Well I am discussing what has been the topic of this thread, the classic twins paradox in which one twin stays on earth and the otehr goes to alpha centauri and comes back. In fact I stated that quite recently. So if you are talking about something else: e.g. both twins go in different rockets somehere, and then come back, we are talking at cross puposes and indeed the problem is not so interesting!happyjack27 wrote:we are not changing frames we are comparing them. if you want to introduce a frame change then you need to also introduce a frame change in the other side, otherwise you're talking about two different trajectories. - comparing apples to oranges.tomclarke wrote:I think we are finally getting somewhere.happyjack wrote: utterly pointless. you still don't frickin' get it. you can put whatever you want in there.
t(a in b over journey) = t(a in b) _S! + t(a in b)S2 + t(a change from S1 to S2)
t(b in a over journey) = t(b in a) _S! + t(b in a)S2 + t(b change from S2 to S1)
There is no change in the A frame, since A stays in one inertial frame. There is a change in the B frame, from S1 to S2.
Hence the two equations are not the same, viewed from B, which changes frame, or A, which does not.
I have been saying this for some time, but perhaps this will help you more than previous posts.
Note that the time shift element is nothing to do with relative velocity changing. When calculated in B's frames it is independent of the velocity of A, and depends only on the change in velocity (and therefore frame) of B and the distance between B and A in the S1 (or S2) frame. Thus it is not symmetrical between A - which never changes frame, and B, which changes from S1 to S2.
Time shift is a correction needed in a relativistic world when an observer's frame changes. It affects all his calculated times of distant clocks. These times must be calculated because direct comparison is impossible. The change in (calculated) time of a distant clock seems a bit weird but not when you consider that in relativistic space there is no such thing as absolute "now". The set of spacetime events corresponding to "now" depends on the frame in which "now" is measured.
Thus the distant clocks do not change time, rather the distant clock time considered the same as the local time varies when the local frame changes.
i see now you are assuming the conclusion. you are comparing apples to oranges and wo and behold they don't equate. i am comparing apples to apples. have you not figured that out yet?
Anyway, I guess from your reply there is now no argument?