According to the theory of relativity, time passes more slowly for someone moving away from the Earth at a certain speed (relevant only if approaching the speed of light). Traditionally, it is always said that a space traveler has remained relatively young compared to those who have stayed at home.
However, the same theory of relativity also says that we can just as well say that the earth moves at a certain speed in the opposite direction of the space traveler. So who is aging the most compared to whom?
Answer
It’s not that you can swap the roles of the stay-at-home and the traveler on the grounds that they move opposite each other at a constant speed. They don’t. On the outward journey, the traveler moves away from Earth, but on the return journey, toward Earth. The traveler thus makes use of two different frames of reference, each of which can be exchanged symmetrically with the frame of the earth, but not together. The stay-at-home person always stays in his frame that moves at a constant speed, but the traveler does not do this. He has to switch frames halfway through, at the furthest point of his journey. He has to slow down, turn around and accelerate again. Even if he does this instantaneously, the situation is not symmetrical. The traveler uses two frames that move opposite. The stay at home will be older than the traveler at the reunion.
You understand that this forum does not offer the possibility to offer many formulas, and in such a case I try to offer the questioner a link on the internet where the necessary formulas, graphs… are located. Have a look at:
http://www.einsteins-theory-of-relativity-4engineers.com/twin-paradox-2.html
There the problem is looked at from the perspective of the stay-at-home person. The earth is thus spatially stationary, and the traveler makes a forward movement and a return movement.
But then it is also looked at from ONE OF THE two frames of the traveler, namely the frame of reference of his return. Now the stayer at home moves all the time with a constant speed, and the traveler first moves with a double speed (= his outward journey, opposite the moving frame of his return journey) and then stands still (his return journey). In both cases the same conclusion is reached: the stay-at-home person is older than the traveler in the end.
Otherwise, surf to the keywords “twin paradox”.
However, the situation of our twins is not symmetrically interchangeable, because one always remains in its own frame, and the other changes frame of reference halfway.
Answered by
prof.dr. Paul Hellings
Department of Mathematics, Fac. IIW, KU Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/
.