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At the crossing point of two EM waves - do we have two photons?

Is every single "point" of the wave's occupied volume a potential photon?

Also, can a photon be viewed as "the cross-section" of a radiating EM wave?

Adelina Mitkova
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    What is the "crossing point" of two EM waves? – WillO Jan 31 '22 at 03:41
  • If two waves travel at an angle towards one another in a 2d plain, they will meet somewhere. Assume that 3d space is represented as infinitely thick layer of 2d plains for the purpose of my question. – Adelina Mitkova Jan 31 '22 at 10:32
  • Best way to think about it is that a single photon is a wave in the EM field. 2 photons can pass thru each other just like sounds can cross each other in air. The EM field is everywhere but we can never observe it directly ... we only see light when the photon (which was created by an electron atom) is absorbed by an atom/electron. We can make single photons or many like in a radio wave, but the photons behave individually ... there's a lot of probability involved also called Quantum Mechanics. – PhysicsDave Feb 01 '22 at 00:21

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At the crossing point of two EM waves - do we have two photons?

Short answer: you ask an impossible question but... Kind of.

Wave-particle duality is notoriously hard to interpret. The delayed choice experiment and HOM effect all show rather clearly that one can not just establish a 1:1 mapping between waves and particles and use them interchangeably. Nearly everything that follows is an oversimplification of some kind, and there is a heated debate to this day about the right way of thinking about all this.

Ask yourself this: could you construct a single EM wave such that at any point at time you look at it and say "there are exactly two photons with such and such energies at this point in space"? Generally speaking, the answer would be no: one can only decisively note something about individual photons when they interact with matter. One could not even create your proposed experimental setup with coherent single-photon sources. But, for what it is worth, if there somehow would exist two single-photon wave packets overlapping in a certain region of space and time and someone puts a detector there, they, indeed, would be able to detect two photons. With some probability. Or maybe none - see HOM effect above. In the setup of your question, Delbrück scattering is also an interesting thing to consider: photons actually can interact with each other!

All in all, quantum mechanics is all about statistical qualities and probabilities, and that mindset might be hard to adopt. When considering an individual particle level, preface all your judgements with "with some probability, what we observe would be X": this is the only way the wave-particle duality works.

Is every single "point" of the wave's occupied volume a potential photon Also, can a photon be viewed as "the cross-section" of a radiating EM wave?

EM waves are composed of wave packets, they are not just sine waves. For the purposes of quantization, anyway. See above how they relate to statistical quantities - in a typical real-world scenario, the number of photons coming from a light source is huge, which is why we treat a technically discrete Planck's distribution as a continuous one.

If you are interested in learning more, I would recommend finding some popular lectures on QED (Feynman's "QED: The Strange Theory of Light and Matter" might be a bit hard, but I do not happen to know a better book for beginners, unfortunately).

Lodinn
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  • Lodinn, As I read about the "Delbrück scattering" in Wikipedia, I find the following: The lowest order diagram has four vertices and consists of two incoming photons, which annihilate into a virtual electron-positron pair, which then annihilates into two real photons again." Does this imply that, by some hypotetical special circumstances, EM waves can interact to give off massive particles? (Thanks for the enriching information and the book, as well!) – Adelina Mitkova Feb 01 '22 at 00:00
  • @AdelinaMitkova Unfortunately, no, but it is tempting to say yes - the nature is pretty exciting! Sorry for baiting you there a bit ;) Sadly, virtual particles are stuck in a deeply unsatisfactory state of affairs. You can not think of them as of real particles :( Sorry! FWIW, I (and many fellow HEP students) made that assumption as well during our studies, so it is easily confusing. The real takeaway from this effect: they teach you in the school light doesn't interact with light. Practically true but factually is a lie :) – Lodinn Feb 01 '22 at 09:28
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My recommendation is to follow these steps:

  1. Calculate the distribution of electric fields for a given frequency (with multiple waves, there could be interference).
  2. Square the field distribution and take the time average to get the average power distribution.
  3. Imagine there is a small photon detector, such as an appropriate atom, which is somewhere in the fields but does not perturb the field distribution.

The likelihood of the detector detecting a photon within some time period is proportional to the power at its location.

Gilbert
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