Arrival times in quantum theory from an irreversible detector model

Abstract

We investigate a detector scheme designed to measure the arrival of a particle at x = 0 during a finite time interval. The detector consists of a two-state system that undergoes a transition from one state to the other when the particle crosses x = 0, and possesses the realistic feature that it is effectively irreversible as a result of being coupled to a large environment. The probabilities for crossing or not crossing x = 0 thereby derived coincide with earlier phenomenologically proposed expressions involving a complex potential. The probabilities are compared with similar previously proposed expressions involving sums over paths, and a connection with time operator approaches is also indicated.