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Quantum Paradoxes: To Resolve or To Acquiesce?

Ruth E. Kastner

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

At the dawn of the Quantum Age, Ervin Schrodinger presented his Cat Paradox as a reductio ad absurdum of the problem of measurement in quantum theory in its standard formulation. Not long after, Eugene Wigner accentuated the paradox by considering himself and a Friend as among the correlated systems allegedly described by quantum theory but lacking any principled account of the conclusion of a 'measurement.' This basic problem facing the standard formulation has never gone away. Instead, it has recently been brought to head by the latest, most grotesque version of the same paradox by Frauchiger and Renner. This situation entails two basic options for researchers: (1) to regard the problem of measurement as inevitable, as something to which we should acquiesce as a feature of some 'appropriate lesson' of quantum theory; or (2) to regard it as a symptom of a fundamental, but curable, problem afflicting the standard formulation of quantum theory. This talk briefly critiques option (1) and explores option (2), in concert with Paul Arden's observation that "If you can't solve a problem, it's because you're playing by the rules." It is proposed that the simplest and most elegant solution has been overlooked due to deeply seated metaphysical and cultural ground rules that are overdue for critical examination.

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At the dawn of the Quantum Age, Ervin Schrodinger presented his Cat Paradox as a reductio ad absurdum of the problem of measurement in quantum theory in its standard formulation. Not long after, Eugene Wigner accentuated the paradox by considering himself and a Friend as among the correlated systems allegedly described by quantum theory but lacking any principled account of the conclusion of a 'measurement.' This basic problem facing the standard formulation has never gone away. Instead, it has recently been brought to head by the latest, most grotesque version of the same paradox by Frauchiger and Renner. This situation entails two basic options for researchers: (1) to regard the problem of measurement as inevitable, as something to which we should acquiesce as a feature of some 'appropriate lesson' of quantum theory; or (2) to regard it as a symptom of a fundamental, but curable, problem afflicting the standard formulation of quantum theory. This talk briefly critiques option (1) and explores option (2), in concert with Paul Arden's observation that "If you can't solve a problem, it's because you're playing by the rules." It is proposed that the simplest and most elegant solution has been overlooked due to deeply seated metaphysical and cultural ground rules that are overdue for critical examination.
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.
Quantum theory in its conventional formulation is notoriously subject to various measurement-related paradoxes, as exemplified by the “Schrödinger’s Cat” and “Wigner’s Friend” thought experiments. It has been shown, for example, by Frauchiger and Renner, that nested measurements such as those occurring in the Wigner’s Friend experiment can lead to inconsistencies concerning the putative outcomes of measurements. Such inconsistencies are commonly presumed to remain private and incommensurable, but this is not the case. A counterexample, in which the inconsistencies can be revealed among the observers, is reviewed. The implications for a recent attempt to shield Relational Quantum Mechanics from such inconsistencies are considered, and it is concluded that the attempt is not successful. Further implications for the state of the debate concerning the viability of quantum theory in its various formulations are discussed.
The Frauchiger-Renner Paradox is an extension of paradoxes based on the “Problem of Measurement,” such as Schrodinger’s Cat and Wigner’s Friend. All these paradoxes stem from assuming that quantum theory has only purely unitary (linear) dynamics, and the attendant ambiguity about what counts as a ‘measurement’—i.e., the inability to account for the observation of determinate measurement outcomes from within the theory itself. It is generally forgotten that Schrodinger constructed his ‘Cat’ Paradox as a reductio ad absurdum of unitary-only quantum theory (i.e., quantum theory without a well-defined non-unitary process of collapse or reduction), and the FR paradox is an accentuation of that absurdity. This paper discusses a basic inconsistency arising in the FR scenario at a much earlier point than the derived contradiction: namely, the inconsistency inherent in treating an improper mixture (reduced density operator) as a proper, epistemic mixture. This is an illegitimate procedure that is nevertheless endemic if quantum theory is assumed to be always unitary. In contrast, under a non-unitary account of quantum state reduction yielding determinate outcomes, the use of a proper mixture for measurement results becomes legitimate, and this entire class of paradoxes cannot be mounted. The conclusion is that the real lesson of the FR paradox is that it is the unitary-only assumption that needs to be critically reassessed.
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.
The Wigner's friend paradox, like the Schrödinger's cat paradox, challenges our understanding of the foundations of quantum theory. The paradox is best illustrated by a brief scenario featuring two observers who draw different conclusions. We describe the Wigner's friend scenario as told by E. P. Wigner, and then an earlier version as told by Hugh Everett. Wigner and Everett offer different resolutions of essentially the same paradox. Decoherence theory provides a third resolution. Despite different interpretations (or their absence), these three stories fit together to form a consistent picture without a paradox.