Stone's derivation of Thomas rotation

[yuiop]

Hi Rasalhague.

There are far too many questions in you last post!

I feel confident I can answer them, but it would be too time consuming. Could you pick one scenario or issue you most want addressing and describe it in careful unambiguous detail?

 

[Rasalhague]

Okay, fair enough. It was a very rambly post! A lot of that was me just thinking aloud, trying to blunder onto solid ground. With a bit more brain-racking, I hope I'll be able to home in on a more-or-less coherent question. But for now, how about this? It refers to your post #137 and the attached diagram, and deals with the basic issue of whether there are two different kinds of rotation associated with a single boost, one due to the alignment of a rod or displacement vector, the other due to the direction of a rod's velocity wrt that of the boost.

If A was at rest in S'', would it rotate in the opposite direction (clockwise) to that shown in your diagram (counterclockwise) when we boost coordinates to S'? And if so, does this mean that it would be possible, given an appropriate choice of alignments and velocities, for the rotation due purely to a rod's alignment wrt the boost (the rotation for which we each found a formula earlier in this thread) to be canceled out by the rotation due to the direction of the rod's velocity wrt that of the boost?

 

[yuiop]

If A was at rest in S'', would it rotate in the opposite direction (clockwise) to that shown in your diagram (counterclockwise) when we boost coordinates to S'? And if so, does this mean that it would be possible, given an appropriate choice of alignments and velocities, for the rotation due purely to a rod's alignment wrt the boost (the rotation for which we each found a formula earlier in this thread) to be canceled out by the rotation due to the direction of the rod's velocity wrt that of the boost?

Hi Raselhague. I started answering your question, but while working on some examples I ran into some paradoxical situations, so it is quite possible that some of your concerns are valid and that Jason's comments about requiring actual acceleration rather than just a transformation boost to another frame is required. I will have to give it some more thought. Bear with me!