Time Dilation Question: A vs. B Clocks in Motion Experiment

[Thomas2]

When two objects collide, everyone agrees that they collide "at the same time". (Otherwise, how could they collide? ) But in your example, the clocks do not start or stop at the moment of the mechanical collision. Since the clocks are not collocated with the collisions, it takes time for the signals to reach them.

Yes but this is merely a constant offset (if any) depending on the proper length of the rods and the location of the clocks and the signal propagation speed (e.g. the speed of sound within each rod).

Where's the paradox? Not everything is a paradox. For example: Frame A says that rod B is contracted... But frame B says that rod A is contracted! Paradox? No... just standard relativity describing the relationship between observations made in two inertial frames.

Likewise you couldn't agree about the frame in which the time dilation is supposed to occur, i.e. we have a ambiguous (paradoxical) situation.

 

[Doc Al]

time dilation works both ways---as always

When two objects collide, everyone agrees that they collide "at the same time". (Otherwise, how could they collide? ) But in your example, the clocks do not start or stop at the moment of the mechanical collision. Since the clocks are not collocated with the collisions, it takes time for the signals to reach them.

Yes but this is merely a constant offset (if any) depending on the proper length of the rods and the location of the clocks and the signal propagation speed (e.g. the speed of sound within each rod).

It's only a constant offset for the clock within a given frame. Frame A observers will agree that the travel time for the signal to start and stop clock A is a constant offset and can be ignored. But frame A observers will not agree that the travel time (measured in frame A) for the signals to start and stop clock B is a constant offset.

Where's the paradox? Not everything is a paradox. For example: Frame A says that rod B is contracted... But frame B says that rod A is contracted! Paradox? No... just standard relativity describing the relationship between observations made in two inertial frames.

Likewise you couldn't agree about the frame in which the time dilation is supposed to occur, i.e. we have a ambiguous (paradoxical) situation.

What are you talking about? There is nothing ambiguous or paradoxical here. Time dilation would be observed by both frames, of course, as always. Frame A sees clock B running slow, and vice-versa.

You seem to think that the clock times recorded in your setup somehow should reflect "time dilation" in a simple way. Not so! To illustrate time dilation you would need to have frame A measure the start and stop time (according to frame A clocks) of clock B and then compare that time interval to the elapsed time on clock B. If your setup did this, then you would find that if clock B says that \Delta t_B has elapsed, then frame A will say that the elapsed time according to frame A clocks is \gamma \Delta t_B because frame A sees clock B as running slow.

Of course, the same argument works for frame B observing clock A.