We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability distribution arises from the Born rule and which has a clear physical interpretation. The same procedure can be employed to measure the "time at which some event happens" for arbitrary events (and not just specifically for the arrival time of a particle).

arXiv:1810.12869Physical Review LettersMar 16, 202057 citations

arXiv:quant-ph/0003130 · Journal of Physics A Mathematical and General

Temporal ordering in quantum mechanics

Jonathan Oppenheim, B Reznik, W G Unruh

Published Aug 20, 2002• 5 citations

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Abstract

DOI: 10.1088/0305-4470/35/35/308

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{E}_{k}

is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.