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This comes from the Interference of Photons section in the book The Principles of Quantum Mechanics by P Dirac:

We shall discuss the description which quantum mechanics provides of the interference. Suppose we have a beam of light which is passed through some kind of interferometer, so that it gets split up into two components and the two components are subsequently made to interfere. We may, as in the preceding section, take an incident beam consisting of only a single photon and inquire what will happen to it as it goes through the apparatus. This will present to us the difficulty of the conflict between the wave and corpuscular theories of light in an acute form.

Corresponding to the description that he had in the case of the polarization, we must now describe the photon as going partly into each of the two components into which the incident beam is split. The photon is then, as we may say, in a translational state given by the superposition of the two translational states associated with the two components. We are thus lead to a generalization of the term "translational state" applied to a photon. For a photon to be in a definite translational state it need not be associated with one single beam of light, but may be associated with two or more beams of light which are the components into which one original beam has been split. In the accurate mathematical theory each translational state is associated with one of the wave functions of ordinary wave optics, which wave function may describe either a single beam or two or more beams into which one original beam has been split. Translational states are thus superposable in a similar way to wave functions.

  1. Is this the view held by leading physicists today?

  2. Can we really talk of the incident and exiting photon in the beam splitter being the same photon?

  3. Is Dirac saying that the photon is partly in the two split beams, but no where else in space?

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Let me begin by saying that I hope there are multiple answers to this because it's a question that forces one to make some judgement calls, and I think other peoples' opinions would be valuable. Here's my take:

Whenever reading an old text like this, especially on quantum mechanics, I think it's important to take the language of the text with a grain of semantic salt, and this affects the answers to your questions:

  1. I think I understand quantum mechanics (with some conceptual exceptions), and when I read this description, I thought it was pretty decent. I speculate that most physicists who understand quantum mechanics would probably read this description and agree. In my view, one issue with Dirac's description is that that someone just learning the subject might read the following statement and get the wrong idea:

    we must now describe the photon as going partly into each of the two components into which the incident beam is split

    because it, at least in my opinion, might lead such a person to believe that the photon is somehow in two places at once. I would instead probably describe the situation using probabilities to emphasize that stating where the photon is at any given time is not meaningful in quantum, but stating what the probability is that one will find it in a particular location after measurement is meaningful.

  2. I would characterize such questions as being of a philosophical as opposed to physical nature in the realm of quantum mechanics. In classical mechanics, particles are modeled to move along well-defined trajectories in space, so we can keep track of where particles are and whether one particle is the same or different from another. But since this is not possible in the context of quantum mechanics, I am not aware of a reasonable operational definition of "sameness" that would allow one to claim that the outgoing measured photon is the same as the ingoing measured photon.

  3. No. It's unclear to me what it would even mean in this context to say that a single photon is "in a beam." A photon is fired, and there are certain probabilities that if one were to measure the position of the photon, then one would find it at a specified location in space.

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