The importance of velocity in simultaneity

[PeterDonis]

I am talking about my original scenario as described above (where C&D are merely the points where lightning bolts will strike when A&B reach them.

Ok; but then I can just define two clocks, E and F, which happen to pass by C and D, respectively, at the exact same instants that clocks A and B reach them and the lightning bolts strike, and which are moving at the exact same speed as A and B are at those instants. Then just substitute E and F for C and D in everything I wrote.

The point I was trying to make with C and D (or E and F in the new nomenclature) was not to construct a new scenario; it was to make it easier to see explicitly aspects of your original scenario that you were not considering. The frame in which E and F are at rest exists, and can be used to analyze your scenario, regardless of whether clocks E and F are actually there. Putting them there just helps to give an actual physical realization of the frame. And A and B end up at rest in that frame--the one I was calling frame CD, and will now call frame EF--regardless of whether clocks E and F are there to compare with. And the procedure I described by which A and B can exchange light signals after they have accelerated and confirm that their clocks are now out of sync and the distance between them has increased, can be done regardless of whether clocks E and F are there.

You can't make the non-synchronization of A and B at the end of your scenario go away by sticking to your original frame (what I call frame AB); once A and B start accelerating, they are no longer at rest in that frame, there's no way around that, so the fact that various events happen at the same time in that frame is no longer relevant for assessing the synchronization of clocks A and B. You can analyze the procedure A and B can follow to exchange light signals after they accelerate in frame AB if you like; it will still tell you that A's and B's clocks are out of sync, in the precise sense I described (the light signals they receive from each other show clock readings that are different than what a synchronized clock would be sending, given the light travel time delay), and that the distance between them has increased (as measured by light travel time).

 

[Micheth]

Now, once A and B have completed their acceleration, and are now co-located with C and D and moving inertially, at rest in frame CD instead of frame AB, they can repeat the above process. And when they do, they will find: (1) that the distance between them has increased, based on the round-trip travel time of light signals between them; and (2) that their clocks are no longer synchronized

I think I understand what you're saying here. At least I hope so.
A and B will find their measurements between them to be actually different in their new frame.
I may not like it, but if SR is correct it'll just have to be accepted, AND in fact I think I can retract any of my logical "objections" if (and i guess only if) the answer to the following question is "yes".
(Please tell me the answer is yes! :-)
If A and B are the only objects in the universe (they carry out the process you describe to synchronize their clocks). Then A and B (persons with them) go to sleep, during which time both vessels are accelerated by the same degree).
When they wake up (not knowing they have accelerated, or having any way of knowing that they are in a different frame than before), they carry out the same process but surprisingly find that, as you describe above, now (1) they are further apart than before, based on the round-trip light signal times, and (2) their clocks are no longer synchronized.
And they would find this strange - strange enough to conclude that they must have accelerated, correct?
(If this is what they would find then I am satisfied, and I have no further questions.)

 

[PeterDonis]

A and B will find their measurements between them to be actually different in their new frame.

Yes.

If A and B are the only objects in the universe (they carry out the process you describe to synchronize their clocks). Then A and B (persons with them) go to sleep, during which time both vessels are accelerated by the same degree).
When they wake up (not knowing they have accelerated, or having any way of knowing that they are in a different frame than before), they carry out the same process but surprisingly find that, as you describe above, now (1) they are further apart than before, based on the round-trip light signal times, and (2) their clocks are no longer synchronized.

Yes.

And they would find this strange - strange enough to conclude that they must have accelerated, correct?

Yes.

 

[Micheth]

Yes.

Thank you :-)