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The question is not about the real photons bursted out of an atom and their size (I call them real photons) but about the quantized modes in a box and that they are called photons (I call them QED photons). I wonder what common has the real photon and the QED photon with each other.

According to QED quantization procedure of the EM field as known Debye decomposed EM field in a box in Fourier components, then Born, Jordan and Heisenberg quantized the amplitude of the standing waves (SW) so the energy was devided into pieces hv and hence the amplitude of the SW is multiple of n (integer). So it turns out that the photon in QED is a standing wave with energy = hv whereas its length seems = length of the box. There are some questions about this notion of photon (as pictured in QED) I want to find answers.

  1. The standing wave fills the whole box at once – so a photon appears on top of the existing standing wave like dropping above immediately, whereas the atom in the walls should have delivered the energy hv and this seems not relativistic (there should be some moment that energy left the wall, so at that moment there can not be EM amplitude near the other wall or in the center of the box).
  2. As the length of box can be varied it turns out that the length of the photon depends on the length of the box, which is unknown to the atom.
  3. For distant objects this seems extremely unbelievable as for item 1 so for item 2. (but QED says that one easily stretches the box to infinity and all is the same.)
  4. In order to insure the release of proper frequency an instantaneous process is needed which to measure the distance of the box and to deliver the info to the emitting atom.

I think some answers maybe based on Heisenberg uncertainty principle though I haven’t seen these questions ever asked anywhere and nonetheless some answers. I hope someone knows a paper or book where they are posed and cleared and will be so kind to share this knowledge.

Mercury
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    Possible duplicate of 'size' of a photon, What is Size of Photon?, Does a photon have any measurable size as a “particle”?, Does photon have size measurement because of its particle nature, Is the size of a photon dependent on its wavelength?, How is wavelength actually related to space (/distance)?, and multiple links therein. – Emilio Pisanty Mar 01 '18 at 10:37
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    Photons don't really exist; the EM field (which is the sum of all the photons) is what is real. Standing waves (photons) are a basis for the EM field. When you look at the evolution of the sum of all the basis elements, you will see that the energy slowly moves away from the wall, even though if you just consider any specific element in the sum, it can be large even as $t$ → $0$. – Peter Shor Mar 01 '18 at 10:44
  • @EmilioPisanty thanks for the links. I found a sort of answer in your answer to the last link. I don't know what you mean exactly though but my impression is that you also think that the QED photons are just mathematical constructs which has nothing to do with real (even virtual) photons, but are just a convenient tool for calculations. (something like a mass point etc.) – Mercury Mar 03 '18 at 08:53
  • No, that's not correct - photons are perfectly physical, and definitely not just mathematical constructs. They're not hard balls with a pointlike position (even if you later try to spread that position around) but that doesn't mean that they're not physical. – Emilio Pisanty Mar 03 '18 at 12:26
  • I mean the QED photons (the quantized standing waves) which pop out in existence as EM excitation in the whole box are pure math items. It can not be they are real! Are you talking about them or about the wavepackets bursted out of the atom when E1-> E0 decay is made? The second one is surely real photon emitted. – Mercury Mar 03 '18 at 14:58
  • There's no such thing as non-QED photons, beyond perhaps a lies-to-children version taught to undergrads who are not yet ready for the full QED treatment. If the state has a nonzero probability amplitude then it's real, plain and simple. – Emilio Pisanty Mar 03 '18 at 16:48
  • @PeterShor Do you mean that (speaking honestly) QED photons are just a mathematical trick (very successful indeed but unphysical in its roots)? Then I have a further question: when there is a real 'atomic' photon how is it expanded on the QED photons by taking into mind that 'atomic' photon has E=hv (let lambda=c/v is = to the first mode of the box). If you take more QED photons your energy would be more. – Mercury Mar 03 '18 at 18:58
  • @EmilioPisanty I can not see how a photon emitted by an atom can be at all a QED photon? A sum or integral of many QED photons surely (with probably fractional coefficients) but this does not mean that it is QED photon. QED photons have amplitudes to be non zero at the other wall at t=0 pointing to speed above c. Well I admit I never found a QM book to treat this question (basically they are committed to math). You surely are lucky to find a book about the physical meaning of quantization - can you site it here? – Mercury Mar 03 '18 at 19:57
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    Again: There's no such thing as a photon outside QED. It's impossible to say anything further because you haven't actually positively defined what you mean by "a real photon" or "a photon emitted by an atom" (i.e. you've said a bunch of things about what you think they're not, but you haven't said anything about what you do think they are). As to literature, Cohen-Tannoudji's Photons and atoms does an excellent job at explaining things. – Emilio Pisanty Mar 03 '18 at 20:07
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    Consider a vector space. You can express the vector $(1,2)$ as $1\cdot \vec{x} + 2 \cdot \vec{y}$. Or you could choose a different orthonormal basis, in which case it might be $\sqrt{5} \cdot \vec{s} + 0 \cdot \vec{t}$. Is the first vector longer than the second because more basis elements contribute to it? No. And arguing that one basis is more "real" than a different basis is a futile endeavor. – Peter Shor Mar 03 '18 at 20:18
  • @PeterShor My answer is of course the vector is real and the basis is something which is in our mind. But can you be more concrete about what I call QED photon (which are the basis in the case). I think you say they are mathematical constructs, but Emilio Pisanty insists they are real. – Mercury Mar 04 '18 at 12:17
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    @EmilioPisanty Look at the Mach Zehnder interferometer - the leg which is empty is empty because the two waves overlap 180 out of phase. If QED photons are real, one can say that there two photons in this leg, without EM field there at all. – Mercury Mar 04 '18 at 12:18
  • @Mercury You keep using that terminology after being explicitly told it's meaningless - that's not a constructive way forward. As for your MZI - no, you can't say that there are two photons on the empty leg, since that state has a zero probability amplitude. That's just the standard QM fact that the amplitudes for events can interfere destructively and there isn't anything specific to QED or photons in that situation. I'm not sure much else can be achieved in this discussion, though. – Emilio Pisanty Mar 04 '18 at 13:07
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    @Mercury: The vector $(1,0)$ is just as real as any other vector, even though it's part of a basis. It's when you consider the expansion of another vector as a sum of basis elements that the reality of $(1,0)$ in that particular situation is questionable. Similarly, the QED photons are just as real as any other photons. But it might be a mistake thinking of them as real when you express an arbitrary photon in the basis of the QED photons. – Peter Shor Mar 04 '18 at 14:33
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    @EmilioPisanty what is the amplitude of a recent burst of the sun to be near Andromeda at the same time? I can not see arguments in your opinion. – Mercury Mar 04 '18 at 18:38
  • @PeterShor I can not accept QED photons real because they occupy whole space at the same time (though can be regarded as basis at will and convenience purposes). There can not be a physical object comprising all space and compensated almost everywhere by many others of that kind. The examples you give are mathematical objects. Of course they are as real (in math sense) as any other. – Mercury Mar 04 '18 at 18:58
  • @Mercury I can't see any arguments in your opinion, either (or more specifically, any real responses to the criticism already raised), so I'm stepping out of this discussion. Have a good day! – Emilio Pisanty Mar 04 '18 at 19:09
  • @Mercury: You started out in the OP by doubting whether "quantized modes in a box" are real, and now you're talking about the sun and the Andromeda galaxy. If you keep changing what you mean by "QED photons", we'll never get anywhere. – Peter Shor Mar 04 '18 at 19:22

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