Measurement of Time-of-Arrival in Quantum Mechanics

Y. Aharonov, J. Oppenheim, S. Popescu, B. Reznik, W. G. Unruh

Published 1997-09-14, updated 1998-01-29Version 3

It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta t_A \sim 1/E_k$, where $E_k$ 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.