The Statistical Interpretation of Quantum Mechanics

TLDR

Quantum theory is often interpreted as describing individual systems, but arguments favor treating the quantum state as an ensemble description, and many measurement problems arise from insisting on the individual-system interpretation. The paper proposes the Statistical Interpretation to provide a sound, assumption‑minimizing understanding of quantum theory. It formulates quantum theory by treating the quantum state as an ensemble description, thereby avoiding additional assumptions. Hidden variables can reproduce quantum predictions, but Bell’s theorem forces any such theory that matches all quantum mechanics to exhibit pathological nonlocality for spatially separated systems.

Abstract

The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems.