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I am currently puzzled over one aspect of the notion of photons regarding its property of being localized and having a direction (as opposed to the classical EM picture of a spherical wave). I have come up with a thought experiment that illustrates my idea.

A charged particle is located at the origin of the laboratory frame, and there is a mechanism that can induce movement on the charge (for example, generating an external E field onto the particle, or perhaps varying a gravitational field that causes it to accelerate in a certain direction).

At a certain distance from the particle, a bunch of photodetectors are placed uniformly in a circular manner around the origin, so they are all at the same distance from the particle initially. We can assume that the particle has zero velocity in the laboratory frame, so that the detectors are motionless with respect to the particle's inertial frame of reference.

Suddenly, the experimenters induce an acceleration on the particle by one of the methods described above. In the classical EM picture, the accelerated particle will generate electromagnetic radiation propagating in all directions. After some time, all the detectors will measure a certain EM field intensity, and this should happen at the same time for all of them since the wave propagates at the same speed in all directions. The intensity distribution will not be uniform since the radiation will not be spherically symmetric (it would follow the Liénard-Wiechert equations), but there will definitely be nonzero measured intensities in most detectors.

Now looking at the quantum picture, it would seem that we think of the situation as the accelerated particle emitting a photon. The photon will then have a certain momentum and energy, and this should mean (assuming my understanding is correct) that it will reach only one detector. Therefore, we should be observing an intensity distribution where one detector has a large measured intensity, and all other detectors have zero intensity measured.

One can perhaps argue that the particle generates much more than one photon, and that the directions are statistically distributed in such a way that the classical intensity pattern matches the probability distribution of photon directions. But in that case, it should still be possible to experimentally distinguish the two situations by measuring correlations between detection times for different detectors. Presumably a stream of discrete photons will produce individual detection events spaced out by certain time intervals, so it should be possible to determine whether the intensities are measured simultaneously across all detectors, as would be predicted classically, or if the intensities accumulate over time by discrete events.

Is this an accurate description of what would be predicted by quantum mechanics?

Has such an experiment been performed in practice, and do the observations correspond to this prediction?

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  • $\begingroup$ are you aware that experiments with single photons are prerformed ? see sps.ch/en/articles/progresses/… $\endgroup$
    – anna v
    Commented Mar 16, 2019 at 7:26
  • $\begingroup$ What I was aware of was experiments involving single photons that are produced from lasers. I did not want to ask about those because I assume the situation is slightly different since the lasers are designed to emit radiation in a very narrow beam, so the question of omnidirectionality would not really be addressed. By using a charged particle that is "shaken" we make sure the "beam" is (classically) omnidirectional. But if you believe the two situations are equivalent, I would be interested in an answer that explains this. $\endgroup$
    – Tob Ernack
    Commented Mar 16, 2019 at 7:50
  • $\begingroup$ I suppose that one could actually do the same with lasers, taking into account the Gaussian field intensity distribution with respect to distance from the optical axis. So perhaps they do work fundamentally in the same way. The question would then be the same, except the detectors would be placed at sufficiently small distances on a receiving screen such that the beam width of the laser is much larger than the detector size. $\endgroup$
    – Tob Ernack
    Commented Mar 16, 2019 at 7:58
  • $\begingroup$ Anyways, some time after posting the question, I realized that there might be two equivalent ways to think of the same phenomenon which wouldn't be distinguishable from that experiment alone (one way is by using quantization of field into photons, and the other is by modelling the field classically but assuming random excitations in the detectors themselves, with rate proportional to the field intensity). The second way seems to relate to the semiclassical explanations for things like the photoelectric effect. $\endgroup$
    – Tob Ernack
    Commented Mar 16, 2019 at 8:05
  • $\begingroup$ I think either way you do your experiment you're going to run into the probabilistic nature of the interaction when you have any more than one detector. Photons are truly quantized and as Anna states have been experimented with on a single basis. They can radiate in any direction but only choose one! $\endgroup$
    – PhysicsDave
    Commented Mar 17, 2019 at 17:42

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Good question, in radio we have electrons moving in antennas, assuming we could just move one electron (but in reality there is noise) than an electron in a receiving antenna would sense the acc'n thru something called virtual photons. There is no real photon until the energy gets transferred to the receiving electron in the other antenna. With only one electron and say ten detectors, all ten would sense thru virtual photons but only one antenna would receive, and it would be based on probability. There is no way to see that the 10 antennas are sensing the single electron. If you increase the current to say 10 electrons you would get still get some antennas receiving zero and others multiple based on probability. You can think of electron in an atom in the same way, it gets excited, it may be sensing (thru virtual) 1000s of other electrons in atoms, but just chooses one and voila a photon is produced.

It would be interesting to place the antennas a different distances (wavelengths) to see which got more photons, i.e. bias the direction. In atoms though the wavelengths are very short, it would require single atoms placed very accurately to bias the outcome.

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Most nuclear physics experiments deal with precisely the kind of experiment you’re proposing. They have an array of photon detectors around the sample and they look at the angular distribution of photons emitted by various nuclear reactions to work out the energy levels. The angular distribution profile tells about the angular momentum carried by the photon (and this acts as a label for the reaction it came from).

What’s more is some reactions necessarily emit two photons, some three and so on. In these cases they look at coincidence between various detectors to work out the properties. In fact when you start talking about coincidences is when you see that the semi classical approach of treating light as an EM wave and just treating matter (of detectors) quantum mechanically is insufficient. To understand these events one needs to treat light also quantum mechanically, in terms of photons.

When you go for a PET scan, you are essentially looking at such array of detectors around you and you map out the sample by looking at various coincidences in the detectors.

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