Quantum 2025 – scientific programme

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FRI: Friday Contributed Sessions

FRI 10: Foundational / Mathematical Aspects – Unconventional Approaches

FRI 10.3: Talk

Friday, September 12, 2025, 11:15–11:30, ZHG103

A heuristic solution to the time of arrival problem via mathematical probability theory — •Maik Reddiger — Anhalt University of Applied Sciences

There does currently not exist any scientific consensus on how to predict the probability that a single quantum particle impinges on an ideal detector in a given interval of time. The apparent simplicity of the problem is overshadowed by the deep conceptual discrepancies, which are exposed by the multitude of solutions proposed so far. Ab initio approaches need to model the ideal detector in such a manner, that it is compatible with quantum dynamics. A corresponding boundary condition for the Schrödinger equation was suggested by Werner in the 1980s, yet there is reason to question the physical validity of this detector model. In this talk I present an approach via mathematical probability theory and a physically natural adaption of the Madelung equations, which assures that the detector is perfectly absorbing. The presented solution is heuristic in the sense that a full solution would require a well-posedness result for the Cauchy problem of the corresponding system of PDEs for sufficiently regular initial data.

This solution of the time of arrival problem is obtained within the more general framework of geometric quantum theory. Geometric quantum theory is a novel adaption of quantum mechanics, which makes the latter consistent with mathematical probability theory.

Keywords: Time of arrival; Time of flight; Time operator; Quantum measurement; Quantum potential