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arXiv:2103.11530

Defending Quantum Objectivity

Elias Okon

Published Mar 22, 2021• 0 citations
arXivHTMLPDF

Abstract

A recent argument, attributed to Masanes, is claimed to show that the assumption that quantum measurements have definite, objective outcomes, is incompatible with quantum predictions. In this work, a detailed examination of the argument shows that it has a much narrower field of application than previously recognized. In particular, it is found: i) that the argument only applies to hidden-variable models with a particular feature; and ii) that such a feature is not present in most hidden-variable models, including pilot-wave theory. It is concluded that the argument does not succeed in calling into question the objectivity of quantum measurements.

DOI
10.48550/arxiv.2103.11530

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A recent argument, attributed to Masanes, is claimed to show that the assumption that quantum measurements have definite, objective outcomes, is incompatible with quantum predictions. In this work, a detailed examination of the argument shows that it has a much narrower field of application than previously recognized. In particular, it is found: i) that the argument only applies to hidden-variable models with a particular feature; and ii) that such a feature is not present in most hidden-variable models, including pilot-wave theory. It is concluded that the argument does not succeed in calling into question the objectivity of quantum measurements.
Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum predictions. From this, it is concluded that the results of measurements cannot be thought of as being actual or objective. Here, I show that these arguments depend upon a mistaken assumption, regarding the ("mixed") correlations between the results of the friends and those of "the Wigners", which leads to invalid predictions. It is not, then, that the assumption of definite outcomes leads to trouble, but that the results derived with such an assumption are contrasted with faulty predictions. Next, I explore the more famous no-go theorems by Frauchiger and Renner and by Brukner, on which these recent arguments are motivated. Regarding the first, I show that, although it is cast in a different form, it also rests on the mistaken assumption regarding "mixed" correlations--rendering it invalid. Regarding Brukner's theorem, I point out that it depends on the quite unattractive assumption of locality, a fact that fully diminishes its force. Throughout, I illustrate my claims with explicit calculations within pilot-wave theory.
Abstract Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. This essay restates and analyzes these arguments. The import of the first two is diminished by their dependence on assumptions about the outcomes of counterfactual measurements. But the third argument establishes its intended conclusion. Even if every well-conducted quantum measurement one ever makes will have a definite physical outcome, this argument should make them reconsider the objectivity of that outcome.
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual compatibility of apparently reasonable classical assumptions. We analyze a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (the assertion that quantum systems are, at any moment, either particles or waves, but not both). These three ideas are incompatible with any theory, not only with quantum mechanics.
Abstract In chapter 12 we give an overview of the historical development of hidden-variable theories aiming to attribute ‘hidden’ definite outcomes to any potential measurement on a quantum system. We start with a discussion of von Neumann’s assumption on hidden-variable models, which was later realized not to hold by Hermann, Kochen, Specker, and Bell, going into detail on Bell’s refutation of von Neumann’s arguments. We then turn to the notion of contextuality, which severely restricts hidden-variable models: we discuss Gleason’s theorem before stating and proving the famous Kochen-Specker theorem, as well as the simpler versions of Peres’ nonet and Mermin’s pentagram. These results show that quantum mechanics is not compatible with the assignment of definite measurement outcomes to all possible measurements, and such assignments can hence only be made once a restricted set of observables, a context, is selected
I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it. Instead, the theory offers reliable advice on when to expect an event of one kind or another, and on how strongly to expect each possible outcome of that event. The actual outcome is a perspectival fact: a fact relative to a physical context of assessment. Measurement outcomes and quantum states are both perspectival. By noticing that each must be relativized to an appropriate physical context one can resolve the measurement problem and the problem of nonlocal action. But if the outcome of a quantum measurement is not an absolute fact, then why shoud the statistics of such outcomes give us any objective reason to accept quantum theory? One can describe extensions of the scenario of Wigner's friend in which a statement expressing the outcome of a quantum measurement would be true relative to one such context but not relative to another. However, physical conditions in our world prevent us from realizing such scenarios. Since the outcome of every actual quantum measurement is certified at what is essentially a single context of assessment, the outcome relative to that context is an objective fact in the only sense that matters for science. We should accept quantum theory because the statistics these outcomes display are just those it leads us to expect.