If a photon is absorbed, does the associated wave function disappear instantaneously, or at the speed of light?

Question

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?

Answer 1

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.

Answer 2

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.