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Originally Posted by MacM
You are almost there.
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Why thank you
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What you fail to recognize is that the A/B and A/C dilated accumulated time is incompatable with the B/C C/B frame unless you include simultaneity which is an illusion of motion and not a change in gamma.
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For a start, there is a frame in which A is at rest, a frame in which B is at rest, and a frame in which C is at rest. I don't know what you mean by the B/C C/B frame. In each of the three frames of interest the plane (or whatever it's called) of simultaniety is different because they are moving relative to each other. Your refutation of this seems to depend on the assertion that the relativity of simultaneity is just an illusion. You haven't demonstrated how inconsistencies arise from it. Your thought experiment only has a hint of inconsistencey because you try to sum up all points of view from one - which you just can't do is SR. The reality of the situation in every day notions of distance and time are relative to the observer.
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You distort your test by changing the standard to produce the appearance of consistancy but in reality there is no consistancy and it is impossible to produce data supporting that view of time dilation.
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So you claim. But can you actually derive an inconsistency from SR?
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But the gedanken eliminates the requirement to make such turn around and include the confusion of GR and simultaneity affects.
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You don't need GR to figure out the twin paradox. And the relativity of simultaneity is right there in SR (and at the heart of the twin paradox). Your thought experiment has only demonstrated that your requirement of an absolute sense in which spatially separated and relativy moving clocks can be reckoned is inconsistent with SR, not that SR is itself inconsistent.
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Yes. But again the gedanken makes it unnecessary for the round trip to be timed. The one way Gamma is demonstrated valid and the recipocal gamma claim is demonstrated impossible.
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You'd better go into more detial, because I don't think anyone else can see how you've demonstrated anything of the sort.
The important thing about you agreeing with the twin paradox (where your B and C turn around) is that you agree that this effect is the same for both even though A is arbitrary, so you can't believe in any sort of absolute frame of reference afterall. And you agree that the amount by which A's and B's clocks differ on return can be lengthened simply by altering the interial parts of their flight - so you must agree that our arbitrarily (but inertially) floating A attributes their loss of time purely down to time dilation due to relative motion (in both directions). Of course, if A were to head off after B and B were to carry on inertially then B would account for A's lost time identically when A caught up with B, so the time dilation while A and B are separating must be equally real for both of them.