🚀 go-pugleaf

There is no twin paradox in special relativity, as I suppose most
of the posters have said.  Here's an approach to understanding
the phenomenon and explaining it to students.

Suppose on twin travels to Alpha Centauri, 4 light years away
at half the speed of light and immediately returns at the same
speed.  Consider the event of his arriving At Alpha Centauri.

What event on earth is simultaneous with it?  According to
special relativity, this depends on the co-ordinate system.
There are three relevant co-ordinate systems, that of the
stay-at-home twin, one moving at half the speed of light
from earth in the direction of Alpha Centauri, and one moving
at half the speed of light in the opposite direction.

1. In the stay-at-home system, the traveler's arrival at Alpha Centauri is
eight years after his departure from earth.

2. In the going-out system, the arrival is  4 sqrt(3) years have
elapsed, because in that system, Alpha Centauri wasn't 4 light years
from earth but only 2 sqrt(3) light years.  The stay-at-home twin
has aged only that amount of time in that co-ordinate system.

3. In the coming-back system, the clock at home reads 16 - 4 sqrt(3)
years when the traveller turns around at Alpha Centauri.

In this approximation we imagine the traveller to turn around
instantaneously, i.e. to switch from going at half light speed
towards alpha centauri to going at half light speed back towards
Earth.  Taking into account a finite acceleration would make the
problem somewhat more complicated but change the numbers only
a small amount if the acceleration was high enough.  If you don't
like high accelerations, consider a longer journey in which the
time for reversal of direction would be smaller in comparison
with the time spent going at constant speed.

To get the aging of the traveller, not that he spent 4 sqrt(3)
years going out by his own watch and the same time coming back,
so he is 8 sqrt(3) years older when he arrrives at Earth.  His
twin is 16 years older.

The apparent symmetry between the twins, which has misled many people
into believing there is a paradox, is broken by the fact that
the travelling twin is involved with two co-ordinate systems,
which differ in what Earth event is simultaneous with the
turn-around at Alpha Centauri.
--
John McCarthy, Computer Science Department, Stanford, CA 94305
*
He who refuses to do arithmetic is doomed to talk nonsense.