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You are forgetting the relativity of simultaneity.
Possibly, Michael Huemer resolves the issue.http://www.owl232.net/papers/twinparadox.pdf
Its simple using GR.
Quote from: Bill BTW, have you read Heumer’s paper?I read enough of it to know that I don't agree with him at all. He says acceleration isn't important. I say it is vital in resolving the twin "paradox".
BTW, have you read Heumer’s paper?
[...] Time dilation is difference in tick rate between an observer's clock and the observed clock at any given in instant in time as measured by the observer. [...]
I read enough of it to know that I don't agree with him at all. He says acceleration isn't important. I say it is vital in resolving the twin "paradox".
I don't know how you derived the expression, but here is one method from a spacetime graphic. The axis of simultaneity is red and light path is blue. The angle ( provides similar triangles because the t and x axes are symmetrical relative to light path. j=time jumpj/x = x/t = v, thus j=xvsince x is the same for outbound and inbound,j1+j2 = x(v1+v2) cado-jump.gif (5.37 kB . 435x687 - viewed 4578 times)
[...]The error: [...] There is no 'jump'.[...]