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I am probably missing an important aspect here, but here are two thought experiments I came up with that make me quite a bit confused. Can some one explain to me, if I am missing any important aspects or making any logical mistakes? Sorry for a little mess in my descriptions, I have a bit of a hard time to organize my thoughts here.

  1. The speed of light is an invariant and constant in any inertial frame. Let us take a frame of a photon. Imagining if a photon could emit another photon, would it observe the newly emitted photon to also move with the speed of light relative to the emitting photon?

And the question above can reconcile with the time dilating to zero at the speed of light, but that brings my second thought experiment.

  1. If we could affix a clock to the photon, it would never tick from the external observer perspective. But then, considering relativity, no clocks in the universe would tick from the perspective of the photon, right (not like there was any way to communicate it anyway, but still)? Imagine we launch a photon from $A$ in the direction of $B$. At $B$ we have a gate which toggles open/closed at random time intervals. From our perspective, it will take time for the photon to reach the gate, but from the photon perspective, no time in the world would have passed, which means the fact of whether it will hit the gate or not is in some way determined right at the moment when the photon was emitted, like if it was not a "particle" that was emitted, but the whole trajectory (in a loose way, due to wave function nature) was emitted at once, spanning both space and time.

The above experiment probably confuses some things, but if not, it has some weird implications, that at the time of emission, the state of the whole universe along the space-time trajectory is frozen and is used to determine what is gonna happen. That solves kinda the double slit experiment, because we never issued a particle flying through space in the first place, for all practical reasons we emitted the place where it will hit the screen in the future, and that was accounting for all possible interference along the path (which for us appears stochastic due to indeterminacy, but that may or may not be truly stochastic, i.e. a superdeterministic universe, which does sound plausible if at any time we emit the whole trajectory for even massive particles..)

Brendan Darrer
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DKOIMAN
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  • Yes it's possible that paths are predefined ..... the excited electron is already intensely interacting (via virtual photons) with the EM field even before real photon emission. I don't think your proposed experiment helps resolve anything. But your question does help resolve the DSE observations. – PhysicsDave Jul 24 '22 at 18:54
  • Your first two sentences after 1. are in immediate contradiction. By "the frame of a photon" you can only mean a inertial frame where the photon has speed 0, but that contradicts the previous sentence. By the way, the is no point in invoking quantum mechanics (via the notion of a photon) in a question about relativity. In fact it seems like you think of a photon like you could think of a mosquito: if it is a thing, it could in a thought experiment be me. It cannot; you can never be a photon (nor can a photon be you). – Marc van Leeuwen Jul 25 '22 at 08:51
  • If you are observing a star with or without a telescope, you can decide whether or not to use the telescope after the photon leaves the star but before you see it; this will alter the path of photon. – Henry Jul 25 '22 at 10:33

3 Answers3

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The mistake is at the beginning: the "frame of a photon" doesn't exist, since a massless object cannot be at rest in any frame. So any reasoning that starts by working in the frame of a photon is bound to fail.

Miyase
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    Why can't a massless object be at rest? – Greendrake Jul 24 '22 at 12:43
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    @Greendrake That's a fundamental result of relativity. Just take the usual formula describing the change of inertial frame: 1) There's no frame where a massive object has a velocity equals to $c$. 2) There's no frame where a massless particle has a velocity other than $c$. – Miyase Jul 24 '22 at 12:50
  • @Miyase are you talking about the velocity addition formula? That formula only implies that an object that has a velocity of c in one frame has a velocity of c in every frame. It does not say anything about massless objects in general, in fact it does not involve mass at all. – Aetol Jul 24 '22 at 14:17
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    The "massless" argument is way too complicated (and it depends on what exactly you mean by mass). There cannot be a "frame of a light wave" (in vacuum) because that would be a frame where that light wave has zero speed, but by postulate light always moves with a constant (nonzero) speed regardless of the inertial frame. – Marc van Leeuwen Jul 25 '22 at 09:04
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As @Miyase's answer mentions, it's not possible to work in the frame of reference of a photon.

A good way of solving this problem is to hypothesise about "what if we could", and then realise it leads to contradictions. Along the way we will also get an appreciation for the problem itself.

So, what if we could put ourselves into the frame of a photon? We'll be a little hand-wavy with the mathematics here, and assume that the limit of the relativistic functions as they approach c is the actual value. As you've already observed, the time "experienced" by the photon drops down to zero. Furthermore, due to length contraction, the photon also experiences zero distance. As far as the photon is concerned, it was emitted and absorbed in the same place, at exactly the same time.

At this point, the reference frame seems quite silly. No time can pass in it, and the entire universe is compressed into an infinitely flat disc along the direction of travel of the photon.

In this reference frame, one could say that the photon's path was pre-determined. However "pre-determined" implies a causality, which implies the existence of time. However time does not exist in this reference frame, and so nothing can be the result of anything else.

Hannesh
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  • Yes, thx, I generally understood the point. Though, I would want to stretch a little bit more something you described in the last paragraph. When you say the pre-determined path implies causality, we can have that by-passed if we remove "evolution" aspect all together - i.e. nothing emits anything or consumes anything, but the whole universe is just a static 4D structure we somehow trace along one axis, from which time passage arise. Wouldn't that be a possibility which also aligns with superdetermenism? – DKOIMAN Jul 24 '22 at 02:36
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    @DKOIMAN I think the point is photon reference frame can't exist in that 4 dimensional structure. – justhalf Jul 24 '22 at 13:43
  • Note that in this frame the photon's energy would be zero. So it cannot do any work on the massive objects that emit and absorb it and are moving at the speed of light in that frame and are thus massless ... what a weird world that would be. Now of course comes the part where a photon whose emission and absorption is pre-ordained is a virtual particle that can be off-the-mass-shell and we finally enter the world where nothing makes any sense any longer without doing proper quantum field theory – tobi_s Jul 25 '22 at 03:16
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In general, you cannot even determine the path a photon took in retrospect. Electromagnetic propagation is a wave phenomenon. Waves take every available path simultaneously.

Don't use particle models to analyze wave phenomena.

John Doty
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