The wavefunction as a true ensemble

TL;DR

This paper explores the interpretation of the quantum wavefunction as a true ensemble of hidden-variable states, analyzing its implications and consistency with known theorems and experiments, and relating it to superdeterministic theories.

Contribution

It proposes a new definition of ensemble interpretations, shows local ψ-ensemble theories violate Statistical Independence, and connects these ideas to quantum phenomena like delayed choice and Wigner's Friend.

Findings

Local ψ-ensemble interpretations violate Statistical Independence.

Superdeterministic or retrocausal theories are necessary for certain ensemble interpretations.

This interpretation clarifies puzzling quantum phenomena such as delayed choice experiments.

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.