Bouncing light question faster than c?

[RespeckKnuckl]

I'm confused again by a relativistic situation. On train A a mirror is placed atop another, with distance h between them. A light beam is bouncing back and forth between them. Now 1 light-hour away, spaceship B is traveling almost towards A at half the speed of light. not traveling in a directly straight line to point A, but maybe a few meters to the side of A. This way the line that the light beam appears to travel is a diagonal line to B.

This diagonal has height h and width whatever it is, depending on the angle of B and its speed and what not, as long as it's greater than zero, we'll call it w. Basic Pythagorean theorem gives the distance that the light beam travels between mirror hits:
sqrt(h^2+w^2)
Now the doppler effect should make A's clock seem to be moving faster than it actually is. Does this mean that for B, it sees the light beam as traveling faster than the speed of light?

the reason is that if B were at rest relative to A, the light beam would cover a distance of h in t amount of time. (traveling at c). But when moving towards A, it covers what appears a greater distance sqrt(h^2+w^2) in even quicker time (doppler shift), requiring a velocity faster than c? What am I missing?

 

[HallsofIvy]

No. All observers see the speed of light as the same thing, c. The fact that one's clock is slower than than the others means that one will see a different frequency than the other.

 

[JesseM]

I'm confused again by a relativistic situation. On train A a mirror is placed atop another, with distance h between them. A light beam is bouncing back and forth between them. Now 1 light-hour away, spaceship B is traveling almost towards A at half the speed of light. not traveling in a directly straight line to point A, but maybe a few meters to the side of A. This way the line that the light beam appears to travel is a diagonal line to B.

This diagonal has height h and width whatever it is, depending on the angle of B and its speed and what not, as long as it's greater than zero, we'll call it w. Basic Pythagorean theorem gives the distance that the light beam travels between mirror hits:
sqrt(h^2+w^2)
Now the doppler effect should make A's clock seem to be moving faster than it actually is. Does this mean that for B, it sees the light beam as traveling faster than the speed of light?

No, in B's coordinate system the light moves at c, and thus the clock is ticking slower in B's frame because it has to move farther between mirrors. Because the mirrors are moving towards B, the light from each subsequent tick has a shorter distance to travel and this causes B to see the clock ticking faster (the Doppler effect), but you have to distinguish between what B sees and what time-coordinates B assigns to events in his own frame; the time-coordinate B assigns to each tick is either based on compensating for the light signal delay (so if B sees an event 5 light-seconds away at t=8 seconds, he'll assign the event a time coordinate of t=8-5=3 seconds), or it's based on B looking at the reading on a clock at rest in his frame which was next to the event as it happened, and which is synchronized with his own clock in his frame. See this thread for a bit more on the distinction between the time-coordinate that events happen and the time an observer actually sees them.

 

[Constructe]

If light is bouncing a to b then you will see nothing unless it is leaking light to you at your angle. If it is, you will see it blue shifted. Maybe it is traveling through dust let's say. You are then not witnessing it traveling from a to b but the secondary effect of the light hitting dust. Thus I think you will then be missing your attempts to violate the speed of light issue you are constructing.

 

[ZikZak]

Now the doppler effect should make A's clock seem to be moving faster than it actually is. Does this mean that for B, it sees the light beam as traveling faster than the speed of light?

the reason is that if B were at rest relative to A, the light beam would cover a distance of h in t amount of time. (traveling at c). But when moving towards A, it covers what appears a greater distance sqrt(h^2+w^2) in even quicker time (doppler shift), requiring a velocity faster than c? What am I missing?

You are missing the word "seems" in your first sentence. When we say that B "observes" that A's clock is ticking slowly, we mean that B is intelligent enough to correct for effects of light travel time before he calls it an "observation." It is merely effects of light travel time that you are talking about when you discuss your Doppler Effect.

An observation is not what you directly see through your telescope. It is an event that is recorded to have happened at a certain (t,x,y,z) in your reference frame. It may take you some time to observe events separated from you by a distance, but you don't record the time you saw it; you record the time that you calculate it happened, given the time required for the information to get to you.

Alternatively, you can imagine that B has a cadre of graduate students, equipped with synchronized clocks and meter sticks, all at rest relative to him, at every point in the universe. It is B's graduate student immediately next to A's light-clock that makes the observation, and then transmits the observation to B himself, who records it verbatim in a notebook.

 

[MeJennifer]

An observation is not what you directly see through your telescope.

This is, I think, one of the root problems why people will remain to have trouble with Relativity, but it will give educators a guaranteed job. Relativity is much simpler and above all empirical when you talk about what an instrument actually measures instead of constructing some mental Galilean frame of simultaneity. Unfortunately working through relativity using the simple and straightforward relativistic Doppler formula seems to be a bad thing for some here.

B is intelligent enough to correct for effects of light travel time before he calls it an "observation."

If relativistic space travel ever becomes reality people will be intelligent enough to understand that questions like: What time it is right now in Andromeda? are absolutely useless.