of Quantum Foundations).

DOI
10.48550/arxiv.1409.3478

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"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. Others have managed to read past the title, but are still unsure whether to credit the result with any fundamental significance. In this article, I would like to explain why I think that the PBR result is the most significant constraint on hidden variable theories that has been proved to date. It provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell's theorem. Before getting to this though, we need to understand the PBR result itself."

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Minseong Kim

Pusey-Barrett-Rudolph theorem claims that $\psi$-epistemic understanding of quantum mechanics is in trouble. Not considering whether the theorem only applies for realist understanding of quantum theory, this paper instead shows that the actual issue the theorem exposes is whether every quantum state should be interpreted as representing all sub-ensemble possibilities. For example, if $|+\rangle$ was ``measured'' at time $t=0$ where $|+\rangle = (|0\rangle + |1 \rangle)/\sqrt{2}$, should we consider this quantum state as being solely $|+\rangle$, or representing all possible sub-ensembles such as $(+,0), (+,1)$? This question suggests that PBR theorem does not rule out realist/non-realist $\psi$-epistemic theory.

•Mar 13, 2016•0 citations
The aim of this paper is to present an analysis of the new theorem by Pusey, Barrett and Rudolph (PBR) concerning ontic and epistemic hidden variables in quantum mechanics [Nature Phys. 8, 476 (2012)]. This is a kind of review and defense of my previous critical analysis done in the context of Bohmian mechanics. This is also the occasion for me to review some of the fundamental aspects of Bohmian theory rarely discussed in the literature. The paper is submitted for the issue PBR theorem and Beyond of IJQF (International Journal of Quantum Foundations).
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.
"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. Others have managed to read past the title, but are still unsure whether to credit the result with any fundamental significance. In this article, I would like to explain why I think that the PBR result is the most significant constraint on hidden variable theories that has been proved to date. It provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell's theorem. Before getting to this though, we need to understand the PBR result itself."
Pusey-Barrett-Rudolph theorem claims that ψ\psiψ-epistemic understanding of quantum mechanics is in trouble. Not considering whether the theorem only applies for realist understanding of quantum theory, this paper instead shows that the actual issue the theorem exposes is whether every quantum state should be interpreted as representing all sub-ensemble possibilities. For example, if ∣+⟩|+\rangle∣+⟩ was ``measured'' at time t=0t=0t=0 where ∣+⟩=(∣0⟩+∣1⟩)/2|+\rangle = (|0\rangle + |1 \rangle)/\sqrt{2}∣+⟩=(∣0⟩+∣1⟩)/2​, should we consider this quantum state as being solely ∣+⟩|+\rangle∣+⟩, or representing all possible sub-ensembles such as (+,0),(+,1)(+,0), (+,1)(+,0),(+,1)? This question suggests that PBR theorem does not rule out realist/non-realist ψ\psiψ-epistemic theory.