Past of a quantum particle: Common sense prevails

Abstract

We analyze Vaidman's three-path interferometer with weak path marking [Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, "the particle's path" has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.

Reply to “Comment on ‘Past of a quantum particle revisited’ ”

“…1, for a particle detected at exit iii, a variant of Fig. 2 in [2]. The thickness of the blue lines is proportional to the squared amplitudes of the forward wave function, and likewise for the red lines and the backward wave function.…”

“…Upon this observation, we then proceed with the accounting exercise in Sec. IV B of [2] that culminates in the conclusion that all particles reach exit iii through checkpoint C when → 0.…”

“…In their Comment [1] on Ref. [2], Peleg and Vaidman correctly state that there is a fundamental difference in the way Vaidman answers the question Where was the particle after entering and before leaving the interferometer? and our traditional approach.…”

“…( = 0 in [2]), or to the conditioning on the inconclusive outcome of the unambiguous path discrimination. We observe that the wave function branches associated with the checkpoints A and B inside the inner loop, whether blue or red, do not connect the source S to exit iii.…”

“…Despite being told otherwise, we did examine the traces of a single particle in Ref. [2] and found that all particles in the pre-and postselected ensemble went only through checkpoint C in the limit of ultrafaint traces ( → 0). This is exactly what standard quantum mechanics tells us (see above).…”