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Consider a photon bouncing left and right between two mirrors in a photon clock. Seen from inside the clock, the photon bounces at a constant frequency. Time ticks regularly. No matter whether the clock begins moving relative to some outside observer, the clock continues to tick regularly. Light always moves at the same speed relative to the observer in the clock.

If the clock is moving forwards relative to an outside observer, we know that to that outside observer, the photon clock appears to tick more slowly. This happens because the speed of light relative to that observer is constant, and, since the photon is moving diagonally relative to the outside observer, the distance traveled by the photon in the clock between ticks is greater, so the photon must take longer to pass between the mirrors and the clock must tick more slowly.

But notice how, if you are inside the clock, it continues to tick at the normal speed.

This brings me to my question. It is widely reported (including on this very QA site) that a photon traveling uninhibited in a vacuum experiences no time. This seems to be because all the speed of the photon in the clock is now taken up keeping up with the forwards movement of the clock, so there is no speed left to deal with left/right bouncing and ticking. The clock stops ticking. Well, this is the thing. Surely the clock only stops ticking from the perspective of the outside observer. If you're inside the light-speed clock, time continues to tick normally. The photon continues to bounce. So why do we say a photon experiences no time? Surely we mean it appears to us as stationary observers to experience no time? If you're a photon, time is just the same as it is to the rest of us, right? Fair enough, your average photon might well feel that it got from A to B in no time at all, because distance was compressed to zero and all the other clocks appeared to have zipped along beyond the end of days in less than an instant, but its own clock, if the photon could observe it, is just ticking normally. This leaves my brain mushed, because now the photon has seen the entirety of an infinity of time in no time at all, yet its clock is still ticking. So what does that mean? What happens the moment after the infinity of external time has completely passed? Surely there is nothing left to happen?

Qmechanic
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Nobody
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  • The eigentime (time as measured by a comoving observer) is 0 for a photon (or anything moving at c). – Danu Dec 09 '13 at 23:48
  • But @Danu, why? Given that for an observer moving at c, the photon clock will continue to tick at the normal rate, why do we think that eigentime is 0? Surely time is experienced at the same rate irrespective of movement. It is only how fast external clocks appear to be ticking that is experienced any differently to when at rest. – Nobody Dec 09 '13 at 23:58
  • This has been gone over ad infinitum here. A photon has speed c in any reference frame including the reference frame of any light clock. The light clock doesn't ever stop ticking in any frame of reference because there is no frame of reference in which it moves with speed c. – Alfred Centauri Dec 09 '13 at 23:58
  • Exactly, @Alfred: "The light clock doesn't ever stop ticking in any frame of reference". So, why do we think it stops ticking for a photon? – Nobody Dec 09 '13 at 23:59
  • Because a photon does not have a frame of reference. – David Z Dec 10 '13 at 00:00
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    @user244195, there is no observer moving at c. That must be the misconception that is leaving your brain mushed. An observer is at rest with respect to himself. But, an observer moving at c in one reference frame must move at c in all reference frames - in contradiction with an observer being at rest with respect to himself, his own reference frame. Thus, there is no reference frame for a photon, no observer moving with speed c. – Alfred Centauri Dec 10 '13 at 00:00
  • Just for some background for (presumably) a layman: something moving at $c$ in one frame of reference must move with $c$ in all frames of reference. This is one of the postulates of special relativity. – Danu Dec 10 '13 at 00:07
  • OK - this is making sense. http://physics.stackexchange.com/q/29082/ – Nobody Dec 10 '13 at 00:08
  • It's not easy to find things like that when you don't know what to search for (photon frame of reference did it in the end). Thanks for the pointers. – Nobody Dec 10 '13 at 00:09
  • Hi user244195, this question (v1) has several issues. E.g. it discusses massive clocks moving with the speed of light, which is outside widely accepted physical theories (SR), and therefore off-topic. I close this question as a duplicate, not because it necessarily is, but to point you in the right direction. – Qmechanic Dec 10 '13 at 00:51

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