starship-design: Re: The "So-called" Twin Paradox

[Steve VanDevender <stevev@efn.org>]

Timothy van der Linden writes:
 > Hi Rex,
 > 
 > I had wondered why you had not continued the discussion about the Twin
 > Paradox, since I know your ideas which did not agree with what was written
 > in Steve (VanDevender)'s last letter from 11/29.

Unfortunately it's because both Rex and I were oversimplifying a bit.  I
think we actually still agree, but Rex has certainly pointed out some of
the subtleties required in a more complete analysis of the problem, and
required bringing in some concepts from general relativity.

 > >What difference in their experiences can be used to tell that Paul
 > >will be the younger?  (We can turn Peter's house upside down at
 > >the one-quarter and three-quarter "turnover" times, etc.)
 > >
 > >If neither looks out the window, how can they explain the
 > >difference in their "trip" times?
 > 
 > Probably one can always "trick" someone in a local environment. So to find
 > the symmetry breaking factor in the Twin Paradox you *need* to look at a
 > global (non-homogeneous) environment.
 > 
 > This is why it is called "relativity", this word almost inherently means
 > comparison between global points.

Unfortunately relativity does not recognize any sort of global reference
frame, and just because Peter and Paul might think they are in identical
environments doesn't mean that they will experience the same amount of
time.

In order to bring out more of the subtleties involved in Rex's
formulation of the Twin Paradox, I postulated a third, inertial observer
who would be best equipped to measure the differences in Paul's and
Peter's experiences.  In a sense, Rex's formulation only puts blinders
on Peter and Paul, preventing them from making the observations that
they could make entirely between themselves to determine who should age
less.  If we remove these unreasonable restrictions then they could
easily determine between themselves who should have aged least when they
meet again.  However, even with their blinders on, we can also postulate
any number of additional observers, free to make the measurements that
Peter and Paul cannot, who would all agree that Paul, the traveling
twin, should age less because his path through spacetime has more
curvature, and who will all agree on the amount of proper time that both
Paul and Peter experience between Paul's departure and return.