What Would Happen if 2 People Were 1 Light Hour Apart?

[Paras Patel]

Say for instance me and another person were 1 light hour away from each other. Now at my position I am subjected to a much greater gravitational field and thus, due to time dilation, 1 hour for me is 2 hours for him (at his current position).

If I were to send a beam of photons at him, relativity dictates that the light would reach him in exactly 1 hour for both our frame of references.

But, now there is a problem in that 1 hour for me is 2 hours for him. So if he saw the light after his stopwatch hit 1 hour, only half an hour would have passed for me.

And if I stopped my stopwatch at 1 hour exactly when the light had reached him, 2 hours would have passed for him (and that is when he would stop his stopwatch - but this can't be possible since the light would ALWAYS reach him in 1 hour).

Maybe I'm just being stupid and forgetting something here. And I'm sorry if I am asking a noob question in a forum filled with intellectual threads discussing deep advanced equations. But this question has been bugging me for quite some time.

 

[PeterDonis]

Say for instance me and another person were 1 light hour away from each other. Now at my position I am subjected to a much greater gravitational field and thus, due to time dilation, 1 hour for me is 2 hours for him (at his current position).

So the distance of 1 light-hour is according to you, I assume? Meaning, I assume, that if you sent a light beam to him and he reflected it right back, it would take two hours, by your clock, to return to you? (One hour to get to him and one hour to return to you.)

If I were to send a beam of photons at him, relativity dictates that the light would reach him in exactly 1 hour for both our frame of references.

No, it doesn't. It says it would take one hour by your clock, but two hours by his clock. You've already said that 1 hour for you is two hours for him; that means that, if the light takes one hour to travel between you by your clock, it takes two hours by his.

To elaborate a bit, if a light beam kept bouncing back and forth between you, with each of you just reflecting it back towards the other, then each round trip of the beam would take two hours by your clock (one hour out and one hour back, as above), but four hours by his (two hours out and two hours back).

If what is confusing you is that you specified the distance as "one light-hour", that's not a distance measured by a ruler, that's a distance measured by light travel time. So obviously, what ruler distance that corresponds to depends on whose clock is being used to measure the travel time. The ruler distance between you is the same for both of you; but it takes light twice as long to travel that same distance according to his clock, as according to yours, because you specified that as the time dilation between you.

Maybe I'm just being stupid and forgetting something here.

You are forgetting the implications of your own scenario. See above.

 

[SlowThinker]

relativity dictates that the light would reach him in exactly 1 hour for both our frame of references.

I believe the confusion comes from the general idea that "light moves at the same speed in all reference frames", so if the distance and speed is the same both ways, then the travel time should be the same as well.

The mistake is that the light moves with speed $c$ only close to you. If you look from space at people performing experiments on the surface of a neutron star, their light moves slowly. But if you land on the star, among them, then your clock will slow down and the nearby light will move at $c$.

If there is no heavy star nearby, and you're not accelerating, only then the speed of light can be treated as $c$ even far away.