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I came to this question while thinking about light with extreme wavelengths. Say we had light (em radiation) with a wavelength of 100's of thousands of kilometres and we absorbed a photon of it on earth (perhaps technically very difficult) would the possibility of that photon being detected on the moon disappear instantly or only a second or so later?

Qmechanic
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John Hobson
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  • It is difficult to define the wavefunction of a single photon (but yes, there are some nice attempts), but the principles of QM / QFT requires that the absorption be updating the wavefunction across the universe to be instantaneous. This is because we needed the case of there being only one photon in the entire universe to guarantee that only one detector ever detects it. Any slower updating of the field would have meant that there would be some chance / scheme for another detector to detect it. – naturallyInconsistent Oct 05 '23 at 15:20
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    @naturallyInconsistent if it fully answers the question, just put it as an answer ;) – Señor O Oct 05 '23 at 15:32
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    Alternatively, the quantum state of the system can be described as a combined state involving both em-field and atomic degrees of freedom, and the state can evolve unitarily from (one photon + atom in ground state) to (no photons and atom in excited state), with no updating necessary. – march Oct 05 '23 at 15:38
  • @SeñorO I'm often confused; there were times I had posted short answers, and then got complained that it should just be a comment, and so on. It seems like I just cannot please everybody here. – naturallyInconsistent Oct 05 '23 at 15:38
  • @march it would be evolving unitarily into (no photons and one single atom in excited state), for many different possible atoms... – naturallyInconsistent Oct 05 '23 at 15:39

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  1. While different interpretations of quantum mechanics may disagree on how exactly this comes about (instantaneous wavefunction collapse or split into many worlds or pilot waves or whatever), all interpretations agree that QM will not lead to outright nonsensical (but perhaps counterintuitive!) results - you cannot detect the same particle twice at different places. If you have the state of a single particle and detect that particle on earth, you will not detect it on the moon.

  2. Classical light is modeled a coherent state and in particular a classical EM wave does not have a definite number of photons, see also this question on the number of photons in an EM wave. It does not make sense to speak of "the photons" in classical light - their number is indeterminate and they are indistinguishable, and what you get from the intensity of this light is the probability to detect "a photon" but not any particular one. If the light classically reaches both the earth and the moon then detecting photons from it in one of these places does nothing to the detection of photons at the other place.

Generally the "particle interpretation of light" is much less straightforward than you might be led to believe by the way we often speak about photons, see this question for general relationships between EM waves and photons and this question for specific issues with the notion of "wavefunctions" for photons and their interpretation as spatial probability densities.

ACuriousMind
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You've stumbled into the problem of how Max Born developed the Born rule of quantum mechanics by assigning the square modulus of the wavefunction to be a probability.

He considered the problem of electron scattering and quantum mechanically the wavefunction was computed to be spherical and emanating outward from the scatterer, but he was concerned with the fact that when you have an array detectors surrounding the scattering event along equal radii only one detector would be triggered at a time. Thus, the wavefunction was collapsed upon recording the event, and when that happened no other detected could record an electron. This is similiar to your question, if the photon is received on earth, then indeed one will not be found on the moon. Of course, this assumes that you've sent out a single photon to begin with.

JQK
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  • The requirement for ultra-long wavelengths may be a red herring but this seems to allow for faster than light communication. I know the limiting speed of light should only apply if information is transferred but if photons are absorbed according to a pattern, might not that pattern be instantly picked up a large distance away (as photons being unavailable for absorption)? And a pattern can be information. – John Hobson Oct 08 '23 at 23:29