How would you answer this speed-of-light question? (See details)

If the mirror were moving at the speed of light, then the laser light would never catch it. It’s outside the “light cone”.

Wouldn’t your mirror be right at the exact edge of the light cone? And what would the time dilation be at the mirror relative to your position?

Yes, it would be at the exact edge of the light cone. In terms of the time dilation, I suppose the clock would be stopped.

I believe that is true.

> “If a mirror were moving away from you at exactly the speed of light,” ...

> “and bounce back to your relatively stationary point of observation? (Stationary with regard to the motion of the mirror)”

Those two clauses conflict. I can’t be stationary relative to a mirror that’s moving away from me.

What I was so ineffectively trying to say there is that forgetting anything else in the universe that may be moving, you are sitting in one spot, and the mirror is moving away from that spot at the speed of light. So relative to you, the mirrir is moving 186,000 miles per second and relative to the mirror, you are moving at 186,000 miles per second. or 700 ,o;;ion miles per hour.

OK. So in that case I think the laser would never reach the mirror, and it would stay an hour outside the light cone rather than on the edge. Also, I think the mirror’s time would be stopped, so that means its clock would move infinitely fast.

Compare if you’re watching someone on a train moving half the speed of light shoot a laser towards the front of the train. From your point of view the train is shortened, but from the person on the train’s point of view it isn’t. So the laser should reach the front of the train faster from your point of view. But it doesn’t because the clock of the guy on the train runs faster. His time is slowed, which means he measures everything he sees as taking longer than you measure it – which means his clock runs faster.

Isn’t the speed of light independent of the observer? Because of that, doesn’t the actual answer come out a rather mind boggling 2 hours?

Well, suppose the mirror were moving half the speed of light, so your light beam could actually catch up. In that case you’d fire the laser and an hour later it would get to where the mirror had been. But by then the mirror would have moved half a light hour ahead. So your beam travels for half an hour more and now the mirror’s 15 minutes ahead. Add another 15 minutes of travel and now its 7.5 minutes ahead. Etc. So I think it would hit the mirror around 2 hours after you shot it. Then it’s got to travel back to you for 2 hours. So that’s 4 hours round trip rather than 2, and the fact that light’s speed is independent of the observer won’t change that. Increase the speed of the mirror and the round trip time will increase. Increase it to the speed of light and the round trip time goes to infinity.

@Cirbryn In your half the speed of light example, would the reflected light be redshifted?

@Rarebear Ha. Depends on your point of view. If you’re the guy that fired the beam, then the mirror is moving away and the beam will redshift after it hits it. If you’re the guy with the mirror, then the guy that fired the beam is moving away, and the beam isn’t any redder coming off your mirror than going in. Beam-guy will still see an increased redshift when the beam gets back to him, however, because he’s moving away from the incoming reflected beam.

I am looking at it this way. Realistically, the mirror couldn’t be moving away at the speed of light, but it might me moving at half that speed, and you might be woving in the opposite direction at half that speed. From your point of observation, the mirror is receding at light speed. Now, since the speed of light is always 186,000 MPS regardless of the point of view and motion of the observer, why would the light not reach the mirror and bounce back?

Actually, if I were between mirror guy and laser guy, and both of them were moving away from me in opposite directions at half the speed of light, then mirror guy would see laser guy moving away from him at about 90% of the speed of light. (Likewise for what laser guy saw mirror guy doing.) The speeds don’t add normally around the speed of light, which is why the speed of light can be constant for any frame of reference.

@Cirbryn Exactly. Very interesting stuff. It’s little surprise, though, that things moving as fast as light wouldn’t conform ot our normal frame of reference.

Yeah, the idea I’ve been sort of playing with for a while is that light actually moves instantaneously. So the reason it appears to take time is due to differing times at the locations in question. So if you’re 186,000 miles away from me in space, you’re also 1 second behind me in time. And likewise you think I’m 1 second behind you in time, which is one of the reasons it’s weird and I’m still working on it. So if I bounce a laser beam off your mirror and time its return, what (theoretically) would be happening would be that the beam traverses the distance instantaneously, then undergoes instantaneous acceleration (in the sense of changed velocity) when it hits the mirror. That acceleration changes the “clock” of the light beam to the clock of the mirror, so now the beam sees me as being one second behind it. Then it comes back to me and undergoes acceleration again as it hits the light detector, and now the mirror is one second behind it. Since I was 1 second behind the mirror and the mirror is one second behind the light beam at that point, the light beam gets to me 2 seconds after it left, even though from its point of view it traveled instantaneously.

All of which is very awkward, but it does help make the failure of speeds to add above the speed of light make more sense. No matter how many times you double your speed, you’ll still never be instantaneously fast.

@Cirbryn Fascinating way of looking at it.

Thanks. Yeah it’s funky stuff. Turns out I called it wrong earlier too.

I said the mirror’s clock would be sped up compared to laser guy’s, but if that were true then our clocks would be sped up compared to a light beam’s, and light would take infinite time to get anywhere (from our perspective). But actually, when time slows for something moving fast, that means their clock slows.

Getting back to the example of the guy on the train, if he shines the laser forward, and the train is 186,000 miles long from his perspective, we on the ground would see the train as shorter, so by our clocks it would take less than a second for the beam to reach the end. From train-guy’s perspective it would still take a second. So we consider his clock to be running slower than ours, because the same event takes longer to occur by his clock.

So a mirror moving away from us at the speed of light would, from our perspective, have a stopped clock. Similarly, from the point of view of the wavefront of a lightbeam, everything else is moving past it at the speed of light, so everything else should have clocks that are stopped. So the lightbeam should be able to get anywhere before those clocks register any time as having passed. So if light appears to require time to get somewhere, it must be because of differences in what constitutes “simultaneity” in different locations rather than because of travel time.

This means that movement through time and space is kind of zero-sum. From my perspective my position is always the “origin”, so I move through time but not space. But the faster I see you moving through space, the more your clock slows and the slower you move through time. Light beams move through space but not time.

@Cirbryn My friend Doug (you know who he is) has a beautiful book that demonstrates the geometry of exactly what you’re saying. I’ll get the title from him.

@Cirbryn Yes, the faster you go, the slower your clock runs relative to a clock of someone at rest in relation to you. If you were moving at exactly the peed of light, you would experience the same thing you would in the presence of infinite mass. Time would stand still. Exceed the speed of light, and time runs backwards for you. You are coming to understand how time truly works. I am really looking forward to the book reference that @Rarebear mentioned.

http://www.amazon.com/Very-Special-Relativity-Illustrated-Guide/dp/067402611X/ref=sr_1_1?ie=UTF8&qid=1287429142&sr=8-1

So you’re recommending that book then, Rarebear?

@Cirbryn I saw it at Doug’s house and really liked it. I actually just ordered it myself.

@Rarebear Just added to my reading list. It;s a very long list, though.

Isn’t this just a restatement of Xeno’s paradox but with physics?

I’m sorry I don’t have anything more useful to say.

@Rhodentette I see your point, but no, it’s not. Xeno’s paradox had nothing to do with relativity or light speed.

I’m aware that it didn’t. His was about shooting arrows at tortoises and why, logically, the tortoise could never actually be hit by the arrow.

Maybe “restatement” was the wrong word to use but this question does seem to have several parallels.