On 4 January 2014 04:06, Jason Resch <jasonre...@gmail.com> wrote:
> On Fri, Jan 3, 2014 at 9:21 AM, Edgar L. Owen <edgaro...@att.net> wrote:
>> Lliz, Brent and Jason,
>> Actually Liz is correct here, by GR it is the acceleration. That is the
>> physical cause of the clock time differences of the twins.
> In my experiment, lets say the acceleration lats for a total of 4 minutes:
> one minute to accelerate up to 0.8 c, one minute to slow down at Proxima
> Centauri, one minute to accelerate back up to 0.8 c toward Earth, and a
> final minute to accelerate down to back at Earth.
> If the accelerations alone account for the clock discrepancies, then there
> would be no need to go to Proxima Centauri at all. Pam could spend 4
> minutes whizzing around the solar system and get in all the same
> Is this what you are saying?
> It isn't what *I* was saying.
My point - also made (no doubt better) by Brent - was simply that there is
no reference frame in which Pam's path through space-time can be made
shorter than Sam's, and this is only possible *because of *the
accelerations. The accelerations themselves don't cause the ageing - we
could assume they're 1G and last through the entire trip, and that would
give (more or less) the same result with the clocks, though the
calculations would be a bit harder. If we assume that both Pam and Sam
experience the same acceleration throughout, the equivalence principle
means they age at the same rate due to the acceleration alone. However, and
this is the important point, the acceleration causes Pam's path through
space-time to be bent. For our own convenience we simplify the calculations
by assuming the acceleration period is negligible. (So we could perhaps
assume Pam is in a very, very robust space ship, and stuck inside a Larry
Niven style stasis field for a few minutes of million-G acceleration. Or
maybe she's an AI, or...)
It's just geometry - in all ref frames, Pam's path traces two sides of a
triangle and Sam's traces the third side. You can't have a triangle in
which two sides are shorter than the third side, and the clock discrepancy
is due to the length of the paths through space-time - the shorter path
experiences the longer time (the longer path "trades space for time").
It isn't rocket science! :-)
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