keepitmoving said:
glad to try again. Thanks for your patience.
If a moving emitter moving at .99 c passes a stationary train (relative to the moving emitter) and emits a photon just at that point (simultaneously) and the train takes off in the opposite direction at, say .5 c relative to the train`s stationary starting position, what is the velocity of the photon relative to the moving emitter (is the photon c x time distance from the moving emitter at any point in time?) ( not asking about the distance or velocity from the original emission point).
Also, since the train and the moving emitter are moving in opposite directions, do their measurements (c x time) of their distance from the photon yield different locations for the photon?
Isn`t there a pretty definite location for the point of emission which is also the point where the train began it`s .5 c journey?
This still isn't very clear.
You say that the emitter is moving at 0.99c, but you don't say in what frame. Since you mention a train that's "stationary", I have to assume that the velocity of 0.99c is in the train's rest frame. Right after "stationary" you say "relative to the moving emitter" which contradicts the above since it means that the train is co-moving with the emitter. I'm pretty sure that's not what you meant, so I'll ignore that part.
The emitter emits a photon at the event where it passes the train. There's no need to use the word "simultaneously", since the meeting between the emitter and the train is just one point in spacetime. (Simultaneity is only an issue when you consider at least two points). At this event, the train instantaneously boosts its velocity to -0.5c in its original rest frame. I would have preferred a thought experiment involving a train with a constant velocity, since we're not going to use the fact that the train had another velocity before the emission event, but it's OK for now.
Now you're asking for "the velocity of the photon relative to the moving emitter", but since you used the phrase "relative to the moving emitter"
very incorrectly earlier, I still don't know you mean. What you're actually asking for here (regardless of whether you meant it or not) is the velocity of the photon in the emitter's rest frame. It's c. Light
always moves at c in the rest frame of
any object. (Note that only massive objects have rest frames). So in that frame, the distance between the photon and the emitter is ct, where t is the time measured by a clock attached to the emitter.
Maybe you meant to ask for the velocity of the photon in the train's original rest frame, or the velocity of the photon in the train's new rest frame. It's c in both of them. It's c in
all inertial frames.
What you're probably interested in is the distance in the train's frame between the emitter and the photon at a time t in the train's frame (i.e. measured by a clock attached to the train). This distance is 1.5ct, so it's increasing by 1.5*299792458 meters every second. Note however that even though this quantity has dimensions (i.e. units) of velocity, there's no object that moves with that velocity in any inertial frame.
