A way I have found effective for explaining this to students is to
imagine two infinite conveyor belts moving rapidly in opposite
directions. The two belts are side-by-side and pass right next to the
twins' house here on earth. The first twin steps onto one of the belts
and is whisked into space. The second twin stays at home. At some
point the first twin needs to come home. To get home she has to step
off the belt she originally stepped on, and onto the other belt that
will take her home.
We have three obvious frames of reference: earth, belt 1, belt 2. The
twin who stayed home stayed in one frame the whole time. The twin who
traveled experienced all three frames, and had to make two frame jumps.
Clearly the experiment is not symmetric for the two.
We could make it symmetric. The twins could simultaneously step onto
opposite belts. They would stay on their respective belts for an
agreed-upon time duration that each would measure with his/her own
clock, then each would jump to the other belt and come home.
In the first case (one twin travels and changes reference frames) there
would be an age difference when they are reunited. In the second case
there would not be an age difference when they are reunited.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.