The wavefunction as a true ensemble

Abstract

In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised 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 $\psi$-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local $\psi$-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.

arXiv comment10 pages, 3 figures; accepted in Proceedings of the Royal Society A, matches accepted version

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• A Toy Model for Local and Deterministic Wave-function Collapse
• Experimental Tests of Invariant Set Theory
• Taxonomy for Physics Beyond Quantum Mechanics
• A Solvable Model of a Nonlinear extension of Quantum Mechanics
• Comment on "Experimentally adjudicating between different causal accounts of Bell-inequality violations via statistical model selection"
• Information versus Physicality: On the Nature of the Wavefunctions of Quantum Mechanics
• A Future-Input Dependent Path Integral for Quantum Mechanics
• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
• Quantum theories with local information flow
• What does it take to solve the measurement problem?
• The Quantum Eraser Paradox
• Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications