132 The Poetry of Physics and The Physics of Poetry
Earth. The astronaut will have aged only nine years but all of his friends
will have aged 100 years and hence, are all dead. The astronaut will have
experienced not only a round trip to a star 100 light years away, but he
will also have experienced traveling 91 years into the future. The exploits
of our hypothetical space traveler have given rise to a famous paradox
known as the twin paradox. Let us assume that our space traveler has a
twin brother who remains on Earth during his flight. The twin on Earth
will expect his brother in space to age at a slower rate as a result of his
motion, as we explained above. The formulators of the twin paradox
maintain, however, that the space traveler will also expect his brother on
Earth to age at a slower rate. According to their argument, during his
flight the astronaut, in his frame of reference, will see his brother on
Earth moving away from him and then towards him. As a consequence,
he will observe his brother’s clock slowing down and hence, he, too, will
expect his brother on Earth to age at a slower rate than himself.
One is faced with a paradox. Which brother will actually be the
younger when the two brothers are reunited back on Earth? The brother
who actually traveled to the star and came back to Earth will be the
younger. In resolving the paradox, we must take into consideration the
effect of the traveler’s motion on his observations. The paradox is only
an apparent one because it is based on an assumption, which is not valid.
When we considered the astronaut’s observations of the Earth-bound
clocks, we assumed that his observations were made in a frame of
reference in uniform motion. This assumption is not valid because, in
order for the astronaut to return to Earth, he must change directions in the
middle of his trip. This naturally involves acceleration or non-uniform
motion.
The astronaut was no longer in a non-accelerating frame of reference
during the time that he is turning around and as a result, his observations
of time on the Earth are affected. It is true that, while he is traveling at a
constant velocity, he observes the Earth clocks slowing down with
respect to his. During the time that he is turning around, however, he
observes the Earth clocks as speeding up. Although the time, in his frame
to reverse directions might not take very long, it is during this period that
he observes the passage on Earth of 91 years that will separate the
earthbound clocks from his clock when he returns to Earth.
The twin paradox has also been resolved experimentally. We
mentioned earlier that mesons, which are moving at a constant velocity,
take longer to decay in the laboratory frame. The increase of the