To continue our discussion of the Lorentz transformations and
relativistic effects, we consider the famous ``twin paradox'' of
Peter and Paul. When they are old enough to drive a spaceship,
Paul flies away from earth at very high speed. Because Peter who
is left on the ground, sees Paul going so fast, all of Pauls'
clocks appear to go slower , from Peter's point of view. Of course,
Paul notices nothing unusual. After a while he returns and
finds that he is younger that Peter! Now some people might say
``heh, heh, heh, from the point of view of Paul, can't we say
that Peter was moving and should therefore appear to age more
slowly? By symmetry, the only possible result is that they
are both the same age when they meet''. But in order for them to
come back together and make a comparison, Paul must turn around
which involves decelerating and accelerating, and during that
period he is not in an inertial frame. This breaks the apparent
symmetry and so resolves the paradox.