As I mentioned earlier I feel that MacM is attempting to prove that the preferred observer system that SRT employs when taking on an observers reference frame is inequitable and logically unsound.
I beleive that MAcM is claiming that whilst SR is used to do the math from the entire gedanken overview POV, the observers them selves use Lorentz relativity to do theirs so the claim that MacM is making could be narrowed down to SR mixing theories and thus ending up with time dilation of each clock being slower than the other which is according to MacM an impossibility.
so by temporarilly looking at the situation with out using a preferred observer to do the calculations and maintaining a symetrical approach to who has what velocity you will find most likely how this problem is demonstrated.
By including lorentz relativity in SR you end up with this time dilation issue
so either stick to relative velocity or use Lorentz absolutes but don't use both...is I think what MacM is all about in his complaint.
Maybe he would care to agree or disagree....
You are 100% correct. The simple fact is that the way they apply SR is a form of LR and that is to consider who has actual velocity by imploying frame switching, not merely relative velocity.
The only reason I can see for calling it frame switching is to NOT acknolwdge that to switch frames you must experience F = ma by acceleration for some period or duration thereby causing a change in actual velocity in an absolute sense to your rest frame. That is to have actual velocity and not merely relative velocity.
They never actually use the SR assertion that either can be considered at rest where the resting clock is viewed by the traveling clock as having the velocity and being the dilated clock . That is just rhetoric and BS propagation.
There is no emperical data to support the argument that the resting clock dilates. It is totally irrational and physically impossible. It is possible to have an illusion of motion where one might percieve that each is ticking slower but the emperical data only supports that the one with actual motion does.
They (James R) claims the SR assertion and illusion is physically real but has not and cannot be tested. That is an interseting postion since:
1 - If it is untestable then SR is falsified as a valid theory. A theory must be testable to be valid but;
2 - he asserts the affect is there and that time dilation in both frames is real and is frame dependant because SR says so.
The problem here is I believe that the scenario I posted using radioactive particle decay rates as atomic clocks and then using identical delayed accelerations of negligable duration compared to inertial relative velocity period of test, shows that comparison of the accumulated % decomposition of each clock is the same if both are read in either frame subsequent to having had relative velocity between them during the test period. That is "A" & "B" can be read in the "B" frame and shows that "A" has decomposed less having had actual velocity. Likewise "B" can be moved into the "A" frame and the comparison of % decomposition results are precisely the same.
It completely blows the frame dependant result arguement because reading the % decomposition in either frame is the same.
Dilation is NOT frame dependant as claimed (but untested and hince physical reality is therefore relative velocity is NOT symmetrical at relavistic speeds because each observer is using a different time tick rate standard to measure the trip time and the trip time is only valid if distance does NOT forshorten as claimed by SR.