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When we say a photon is a packet of energy with frequency of f, it means it consists of at least one electromagnetic wave cycle (otherwise we can not measure its wavelength).

Is there any experiment or theory that shows how many wave cycles exist in each photon? I am asking because besides the frequency, this number also can affect the energy of the photon (a photon with two cycles should have two times higher energy than a photon with just one cycle, while they both have the same frequency and wavelengths). This is a little paradoxical to me, because as far as I know the energy of photon only depends on its frequency.

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  • $\begingroup$ This must be a duplicate of some other question, but I can't find it. $\endgroup$ – garyp Sep 10 '16 at 20:55
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A photon has no cycles. It's like asking how many fingers does an apple have.

The thing that oscillates and has cycles is the electromagnetic field. The photon is an excitation of the field. Roughly speaking, adding a photon to a field means increasing the amplitude of the underlying wave.

The size of a photon is a different question. It doesn't really have size either, although one can say that the size is the same as the "cavity" in which the field is defined. To explain that in detail will take us far afield, but take as an example a laser. The cavity of a laser is the space between the mirrors, so we can say that the photons, or excitations of the cavity modes, are the same size as the space between the mirrors. Once outside the laser, the cavity has no boundary. We can approximate the light field in unbounded space by a plane wave which is boundless in all directions. For that (approximate) picture, the size of the photon is infinite. In reality, there are no true plane waves, so the fields are always of limited extent, although it can be very large.

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  • $\begingroup$ Thank you for the nice answer. Actually your second part of the answer ( laser cavity and boundary part) is exactly what I am looking for. Can you suggest a good text book or reading resource please ? It can be of huge help for me. Thanks again. $\endgroup$ – Aug Sep 10 '16 at 21:42
  • $\begingroup$ A couple of possibilities. "Quantum Theory of Light" by Loudon and "Laser Physics" Sargent, Scully, and Lamb. The both have chapters on field quantization. Slightly different emphases, so looking at both would be worthwhile. There are probably even better ones with which I am not familiar. $\endgroup$ – garyp Sep 11 '16 at 1:10
  • $\begingroup$ Although it make more sense for photons to have the oscillating cycles. An electromagnetic field is just passing the problem on to another word. Further more its easy to physically describe an oscillating photon but no one can physically describe a field or even a wave without incorporating photons. $\endgroup$ – Bill Alsept Sep 11 '16 at 6:17
  • $\begingroup$ @BillAlsept Sensible is in the eye of the beholder. How does one describe an oscillating photon without reference to the field? And I think it is easy to describe a wave, we do it all the time in elementary mechanics. And we describe an EM wave in classical EM without photons. The OP seems to have a picture of a photon as a wave packet. Among other things, I'm trying to expunge that compelling but incorrect picture. $\endgroup$ – garyp Sep 11 '16 at 11:02
  • $\begingroup$ There are many ways one could describe an oscillating photon. For instance it could be described the way one describes a cyclical universe expanding out and contracting in as it travels along at the speed of light. Also everyone says they can physically describe a field or wave without photons but no one ever does, ever. It can't be done. $\endgroup$ – Bill Alsept Sep 11 '16 at 12:56

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