#### BELIEVE ME NOT! **-** **-** A SKEPTIC's GUIDE

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Like most "paradoxes," this one isn't. But it sure looks like one
at first glance. Suppose two identical twins part company at age twenty;
the first twin hops aboard a spaceship of *very* advanced design
and heads out for the distant stars, eventually travelling at velocities
very close to *c*, while the second twin stays home at rest.
They give each other going-away presents of identical watches
guaranteed to keep perfect time under all conditions.
At the midpoint of the voyage, while coasting (and therefore in an
inertial reference frame), the first twin looks back at Earth
with a *very* powerful telescope and observes the second twin's
wristwatch. After correcting for some truly illusory effects,
he concludes that the first twin's watch is running slower than his
and that his twin on Earth must be aging more slowly as well.
Meanwhile, the second twin, on Earth, is looking through *his*
telescope at the *first* twin's watch (aboard the spaceship)
and concludes that the *first* twin is suffering the effects
of time dilation and is consequently aging more slowly than *him!*
Who is right? Both, at that moment.

Aha! But now we can bring the first twin *home* after his
relativistic journey and *compare ages*. Certainly they can't
*both* be younger; this truly would create a logical paradox
that goes beyond the mere violation of common sense!

What happens? The first twin, who went travelling, is in fact
younger now than the twin who stayed home. The paradox is resolved
by a meticulous use of the LORENTZ TRANSFORMATIONS,
especially if we make use of the graphical gimmick of the
LIGHT CONE, to be discussed later.

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Jess H. Brewer -
Last modified: Mon Nov 23 10:57:58 PST 2015