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New Theories / Re: What is the Traveler's Perspective in the Twin "Paradox"?
« on: 16/12/2013 17:34:02 »Quote[...] the case where each twin is perpetually inertial (i.e., neither of them ever accelerate)[...] If they are natural born twins and they never accelerate, then they are eternally colocated, and they each know the other's time accurately, with no debate
You are right, of course ... I WAS taking some liberties there, in order to try to keep my posting as short as possible. In the case where the "twins" are perpetually-inertial, the scenario actually has to consist of two separate babies, born to two separate mothers who have some constant relative velocity with respect to one another, and who happen to be momentarily co-located at the moment of the two births. And in this case of perpetual-inertial-ness of both "twins", the "twins" are never again co-located, and so it's not the complete "twin paradox" situation. The reason for initially considering that modified scenario was to construct a situation where each "twin" is obviously entitled to use the Lorentz equations in the determination of their own perspective about the current age of the other "twin". That especially simple modified scenario is important to consider initially, because it is the easiest way to show that the simultaneity results obtained via the Lorentz equations ARE meaningful, and should be taken seriously and at face-value ... they give the same result that the each inertial person can determine using only his own elementary measurements and elementary calculations. Only then is it productive to move to the standard twin "paradox", where the traveler is NOT perpetually inertial. The essence of most of the interesting controversy about the traveler's perspective involves the question of exactly WHEN the traveler is entitled to use the Lorentz equations to determine simultaneity. Some say never. Some say "if he hasn't recently accelerated in the past". Some say "If he hasn't recently accelerated in the past, OR won't accelerate too soon in the future". Others say "he can use it at any unaccelerated instant of his life, regardless of how and when he accelerates at other times". I am a member of that latter group, except that I extend it to include ALL instants, whether he is accelerating then or not.
In the case of the MSIRF solution (which I usually refer to as "the CADO reference frame") of the traveler's perspective in the standard twin "paradox" scenario, it turns out that accelerations that occur at any instant when the twins are co-located don't have any effect on the traveler's perspective. And in general, the larger the separation of the two twins, the larger is the effect of acceleration on the traveler's conclusion about the home twin's current rate of ageing.