On Formalisms and Interpretations

TL;DR

This paper clarifies the distinction between formalism and interpretation in quantum theory, identifying two inequivalent formalisms and proposing a new probability rule for the relative-state formalism, with implications for Wigner's-friend experiments.

Contribution

It distinguishes two quantum formalisms and introduces a new probability rule for the relative-state formalism, highlighting potential experimental differences.

Findings

Identifies two inequivalent quantum formalisms: relative-state and standard.

Proposes a new probability rule for the relative-state formalism.

Discusses the potential for Wigner's-friend experiments to differentiate these formalisms.

Abstract

One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism versus interpretation. In this note, we make a clear distinction between them and show that there are actually two inequivalent quantum formalisms, namely the relative-state formalism and the standard formalism with the Born and measurement-update rules. We further propose a different probability rule for the relative-state formalism and discuss how Wigner's-friend-type experiments could show the inequivalence with the standard formalism. The feasibility in principle of such experiments, however, remains an open question.