English: Counterfactual measurement in quantum mechanics. A Mach-Zehnder interferometer is adjusted so that 100% of the output impinges upon detector B. Having been adjusted in such a manner, 100% of the light will continue to reach B even if the the light intensity is reduced so that only one photon at a time travels through the apparatus. It appears as if the wave function of each individual photon travels both paths and engages in interference at the last beam splitter, so that only the wave to B is constructive. In figure (a), although the photon is illustrated as having taken the "northern" branch of the interferometer, it interferes with itself so that only detector B detects the photon. The same holds for figure (b), although the photon is considered to have taken the "southern" branch of the interferometer.

Figure (c) illustrates the situation where an obstacle has been introduced on the "southern" branch of the interferometer. 50% of the photons are deflected by mirror M, and the remaining photons are split 25% to detector A, and 25% to detector B.

Figure (d) illustrates the fundamental paradox raised by this demonstration. An individual photon arriving at detector A must have traversed the "northern" path and could not have interacted with mirror M. The arrival of a photon at detector A constitutes proof that an obstacle exists on the "southern" path, but no exchange of energy has taken place between the photon and obstacle M. How could the photon possibly have acquired information about M without an exchange of energy?