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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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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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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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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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