From: utzoo!decvax!cca!gwyn@BRL@sri-unix
Newsgroups: net.physics
Title: Re:  paradoxical twins
Article-I.D.: sri-unix.3306
Posted: Thu Sep 16 20:11:53 1982
Received: Fri Sep 17 03:29:37 1982

From:     Doug Gwyn 
In all discussions like this, it is important to specify carefully
just what is measured and how.  A diagram often helps, if you don't
take any distances on it as "absolute".

Acceleration is not relevant.  The twins paradox can be demonstrated
by using three reference frames, one "stationary" (earth-bound) and
two moving in opposite directions with the same speed with respect
to the "stationary" frame.  Then you can (1) transfer your attention
from the earth-bound frame to an "outward-moving" one, (2) after a
suitable interval transfer your attention to an "inward-moving" frame,
and finally (3) transfer your attention to the starting point when it
arrives.  This thought-experiment is equivalent to the space-flying
twin's itinerary, but all accelerations have been removed so that
any time-dilation cannot be ascribed to an object being affected by
pseudo-gravity forces or whatever.

The key to the paradox when cast in this form is the availability of
suitable "universal" time references in each frame; e.g. use a maser
clock or something similar.  Given such clocks, the time dilation
claimed for the twin paradox does in fact occur in accordance with
special relativity.  Yet none of the clocks ever feels an acceleration.

Special relativity does not answer the question, "Why can't the
earth-bound observer, by symmetry, claim HE is younger than the space
traveler?", except by pointing out that the situation is NOT symmetrical
since by no stretch of the imagination can the space traveler (out and
back) consider that he is constantly in an "inertial frame".  In fact,
a minimum of TWO inertial frames must be used, with a changeover in
point of reference at the turn-around point of the journey.
Accompanying this change of viewpoint, one must also insist that the
REST OF THE UNIVERSE has suddenly started moving differently.
Quite apart from questions of Mach's principle in General Relativity,
the introduction of an "outside force" acting on the space traveler
to turn him around (or, equivalently, to give the rest of the universe
a shove) violates symmetry in a fundamental way.

The detailed treatment of the problem necessarily involves agents and
effects outside the province of Special Relativity.  However, the
conventional analysis from the viewpoint of the earth-bound frame
fits within the theory's constraints and is therefore accurate.