Why doesn't light travel instantly? [duplicate]

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I've read that the faster you travel in space, the slower you travel in time. And when you reach the speed of light (which we won't be able to) time will stand still. So when light travels at the speed of light, it doesn't move in time, so no time will have past when the light arrives at it's "destination". Right?

marked as duplicate by Brandon Enright, Kyle Oman, Kyle Kanos, Qmechanic♦Jul 10 '14 at 21:02

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• No time will have passed for the photon. That's exactly right. Time for some other observer will have though. – user21433 Jul 10 '14 at 17:54
• Related: physics.stackexchange.com/q/29082/2451, physics.stackexchange.com/q/16018/2451 and links therein. – Qmechanic Jul 10 '14 at 17:58
• "...it doesn't move in time, so no time will have past when the light arrives at it's "destination". Right?": Yes. From the hypothetical point of view of the photon, proper time and proper distance of a photon in vacuum are zero. You can also say, the spacetime interval between two events a photon is passing is zero. By the way, this is the reason why there can be no clock with respect to a photon: Clocks are measuring time. If there is no time (if time is zero), any use of a clock is meaningless. For instance, nobody will be able to measure zero seconds. – Moonraker Jul 11 '14 at 11:15

1 Answer

it doesn't move in time, so no time will have past when the light arrives at it's "destination". Right?

A photon does 'move in time'. It just that, for a photon, the displacement in time, $c \Delta t$, equals the displacement in space, $\Delta x$.

However, there is no proper time for a photon.

Your proper time is, in words, the elapsed time according to a clock at rest with respect to you.

But, according to special relativity, there is no inertial frame of reference in which a photon is at rest so there is no clock at rest with respect to a photon.

Put another way, a photon propagates with speed $c$ with respect to all clocks.

Note that this is quite different from saying that a clock at rest with respect to a photon 'stands still', i.e., no time passes.

It's more subtle than that since there is no clock at rest with respect to a photon to consult!