Objective and Subjective Probabilities in Quantum Mechanics

TL;DR

This paper explores the distinct roles of objective and subjective probabilities in quantum mechanics, emphasizing their conceptual and numerical differences and clarifying their separate applicability.

Contribution

It clarifies the conceptual and numerical distinctions between objective and subjective probabilities in quantum mechanics, highlighting their separate domains of relevance.

Findings

Objective and subjective probabilities differ conceptually and numerically.

Some quantum probabilities lack meaningful subjective interpretations.

Certain subjective probabilities cannot be represented as quantum probabilities.

Abstract

The concept of probability was prominent in the original foundations of quantum mechanics, and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I argue that, although both objective and subjective probabilities have domains of relevance in QM, their roles are quite distinct. Even where both are legitimate, the objective and subjective probabilities differ, both conceptually and numerically. There are quantum probabilities that have no useful subjective interpretations, and there are subjective probabilities that cannot be realized as quantum probabilities.