Path detection and the uncertainty principle

Abstract

QUANTUM mechanics predicts that any detector capable of determining the path taken by a particle through a double slit will destroy the interference. This follows from the principle of complementarity formulated by Niels Bohr: simultaneous observation of wave and particle behaviour is prohibited. But such a description makes no reference to the physical mechanism by which the interference is lost. In the best studied welcher Weg (‘which path’) detection schemes^1,2, interference is lost by the transfer of momentum to the particle whose path is being determined, the extent of momentum transfer satisfying the position–momentum uncertainty relation. This has prompted the question as to whether complementarity is always enforced in welcher Weg schemes by momentum transfer. Scully et al³. have recently responded in the negative, suggesting that complementarity must be accepted as an independent component of quantum mechanics, rather than as simply a consequence of the uncertainty principle. But we show here that, in any path detection scheme involving a fixed double slit, the amount of momentum transferred to the particle by a perfectly efficient detector (one capable of resolving the path unambiguously) is related to the slit separation in accordance with the uncertainty principle. If less momentum than this is transferred, interference is not completely destroyed and the path detector cannot be perfectly efficient.