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In general, let us have a light emitting point A and two light absorbing points B and C, such that the three points fall on a straight line and B is somewhere between A and C. For simplicity, let us consider all photons emitting from A to travel along this same line in the direction of the points B and C. Also, let the distance from A to B be AB and the distance from A to C be AC.

For the photon, special relativity states that there should be maximum space contraction along it's direction of motion. That means that, for the photon, A, B and C are all at the same point in space. This results in the photon effectively "reaching" B and C at the same time. How then does the photon "decide" that it must be absorbed by point B and not C, so as to be consistent with what an outside observer would see (point B "casting a shadow" on point C)?

Whatshiywl
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  • You need actually quantum mechanics to understand this. In QM view, photon travels in all paths possible at once, and collapses into a final state upon measurement. In what state it will collapse finally - it's undefined. We just can extract probability distribution of final states or so called wave-function. And because hidden-variables theories are denied,- we can't know the exact event - what detector photon will hit at final place. That's how nature on QM level work. – Agnius Vasiliauskas Feb 17 '20 at 13:28
  • Btw, a shadow casting is an effect from a constant photon stream, not a single photon. So our eyes measures only statistical accumulated effect from bunch of photons. Which is some sort of a measurement of photon collapsed state probability distributions – Agnius Vasiliauskas Feb 17 '20 at 13:38
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    Yes, I'm aware that QM has an answer to that. I could use many paths to calculate how much light reaches points B and C and realise that basically all the non-linear paths leading from A to C "cancel" each other out, effectively lowering the probability of the photon hitting C to virtually 0. What I'm trying to understand however is if SR alone has a solution to this problem. – Whatshiywl Feb 17 '20 at 14:17
  • About the shadow, of course, you're correct. I put shadow merely to illustrate the fact that point B blocks photons from point A from reaching point C. – Whatshiywl Feb 17 '20 at 14:48
  • @AaronStevens they are related, yes. The question linked poses the question of whether it is correct to assume that emission and absorption take place at the same space and time for the photon. It does, according to answers, but it is noted that it doesn't make much sense to ask what the photon "sees" as it's not a valid (inertial) frame of reference to begin with. I understand and would accept this answer, but is seems like a way to avoid the problem, indicating SR can't actually solve it. That's fine, but I'm curious if that's all there is to it or if an actual solution has been proposed. – Whatshiywl Feb 17 '20 at 15:01
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    It's difficult to give a good answer to your question. Pure SR talks about rays of light and light flashes, it doesn't "know" about photons. So if you want to talk about photons some mention of QM is unavoidable. But in QM a photon "in flight" doesn't have a well-defined position. The photon model is useful when talking about the emission or absorption of light, but it's not so useful at modeling what happens while the light is traveling. – PM 2Ring Feb 17 '20 at 15:11
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    @PM2Ring ah I understand, so I'm really just looking at the problem the wrong way. Well, fair enough! – Whatshiywl Feb 18 '20 at 00:48

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