Answer to Question #99742 in Mechanics | Relativity for AbdulRehman

Question

In relativity, it is always nice to look at things from several different ref-
erence frames. Let’s look at the same trip of Gaston to Alpha Centauri
and back, with Alphonse staying at home. This time, though, draw the
spacetime diagram using the inertial reference frame that Gaston had on
his outward trip. Using this frame of reference, calculate the total proper
time that elapses for both Alphonse and Gaston between the event where
Gaston leaves Alphonse and the event where they rejoin.

Answer 1

A beautiful diagram of the described situation for Gaston moving at 0.5c and the time measured by Alphonse of 20 years can be found in "Correct Resolution of the Twin Paradox" by Michael Huemer:

In this situation, the proper time experience by Gaston can be calculated according to the following equation:

$T'=20\sqrt{1-0.5^2}=17.32\text{ years.}$