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##

The Twin Paradox

The previous subsection illustrates a curious feature of Special
Relativity that, at first glance seems paradoxical. We argued that
astronauts could travel to a star four light years from Earth and only
age two months if they traveled at 0.999*c*. Meanwhile the people
back on Earth age the full eight years. This seems to contradict one
of the basic postulates of Special Relativity, namely the relativity
of uniform motion. After all, time dilation should be symmetrical, so
how is it that the astronauts age less during the journey instead of
the people on Earth. In fact the prediction that the astronauts age
less is the correct one. It has been experimentally verified,
on a smaller scale, but putting very accurate atomic clocks in orbit
around the Earth, and comparing them to their Earthbound counterparts
after the journey. The clocks that went into orbit were slower in
accordance with the predictions of Special Relativity.
This dilemma highlights a limitation of the Special Theory of
Relativity that we have already alluded to. It only applies to
observers in uniform motion, and not to accelerated frames. In order
for astronauts to go to a distance star, and return to compare clocks
with Earthbound observers, the astronauts' spaceship must accelerate
to near light speeds, decelerate once the reach the star, and the
repeat the process in the other direction. While they are
accelerating, the rules of Special Relativity don't apply, and the
symmetry between the astronauts and the Earthbound observers breaks
down. (This applies to the atomic clocks in orbit as well.) A
detailed examination of the problem therefore requires us to go beyond
Special Relativity (to General Relativity), with the result that time
actually slows down in accelerated frames of reference. However, it
turns out that the calculation we did in the previous sub-section is
approximately correct. We get nearly the right answer for the
difference in aging of the astronauts by ignoring the acceleration and
just taking into account time dilation on the forward and return
journeys. Thus, there is no ``paradox'' associated with this effect. As
with most paradoxes, it merely points to a limitation of the theory
under consideration.

** Next:** Tachyons and Time Travel
**Up:** Other Implications of Special
** Previous:** Space Travel
*modtech@theory.uwinnipeg.ca *

1999-09-29