Talk (Work in Progress): April Zhang (Oxford)

Title:

“Deriving a ‘Tends To’ from a ‘Does’”[1]: A Fresh Look at Born Rule Derivations in Quantum Mechanics

Abstract:

In quantum theory, the emergence of probability is one of the most notorious problems, lying at the heart of the measurement problem. My work examines the origin of probabilistic measurement outcomes—the Born Rule, historically postulated as a pillar of quantum mechanics. By comparing various derivations of the Born Rule, especially the additional nonprobabilistic assumptions they require beyond the unitary quantum framework, I will analyze the necessary and sufficient assumptions under which this foundational rule can emerge. In this talk, I will focus on two important results that remain less familiar outside specialized research fields: Gleason’s Theorem and the Deutsch-Wallace Theorem. I will also briefly review other proofs and analyze how the strength of classicality in the assumptions can affect the validity of the derivations.

[1] This quotation is from D. Deutsch, “Quantum theory of probability and decisions,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 455, no. 1988, pp. 3129–3137, Aug. 1999, doi: https://doi.org/10.1098/rspa.1999.0443.