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Since light is quantized into photons, how can a single rare photon entering one side of a large, [say, 100 meter wide], interferometer from a very dim star, a phton which is only in the interfereometer for a microsecond or so, possibly "interfere" with anything which has entered the other side of the interferometer at exactly the same instant?? Does the photon, arriving still in its wave-packet form, simply interfere with itself? That would imply that the quantized wave-packet, unlike the sub-microscopic photon particle which finally "collapses" and is recorded on the CCD camera, must be at least as wide as the interferometer's separated telescopic inputs, if not, indeed, as wide as the boundary of the entire sphere of the universe surrounding the wave's source at the same distance as the interferometer; something which certainly strikes me as preposterous!! So, how then IS such interference, and therewith, the vastly improved angular resolution of even very dim sources, whose photons may arrive only occasionally over time, actually possible??

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  • $\begingroup$ Single photon interferometric experiments are a thing (indeed, people had to learn how to do those before they could do all the spiffy delayed choice experiments and Bell's inequality experiments that drive discussions of entanglement). Townsend's QM book has a bunch of references in the first few chapters but my copy is in another state. $\endgroup$ Mar 22, 2019 at 17:03
  • $\begingroup$ For less ambiguous cases of single-particle self-interference, you might read some of the literature about neutron interferometers. The neutron beams that feed interferometers tend to quite low-intensity, and in a long experiment where very many neutrons build up an interference pattern, it may well be that the expected number of times there were ever two different neutrons present in the interferometer at the same time was less than once. $\endgroup$
    – rob
    Mar 22, 2019 at 22:34
  • $\begingroup$ Thanks so much for your help on this matter. I will try to pick up a copy of Townsend's book and also read up on neutron interferometers. The problem of two wave packets arriving at the same time turns out to be a bit of a red herring since the wave packet IS capable of interfeing with itself. But that still leaves the great mystery, at least to me, of just how a single tiny photon wave-packet can still be discerable over hundreds of meters in the optical and hundreds of thousands of kms. in the radio spectrum enough to cause an interference pattern. $\endgroup$
    – Wd Fusroy
    Mar 25, 2019 at 15:22

2 Answers 2

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Your intuition is right: each photon wavepacket is spread out all over the place -- even much wider than the telescooe's aperture. The photon interferes with itself. A search for articles relating to "single- photon interference" will help.

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  • $\begingroup$ That is very helpful, but it still doesn't really put my mind at rest since even if the pohton wave packet enters both sides of the interferometer at once and then only collapses as a particle onto the CCD array a microsecond later, there still remains the problem you gloss with your claim that the "photon wavepacket is spread out all over the place -- -- even much wider than the telescooe's aperture." But just HOW wide is it spread? It seems to me that a single photon wave packet could hardly still be robust enough to interact with itself over say thousands of kms, as in radio interfer.s.. $\endgroup$
    – Wd Fusroy
    Mar 25, 2019 at 15:01
  • $\begingroup$ By the way, if one checks to see which side of the interferometer the photon entered does the interference pattern simply disappear as in the double-slit experiment. I assume it must. Also, why is the angular resolution increased through the interference process? Imagine a large aperture telescope with a mask over all of it but for four small 2" circles equally spaced on each side of the tube. Now if one views through the scope when so masked the resolution should be as good as if one viewed through the whole scope unmasked. But how is such an amazing thing possible? $\endgroup$
    – Wd Fusroy
    Mar 25, 2019 at 15:08
  • $\begingroup$ The wave packet amplitude of a photon is indeed extremely small by the time it reaches a telescope from a star billions of light years away. However, the squared amplitude represents probability (density) of interaction or detection. Fire one photon from the star, calculate the amplitude of the wave function at a detector, square the amplitude, integrate over the area of the detector, and that gives the likelihood that the photon will be detected by that detector. The likelihood is extremely small, so it takes a long time to form an image of a distant object. $\endgroup$
    – S. McGrew
    Mar 25, 2019 at 15:15
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Yes, as you write, a single photon can interfere with itself.

The wavefunction discribes the probability distribution of the photon's spatial position (and other characteristics) for all of space.

Now in your case the photon is with a high probability to be found at a certain side of the interferometer, let's say that that would be the point where the photon as particle would interact with the metal lattice of the antenna, and be absorbed by an atom inside the lattice.

Now it is a misconception to think that the photon was traveling in a straight (spatial 3D) path to that point of interaction from the source. The photon in reality is traveling as a wave, and its spatial position's distribution is described by the wavefunction for all of space.

Now in your case the wavefunction would give you a high probability for the photon to be found close to that point on one side of the interferometer. But the probability to find the photon on the other side of the interferometer is not 0. Actually it is not 0 anywhere in space. The photon is spread out in space (as the other answer suggests) everywhere, with different probabilities.

As the photon travels as a wave and reaches the interferometer, the partial waves interact with themselves and create a single photon interference pattern. If you change the interferometer with a screen, you would get bright areas where the interference was constructive and dark areas where the interference was destructive.

You are saying that the photon is only in the interferometer for a microsecond, and how can something at the same instant interfere on the other side of the interferometer. Well this is in part explained by the photon traveling as a wave and partial waves interfere with the interferometer everywhere at the same instant.

It is a misconception to think of the photon as another particle that would have rest mass and would experience time as we do. The photon does not have a rest mass, does not have a rest frame, and you cannot talk about what happens when you are in the photon's frame and move along with it. There is no such frame. The photon moves in the spatial dimensions with speed c (in vacuum, when measured locally) and moves in the time dimension with speed 0. It does not experience time as we do. We do have a rest mass, and we (or another particle with rest mass) move in the time dimension with speed > 0. Thus, we move in the spatial dimensions with speed less then c. Now the photon does not experience time as we do, you could say that it sees the entire time dimension in one, but in reality nobody knows.

What you can say is that the photon travels (if there would be a frame where you would go with the photon) from the source to the point of interaction (absorption) in 0 spacetime distance. You could say that the path the photon travels is lightlike.

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  • $\begingroup$ OK, thanks for that further explanation, which I believe I understand fully. But the real problem I am having, as stated also in my last repsonse above, is that I can't believe that a single tiny photon could possibly carry enough energy, especially at radio wavelenths, for its wave packet to be discernable, much less usable for interferometry, across such huge distances. I know that "theoretically" there must still be some part of the wave function existing no matter how widely one splits the interferometer, but it seems that after a certain distance the function would have dropped to zero $\endgroup$
    – Wd Fusroy
    Mar 25, 2019 at 15:17

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