On the spin dependence of detection times and the nonmeasurability of arrival times

According to a well-known principle of quantum physics, the statistics of the outcomes of any quantum experiment are governed by a Positive-Operator-Valued Measure (POVM). In particular, for experiments designed to measure a specific physical quantity, like the time of a particle's first arrival at a surface, this principle establishes that if the probability distribution of that quantity does not arise from a POVM, no such experiment exists. Such is the case with the arrival time distributions proposed by Das and Dürr, due to the nature of their spin dependence.