Myths
Absolute Space
Points of View
Twin Paradox
Einstein's Train
Andromeda Paradox
Time in Spacetime
Clocks & Time
Velocity of Light
The Twin Paradox
Under Special Relativity, all motion is relative and relative motion gives rise to the dilation of time (as described by the Lorentz transformation). It is commonly assumed that the time dilation is symmetrical. This leads to the mistaken belief that there is a "paradox", which is illustrated by a well known thought experiment...
There are two twins, one of whom stays on the Earth. The other twin travels in a spaceship at a very high velocity to a distant planet orbiting another sun. The spaceship then turns round and travels back to the Earth. From the point of view of the twin on Earth, less time would pass for the traveller than for himself. So when he returned, the traveller would be younger than the twin on Earth. Indeed if the traveller traveled at .866 c (86.6% of the velocity of light) he would experience half the time elapse of his twin. So if they were 20 years old at the start, and the traveller was 50 when he returned, the twin who stayed on the Earth would be 80 years old.
However, that only tells us what takes place from the point of view of the twin who stays on the Earth. If the time dilation is symmetrical, then, from the point of view of the traveller, he is stationary in his rest frame and the Earth, and his twin, recede very fast from him, then return. So, from the point of view of the traveller, the twin on Earth should experience less time passing than the traveller. I.e. the traveller should be 80 and the twin on the Earth only 50 years old!
Paul Langevin's Explanation of the Paradox
It is clear that the assumption that the time dilation is symmetrical leads to an impossible situation, hence the paradox. It is this assumption that Paul Langevin addressed in 1911. He suggested that, as the traveller underwent acceleration at the beginning, turnaround and end of the journey, his rest frame was not inertial. Whereas, the twin on Earth did not undergo acceleration, therefore his rest frame was inertial. Thus the situation is not symmetrical. In effect, this meant that the traveller was actually moving with respect to the Earth.
Note: The suggestion that the traveller is actually moving is not intended to imply or require the existence of an absolute state of rest against which the motion occurs. It merely describes an asymmetry between the motion of the Earth and that of the traveller with respect to the Earth.
Further details of the twin paradox, Paul Langevin's interpreation, and a worked example may be found here.
