Light's speed and relativity

[Joe]

If you were to travel alongside a train, as fast the train, to you the train would seem stationary. I read that if you were to travel along a photon of light, as fast as the speed of light, that photon would not seem stationary. Is this true? If so, why?

 

[Ibix]

You are misunderstanding something. The key point is that you cannot travel at the speed of light - so the question of "what would light look like if you traveled alongside it" can't be answered.

Possibly what you misunderstood was that Einstein's second postulate is that the speed of light is always $c$ in all inertial frames. A frame traveling at the speed of light would therefore lead to a contradiction - that light is stationary (because the frame is moving at the same speed) and also moving at $c$ (because that's part of the definition of an inertial frame in relativity). Since there's a contradiction, you can't have an inertial frame moving at the speed of light. Edit: just to be clear, this does not mean that light isn't stationary if you travel alongside it. The (self-contradictory) conclusion that light wouldn't be stationary even when it must be shows that being stationary with respect to light isn't a coherent concept in relativity.

 

[Joe]

You are misunderstanding something. The key point is that you cannot travel at the speed of light - so the question of "what would light look like if you traveled alongside it" can't be answered.

Possibly what you misunderstood was that Einstein's second postulate is that the speed of light is always $c$ in all inertial frames. A frame traveling at the speed of light would therefore lead to a contradiction - that light is stationary (because the frame is moving at the same speed) and also moving at $c$ (because that's part of the definition of an inertial frame in relativity). Since there's a contradiction, you can't have an inertial frame moving at the speed of light. Edit: just to be clear, this does not mean that light isn't stationary if you travel alongside it. The (self-contradictory) conclusion that light wouldn't be stationary even when it must be shows that being stationary with respect to light isn't a coherent concept in relativity.

Thank you. From what I understood - from your edit - light can seem to be stationary? Two photons traveling alongside each other will seem not moving from each other's perspective?

 

[jbriggs444]

Thank you. From what I understood - from your edit - light can seem to be stationary? Two photons traveling alongside each other will seem not moving from each other's perspective?

There is no such thing as the perspective of a photon.

 

[phinds]

Thank you. From what I understood - from your edit - light can seem to be stationary? Two photons traveling alongside each other will seem not moving from each other's perspective?

You still misunderstand. There IS NO "point of view" (or perspective) of a photon.

EDIT: I see jbriggs beat me to it

 

[Ibix]

Thank you. From what I understood - from your edit - light can seem to be stationary? Two photons traveling alongside each other will seem not moving from each other's perspective?

As jbriggs444 and phinds have noted, it's simply not possible to describe the perspective of a thing traveling at the speed of light. Attempting to do so leads to the contradiction I mentioned.

Unfortunately, something you find as you move away from every day experience is that questions that seem perfectly sensible turn out to be nonsense. You don't even have to go that far outside the every day. Could you tell me which way is north where you are now? Could you tell me which way is north if you were at the north pole? Asking what anyone or anything would see at the speed of light is like that second question. You can't answer because the question has hidden assumptions that are not valid in the case it's talking about.

Note that you do find pop-sci sources (notably Brian Greene) that say things like "time stops at the speed of light". They're the result of forcing an answer at (metaphorical, I hope) gunpoint and don't make coherent sense, but usually satisfy non-physicists enough that they shut up and go away. It's worth noting that I gather that Greene himself does not make this claim in professional publications, only his pop-sci stuff.

 

[Joe]

As jbriggs444 and phinds have noted, it's simply not possible to describe the perspective of a thing traveling at the speed of light. Attempting to do so leads to the contradiction I mentioned.

Unfortunately, something you find as you move away from every day experience is that questions that seem perfectly sensible turn out to be nonsense. You don't even have to go that far outside the every day. Could you tell me which way is north where you are now? Could you tell me which way is north if you were at the north pole? Asking what anyone or anything would see at the speed of light is like that second question. You can't answer because the question has hidden assumptions that are not valid in the case it's talking about.

Note that you do find pop-sci sources (notably Brian Greene) that say things like "time stops at the speed of light". They're the result of forcing an answer at (metaphorical, I hope) gunpoint and don't make coherent sense, but usually satisfy non-physicists enough that they shut up and go away. It's worth noting that I gather that Greene himself does not make this claim in professional publications, only his pop-sci stuff.

Thanks again. Nicely explained!