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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 12: Foundations of Classical and Quantum Mechanics

AGPhil 12.1: Talk

Friday, March 14, 2025, 14:00–14:30, HS XVII

On the applicability of Kolmogorov’s theory of probability to the description of quantum phenomena — •Maik Reddiger — Anhalt University of Applied Sciences, Köthen (Anhalt), Germany

Through his axiomatization of quantum mechanics (QM), von Neumann laid the foundations of a "quantum probability theory." In the literature this is commonly regarded as a non-commutative generalization of the "classical probability theory" established by Kolmogorov. Outside of quantum physics, however, Kolmogorov’s axioms enjoy universal applicability. One may therefore ask whether quantum physics indeed requires such a generalization of our conception of probability or if von Neumann’s axiomatization of QM was contingent on the absence of a general theory of probability in the 1920s.

Taking the latter view, I motivate an approach to the foundations of non-relativistic quantum theory that is based on Kolmogorov’s axioms. It relies on the Born rule for particle position probability and employs Madelung’s reformulation of the Schrödinger equation for the introduction of physically natural random variables. While an acceptable mathematical theory of Madelung’s equations remains to be developed, one may nonetheless formulate a mathematically rigorous “hybrid theory”, which is empirically almost equivalent to the quantum-mechanical Schrödinger theory. A major advantage of this approach is its conceptual coherence, in particular with regards to the question of measurement.

This talk is based on arXiv:2405.05710 [quant-ph] and Reddiger, Found. Phys. 47, 1317 (2017).

Keywords: Quantum probability theory; Quantum potential; Measurement problem; Geometric quantum theory; Stochastic mechanics