C7 Twin Paradox as Seen By Epstein
The following story has disconcerted thinkers time and again: Twins A and B both study space travel. At age 25 B sets off on a prolonged space journey with v = 12/13 • c, while A serves in the control center on earth. After 26 years earth time A is precisely 51 years old, as his brother B returns to earth from his journey. How old is B?
We want to ignore the short acceleration phases when starting, reversing flight direction and landing and assume that B flew away for 13 years with velocity v and afterwards flew back 13 years with velocity -v. The radical term, cos (φ), is 5/13 for our value of v/c. Therefore, for each of the outbound flight and the return flight B aged only 5 years. On his return to earth he is therefore only 35 years old, while his twin brother is celebrating his fifty-first.
“From the point of view of the space traveler is everything reversed, and thus A must be younger than B! Thus the whistle is blown on this swindle of relativity theory.” Heated lampoons against the STR are expressed thus or similarly. Actually, however, the whole arrangement is asymmetrical: Only A is the whole time at rest in an inertial frame, while B is exposed in different phases of his journey to accelerations. During the non-accelerated flight phases B actually has the impression that his brother A works somewhat slowly. The Epstein diagram can present the whole situation beautifully:
The diagram on the left corresponds to the text while the one on the right is somewhat more realistic, since it considers the acceleration phases. It is important that the paths through space-time for both twins are equivalently long: If one straightens the red thread, then one has a length of exactly 26 squares from O to B, and is thus the same length as OA. Since B claims a part of the space-time segment for the spatial distance there remains less for his movement in time. It really is so simple!
Compare this representation of the twin paradox with others which use Minkowski diagrams, e.g. in [18-64] or [19-146f] !