NONLOCAL MOMENTUM-TRANSFER IN WELCHER WEG MEASUREMENTS

A ''which-path'' (welcher Weg) measurement necessarily destroys the fr inges in a double-slit interference experiment. We show that in all in stances one may attribute this destruction to a disturbance of the par ticle's momentum by an amount equal to at least pi h/2d, where d is th e slit separation, in accordance with the uncertainty principle. Howev er, this momentum transfer need not be local; that is, it need not act at either of the slits through which the particle passes. For well-kn own welcher Weg measurements such as Einstein's recoiling slit and Fey nman's light microscope, the disturbance can be understood in terms of random classical momentum kicks that act locally. In some recent prop osals, including that by Scully, Englert, and Walther [Nature (London) 351, 111 (1991)], the momentum transfer is of a peculiarly quantum, n onlocal nature. In this paper we introduce a formalism based on the Wi gner function, as this describes both the local and nonlocal momentum transfer caused by any welcher Weg measurement. We show that for some examples, such as that of Scully, Englert, and Walther, there is no mo mentum disturbance at the slits even though the nonlocal momentum dist urbance is sufficient to destroy the interference pattern. Finally, we discuss the experimental signatures of nonlocal versus local momentum transfer and demonstrate a strong similarity to the nonlocality of th e Aharonov-Bohm effect.