A question about a thought experiment in space

[MeJennifer]

marlos jacob, after 4 pages of argument, I am curious, are you arguing that relativity is in some way wrong or is there something you do not understand?

If it is the first option then there is no point since this forum was created to help people understand relativity not to argue against it.

 

[marlos jacob]

The observer on the ship can never find that Ta is different than Tc, not if his clocks were synchronized using the Einstein synchronization procedure

Thank you Mr JesseM and Mr Matheinste, for your genuine desire to help and for your beeing so patient with me. I have studied the explanation of Mr JesseM last post. I checked all the example, and inclusive used the Lorentz equations and spacetime diagrams to verify what you have exposed. Everything looks ok and I have to agree that all is absolutely consistent with the Relativity Theory, supposing, as Mr JesseM said above, that the clocks were synchronized using the Einstein's procedure.

I then decided to change the Experiment so that we do not need two clocks, avoiding, consequently, the synchronization process. To achieve it, we can consider that A and C are just two mirrors. B, now, is capable of sending the pulses to A and C, both at time T=0. Those pulses wil depart toward to A and C, reflect back on the mirrors, and then reaching B, where the detector will register the times Ta and Tc the pulses needed to make their travels to the respective mirrors and back.

In this new format of the Experiment, is it also true that the observer will never find Ta<>Tc, regardless of the spaceship (uniform) movement? (At this point I should tell you that, considering the reasonings you made on your post, I think that your answer will be "YES". But I would like having it directly from you.

Thank you,
Marlos Jacob

 

[matheinste]

Hello Marlos Jacob. If the observer is in the spaceship YES.

Matheinste

 

[JesseM]

Hello Marlos Jacob. If the observer is in the spaceship YES.

I'd just add that if Ta and Tc now refer to the round-trip time for the signals to leave the center, hit the mirrors at either end, and return to the center, then the answer is actually "yes" regardless of which frame the observer is in--all frames will agree that the signals return to the center at the same moment. Also note that since this new experiment does not depend on any specific ideas about simultaneity or clock synchronization, you don't actually need relativity to get this answer, it would be equally true in Newtonian physics. For example, if instead of light waves you were using sound waves which always travel at the same speed in the rest frame of the air, and a platform moving relative to the air, then if sound waves are emitted from the center of the platform and reflected when the reach the edges, the echoes will return to the center at the same moment (although since there is no length contraction or time dilation in this Newtonian example, different frames would disagree about the speed of the two outgoing waves and the two incoming waves).

 

[Mentz114]

How nice to have this sorted out. Congratulations to everyone.

 

[RandallB]

I then decided to change the Experiment so that we do not need two clocks, avoiding, consequently, the synchronization process. To achieve it, we can consider that A and C are just two mirrors. B, now, is capable of sending the pulses to A and C, both at time T=0. Those pulses wil depart toward to A and C, reflect back on the mirrors, and then reaching B, where the detector will register the times Ta and Tc the pulses needed to make their travels to the respective mirrors and back.

Very good, you’ve duplicated the Michelson–Morley experiments, something to look up wiki… etc.

But you have not avoided synchronization you’ve defined it.
And simultaneity is the most important element that absolutely does apply to this problem.
Not the comment:

Also note that since this new experiment does not depend on any specific ideas about simultaneity or clock synchronization, you don't actually need relativity to get this answer, it would be equally true in Newtonian physics.

The signal is simultaneous when it returns to B because of two things:
1. The mirrors at A & C are in the same reference frame B.
2. The signals reflect (or are sent) at A & C simultaneously as measured in that reference frame B.

But notice, no other reference frame on your line will claim the reflections are simultaneous!
They all claim that one reflection occurs before the other depending on the direction that frame moves relative to your frame B.
That was the point Einstein was making with the lighting strikes you spoke of earlier. Understanding simultaneity is critical to understanding SR.

Also, note that you cannot use sound for synchronization if your frame is going though the air (i.e. not the air inside Einstein’s train).

Classical Michelson–Morley experiments hoped to detect an “ether” for light that would act air does for sound but could not. That’s what lead Einstein to SR, defining nature without an “ether” (more good reading).