Response: Commentary: “Asking photons where they have been” - without telling them what to say

Citation: Danan A, Farfurnik D, Bar-Ad S and Vaidman L (2015) Response: Commentary: " Asking photons where they have been "-without telling them what to say. A commentary on Commentary: " Asking photons where they have been "-without telling them what to say In a recent Commentary, Salih [1] claims that we " devised an elegant experiment investigating the past of photons inside two Mach-Zehnder interferometers, one inside the other-yet drew the wrong conclusions [2]. " He also argues that the story told by the two-state vector formalism (TSVF) that we advocate, is contradictory. Here we answer Salih's criticism. Salih considers three possible options for the past of photons in our experiment and argues that option (1) according to which the photons are present in paths A and B simultaneously, is ruled out. To support his claim he notices that the product of projections on A and on B vanishes. However, for pre-and post-selected systems, as the photons in our experiment, the product rule does not hold [3], and therefore, his argument fails. The photon was in A and in B because it left traces in both places and this is the criterion of the past of the particle we rely on Vaidman [4]. An unavoidable non-vanishing interaction with the environment leads to a " weak measurement " of the presence of the photon in various places inside the interferometer exhibiting " weak-measurement elements of reality " [5]. Our claim, indeed, looks paradoxical. Even if the photon left very small traces in both places, there is a nonvanishing probability that the traces will be identified with certainty. In this case a single photon will be found in two places simultaneously. This is a contradiction: a single photon cannot be detected simultaneously in two places even in a non-demolition measurement. The resolution of the paradox is that the traces in A and in B are entangled and simultaneous detection of the photon in two places cannot happen. The photon changes the reduced density matrix in A and, also, the reduced density matrix in B, but, if this change is detected in A, then the reduced density matrix in B becomes identical to the undisturbed density matrix there, and vice versa. Salih considers a modification of our experiment in which, as he correctly states, we will not observe the presence of the photons in A and in B. However, it is not …