Subjective probability and quantum certainty

TL;DR

This paper explores the concept of certainty in quantum mechanics within a Bayesian framework, emphasizing that quantum certainty is subjective and dependent on an agent’s prior beliefs, contrasting with interpretations that treat certainty as an objective property.

Contribution

It demonstrates how quantum certainty, derived from pure states, depends on an agent’s prior beliefs, challenging interpretations that treat certainty as an objective, preexisting property.

Findings

Quantum states depend on the agent's prior beliefs.

Probability-1 predictions are subjective, not objective.

Certainty implies a subjective belief rather than an intrinsic property.

Abstract

In the Bayesian approach to quantum mechanics, probabilities--and thus quantum states--represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent's prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent's prior beliefs. Quantum certainty is therefore always some agent's certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [A. Stairs, Phil. Sci. 50, 578 (1983)], which applies the Kochen-Specker theorem to an entangled bipartite system.