The Special Theory of Relativity 131
each other do not empirically observe the same things. The unstable
meson only lives 10-8 sec in the frame in which it is at rest and it really
lives 10-8/ 1 −v^2 /c^2 sec in the stationary frame in which its velocity
is v. The quantities that observers measure are only relative to their
particular frame of reference. One cannot make an absolute comparison.
Both observers will really observe the other’s clock as slowing down.
The phenomenon of relativistic time dilation might, some day, make
interstellar space travel possible. The closest star, Alpha Centauri, is four
light years away. A light year is a unit of length equal to the distance that
a beam of light travels in one year or about nine trillion kilometers. This
means that, since the velocity of light is the fastest speed attainable no
matter how proficient our technology became, it would take a minimum
of eight years to send an astronaut to Alpha Centauri and back. Since
there are only a few stars in this corner of our Milky Way galaxy that are
within fifty light years, the minimum time to send a space craft to most
stars would be 100 years or more, which is greater than the lifetime of
even our healthiest astronauts. Even if we were to develop a space craft
which could travel at velocities near the speed of light, it does not seem
that it would be possible to send a man to a distant star and have him live
long enough to return alive.
Because of the relativistic time dilation, however, this is actually
possible. The reason for this is that, while the astronaut is traveling to
a distant star at a velocity close to c, his clock would slow down with
respect to an Earth clock. So, for example, if he was traveling at 0.999c
to a star 99.9 light years away, he would require 100 Earth years to make
the journey to the star. In his own frame of reference, however, he would
age only 4.47 years. (These two times are related by the formulae t =
to/ 1 −v^2 /c^2 , where t = 100 years, to = 4.47 years and v = 0.999c).
One might wonder how it is possible for the astronaut to travel 99.9
light years in only 4.47 years. The reason is, that in his frame of
reference, the distance to the star is contracted by exactly the same factor
that his time is dilated with respect to the Earth and therefore he sees that
the star is only 4.46 light years away and is traveling towards him at
0.999c. Therefore, it takes only 4.47 years for the journey to the distant
star.
The astronaut will only require 8.94 years, according to his clocks, in
order to make the round trip to the star and back again. However, when
he returns to Earth, he will discover that, during the approximately nine
years he was away according to his clock, 100 years had elapsed on