3.2.7 The Twin Paradox
In the first paper on relativity in 1905, Einstein concluded that a moving clock ticks slower. If two clocks were synchronized together, and then one of them was moved away and brought back at relativistic speed, it would be found to be lagging behind the stationary clock. In 1911, he elaborated further on this result by saying:
“If we placed a living organism in a box ... one could arrange that the organism, after any arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had already long since given way to new generations. For the moving organism, the lengthy time of the journey was a mere instant, provided the motion took place with approximately the speed of light.” Resnick (1968)
Other scientists quickly noticed that if a man made such a relativistic travel, while his twin stayed at home, then when the traveler returns he finds his twin brother much aged compared to himself. The paradox is that, in relativity, either twin could regard the other as the traveler, in which case each should find the other younger. For example if the traveler make a trip at a Lorentz factor of
equivalent to his speeding being
of the speed of light, and he remains in a projectile for one year of his time, and then reverses direction. Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth.
This contention is based on the wrong assumption that the situations of the twin are symmetrical and interchangeable, but other versions get around this by supposing that keep sending signals to each other at a constant rate, but this also means that we need to include the relativistic Doppler shift which affects the signal rates. The asymmetry that occurred because only the traveler underwent acceleration, can be removed by introducing the “three-brother” approach, where the traveling twin transfers his clock reading to a third one, traveling in the opposite direction. Another way of avoiding acceleration effects is the use of the relativistic Doppler effect.
Einstein called the result of such relativistic travel “peculiar” but he did not consider it to be self-contradictory and does not constitute any challenge to the self-consistency of relativistic physics. This result appears puzzling because of incorrect and naive application of time dilation and the principle of relativity. Time dilation has been later verified experimentally by precise measurements of atomic clocks flown in aircraft and satellites.