We present surprising experimental evidence regarding the past of photons passing through an interferometer. The information about the positions through which the photons pass in the interferometer is retrieved from modulations of the detected signal at the vibration frequencies of mirrors the photons bounce off. From the analysis we conclude that the past of the photons is not represented by continuous trajectories, although a "common sense" analysis adopted in various welcher weg measurements, delayed-choice which-path experiments, and counterfactual communication demonstrations yields a single trajectory. The experimental results have a simple explanation in the framework of the two-state vector formalism of quantum theory.

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We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32, 050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)

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 because the photons were not there, but because the modification spoils the experiment. The weak value of the projection on A is 1. This means that the effect on any measuring device weakly coupled to the photon in A will be as if there was a single photon in A. The weak value of the projection on B is -1. It does not mean that there is -1 photon, or that the photon has some "negative probability" for being in B. It means that the effect on any measuring device weakly coupled to the photon in B is as if there is one photon in B, but which has a special property of coupling to everything with an opposite sign. The presence of the photon in A shifts the position of the light on the quad-cell detector in one direction while the presence in B equally shifts it in the opposite direction, so the net shift is zero. Salih's modification transforms our experiment to weak measurement of the sum of the projections. When the inner interferometer is tuned in such a wa...

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