Let’s get one more perspective on the twin paradox. It is always interesting
to ask what each twin sees during the trip. Now, note that what you
actually see has to do with light rays, and with when a bit of light happens
to reach your eye. So, to study this question, we should study light rays
sent from one twin to the other. We will again have Gaston go off to
Alpha Centauri (4 light-years away) and back at .8c while Alphonse stays
at home.Now let’s figure out what Alphonse sees. Draw another spacetime
diagram for the trip in some inertial frame (again, Alphonse’s frame
is the easiest one to use), but this time suppose that Gaston emits
one light ray every year (according to his own proper time – you may
have to calculate this). What does this diagram tell you about what
Alphonse sees if he watches Gaston through a telescope during the
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