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Imagine a photon leaving a vacuum and entering a medium, say, air. I have 2 questions:

  1. Some claim that the photon is slowed by the medium so its speed becomes less than $c$. Is that true or does refraction cause the photon to take a longer path so that it only appears to slow down?

  2. Since time does not exist relative to the photon when it was traveling at $c$ in the vacuum, what happens to time relative to the photon when it enters the medium?

Qmechanic
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Steve
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    "Since time does not exist relative to the photon..." Can you clarify what you mean by this? – hft Oct 22 '23 at 22:36
  • In a dielectric material with index of refraction $n$, the speed of light is $v=\frac{c}{n}$. – hft Oct 22 '23 at 22:38
  • Yes, because in a vacuum a photon moves at the speed of light, so it will not observe any passage of time; the proper time felt by a photon is zero. In a medium, the medium itself observes a passage of time, so that should not be too surprising. The mathematical details, however, is not at all as simple as in the vacuum case. The combined effect of a lot of independent scattering events, their resultant disturbances to, say, a crystalline lattice, is combined together into one single quantum particle of great complexity, and it is this particle that moves slower than light. – naturallyInconsistent Oct 23 '23 at 01:16
  • I voted to reopen this because what it's asking about is mainstream enough. The Feynman checkerboard is a simple model where particles that seem to have speeds less than $c$ really take longer zigzag paths at $c$, and you can consistently adopt a similar picture in more realistic theories, as far as I know. Moreover, the rate of scattering amounts to a clock, and that's why a proper time is definable for massive particles and not for massless particles. – benrg Oct 23 '23 at 02:35
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    "Since time does not exist relative to the photon" is not mainstream physics because mainstream physics consists of meaningful statements. – WillO Oct 23 '23 at 02:51
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    This is a perfectly good question, stated at a beginner or enthusiast level of rigor. He's expressing that the proper time interval for any photon path is zero, and wondering if that changes during refraction. People don't come to this site to learn who are already physics PhD's, and I think the community ought to welcome and encourage thoughtful questions of a conceptual nature. – RC_23 Oct 23 '23 at 04:17
  • @Steve the short answer is, in the wave and refraction model (Maxwell) the light wave slows down. In the photon model (Quantum) photons do not slow. But the models are depicting different things and are not interchangeable. The wave model describes the bulk behavior of light and fields (lots of "photons" in a sense), while the photon model describes primarily the interactions between light and matter at the particle level. It's a bit like modeling city traffic either as a continuous moving fluid, vs tracking individual car paths and collisions. – RC_23 Oct 23 '23 at 04:23
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    @RC_23 "He's expressing that the proper time interval for any photon path is zero..." If that's what he is expressing by "since time does not exist for a photon," then why not just as well say "since space does not exist relative to a photon," since the proper time being zero means the proper length interval $-c^2 d\tau^2$ is zero. Stating that time and/or space "do not exist" ("relative" to anything) is seeming nonsense and is not the same as saying that the proper time interval is zero... – hft Oct 23 '23 at 05:31
  • OP, just remove the second part of the question (the part labeled "2"). It's really just bullet point "2" that is nonsense. The question in bullet point"1" seems potentially answerable in some way. – hft Oct 23 '23 at 05:35
  • @RC_23 imo you're making a rather artificial distinction between the wave model and the photon model, wave mechanics still apply to the photon model especially in the linear response regime, the photon part is the fact that your fields are now quantised and obey Bosonic statistics, they still obey Maxwell's equations in the operator sense. In a macroscopic medium it's perfectly valid to describe the photon propagation in terms of the same polaritonic fields you would use in the classical macroscopic Maxwell's equations (see Gruener-Welsch, Hunter-Barnett, Buhmann etc) – AwkwardWhale Oct 23 '23 at 07:25

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