Time dilation underlies the much-discussed clock paradox, which is often formulated as
the twin paradox in something like the following form: We imagine twins A and B who live
on Earth until B decides to go traveling through space at high speed. The simplifying
assumptions are that A remains at rest in an inertial frame
4
while B travels with constant
velocity to a distant object and immediately returns with constant velocity, the two
velocities having the same magnitude. (Note that velocity is a vector, which has both
magnitude and direction; speed is the magnitude of velocity. In the present case the
outgoing and incoming speeds are the same, but as the directions are necessarily different
so are the velocities.) Twin A applies the time-dilation formula of SR to both B’s outgoing
and incoming trips, and concludes that B must return younger than A. But then, to quote
Jammer (p. 165), ‘‘According to the relativity principle, however, one can just as well take
B’s point of view and regard A as the traveler and B at rest.’’ This results in B concluding
that A will be the younger twin upon their reunion, and hence the paradox.
Time dilation underlies the much-discussed clock paradox, which is often formulated asthe twin paradox in something like the following form: We imagine twins A and B who liveon Earth until B decides to go traveling through space at high speed. The simplifyingassumptions are that A remains at rest in an inertial frame4while B travels with constantvelocity to a distant object and immediately returns with constant velocity, the twovelocities having the same magnitude. (Note that velocity is a vector, which has bothmagnitude and direction; speed is the magnitude of velocity. In the present case theoutgoing and incoming speeds are the same, but as the directions are necessarily differentso are the velocities.) Twin A applies the time-dilation formula of SR to both B’s outgoingand incoming trips, and concludes that B must return younger than A. But then, to quoteJammer (p. 165), ‘‘According to the relativity principle, however, one can just as well takeB’s point of view and regard A as the traveler and B at rest.’’ This results in B concludingthat A will be the younger twin upon their reunion, and hence the paradox.
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