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A good demonstration of the delayed-choice experiment is given by a two-path interferometer, the Mach-Zehnder interferometer (MZI). Our discussion is restricted to the case where a single photon is directed to the MZI followed by two detectors. According to the traditional perspective, the nature of the single photon inside the MZI depends on whether or not the second BS is in place. If the second BS is absent, the single photon then travels along just one arm, showing the particle nature.
On the contrary, when the researchers inserted the second BS, the single photon traveled along both arms, exhibiting the wave nature. However, in the REIN (REalistic INterpretation, as opposed to Copenhagen or pilot-wave interpretation), the first BS splits the single photon into two sub-waves traveling along the two arms, whether the second BS is inserted or not. That is, the photon in an MZI is an extended and separated object that exists simultaneously at both arms. In this interpretation, if the second BS is absent, the two sub-waves are directed, respectively, to the two detectors, and with a probability independent of their relative phase, the measurement collapses them into a click in one detector. This is the particle nature of the single photon.