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arXiv:1406.3963 · Physical Review Letters

Determinism, Independence, and Objectivity are Incompatible

Radu Ionicioiu, Robert B. Mann, Daniel R. Terno

Published Feb 13, 2015• 9 citations
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Abstract

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.

DOI
10.1103/physrevlett.114.060405

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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.
Wave-particle duality has become one of the flagships of quantum mechanics. This counterintuitive concept is highlighted in a delayed-choice experiment, where the experimental setup that reveals either the particle or wave nature of a quantum system is decided after the system has entered the apparatus. Here we consider delayed-choice experiments from the perspective of device-independent causal models and show their equivalence to a prepare-and-measure scenario. Within this framework, we consider Wheeler's original proposal and its variant using a quantum control and show that a simple classical causal model is capable of reproducing the quantum mechanical predictions. Nonetheless, among other results, we show that, in a slight variant of Wheeler's gedanken experiment, a photon in an interferometer can indeed generate statistics incompatible with any nonretrocausal hidden variable model, whose dimensionality is the same as that of the quantum system it is supposed to mimic. Our proposal tolerates arbitrary losses and inefficiencies, making it specially suited to loophole-free experimental implementations.
Wheeler's delayed-choice experiment investigates the indeterminacy of wave-particle duality and the role played by the measurement apparatus in quantum theory. Due to the inconsistency with classical physics, it has been generally believed that it is not possible to reproduce the delayed-choice experiment using a hidden-variable theory. Recently, it was shown that Wheeler's delayed-choice experiment can be explained by a causal two-dimensional hidden-variable theory [R. Chaves, G. B. Lemos, and J. Pienaar, Phys. Rev. Lett. 120, 190401 (2018)]. Here, we carry out a delayed-choice experiment by using photon states that are spacelike separated and demonstrate that the experiment is consistent with quantum theory but inconsistent with any causal two-dimensional hidden-variable theory in a device-independent manner. This demonstrates that causality can be used to test quantum theory in a complementary way to the Bell and Leggett-Garg tests.
In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur-Vaidman bomb detector and the extended Wigner's friends scenario.
In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur–Vaidman bomb detector and the extended Wigner’s friends scenario.
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.
An interpretation of quantum mechanics is presented in which there is one hidden variable. While this number of hidden variables is insufficient to explain Bell nonlocality, it can help solve the measurement problem. It also provides an explanation of the delayed choice quantum eraser experiment that is more intuitive than current explanations. In addition, a theory of nonlocality emerges directly from its assumptions. The key idea is that from the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micro-measurements” and as a projection onto some basis of measurement. One particle can “measure” another. Thus, particles will have a defined value on one measurement basis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective uncertainty, at other times a subjective uncertainty and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, while for an “observer” inside the system, only the objective part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.