Decoherent Histories Approach Might be Predictive even when the Decoherence Condition Does Not Hold

Abstract

The decoherent (or consistent) histories approach is applied to the arrival time problem. Since the decoherence condition does not hold for arrival time, a probability distribution of arrival times cannot be defined. Instead, a quasidistribution, which is not positive definite, can be defined in the histories approach. It is shown that well‐known Kijowski's distribution, which is positive definite and often claimed to be the correct distribution of arrival times, is obtained from the quasidistribution when the momentum wave function has certain properties. This suggests that the histories approach still holds some predictive power even when the decoherence condition does not hold.