Re: A Symmetric Twins Conundrum

Mike Fontenot wrote:

I previously wrote:

I quantified this effect in a previous posting. The equation in
that posting applied to an accelerating twin and a stay-at-home
twin. But it can be adapted to handle the symetrical case also.


I've been trying to do what I claimed (in the last sentence above)
could be done, and it's not as easy as I had expected...so far,
I haven't gotten a consistent result. Has anyone ever seen a
description of the symmetrical twin paradox, in which one of the
twins determines the correspondance between their two ages?
I.e., for each instant in the life of one of the twins, what
is the corresponding age of the other twin (as concluded by
the first twin)? (I'm of course talking here about the DEDUCED
simulataneity, NOT the way a TV image of the other twin would
appear to the first twin to be ageing). What does that plot
look like?

Well there's no such thing as a "symmetrical twin paradox", since in any symmetric scenario, the twins ages will obviously remain the same, but if both twins accelerate, just take the relationships you say you already have, between each twin and a "stay-at-home observer" (e.g. the transformation equations that relate their time and distance measurements) and factor out the middle-man to get the relationship between the twins (i.e. if S(x,t) = T1(x1,t1) and S(x,t) = T2(x2,t2), then T1(x1,t1) = T2(x2,t2)).
.

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