On Jan 19, 2006, at 6:35 PM, Stephen A. Lawrence wrote:
[snip a lot of good stuff]
http://www.physicsinsights.org/linear_twins.html
[snip a lot more]
Actually I have a lot of interest but no time to really dig into
this. However, I must say that it does seem to me that the issues
are simplified by looking at things one dimensionally, and such a
simplified system is sufficient to examine the critical issues. The
difficult math seems to me to disappear in a flash! 8^) No longer
are fancy transforms and distance functions required. Further, we
can look at each flash from earth as a single photon.
As the traveler departs in a straight line away from the earth
transmission point, and distance from earth gets greater, the photons
arrive further apart in time, and red shifted for the same reason,
the wave peaks arrive slower, thus time back on earth appears to the
traveler to slow down. However, no matter what kinds of
accelerations the traveler has experienced or is experiencing, he
keeps receiving his regular periodic set of photons from earth. The
only thing that changes are the time increments sensed by the
traveler between photons, and their colors. No matter where he is or
how far he goes or how he accelerates, assuming a fast rate of photon
transmission from earth, there are always photons in route from earth
to the traveler. As the traveler turns about, and returns, the rate
he absorbs those photons increases, and he sees a blue shift as well,
for the same reason, i.e. the wave peaks arrive faster. The earth
increments its clock each time a photon is transmitted. The traveler
can increment his on board "earth clock" each time he receives a
photon. He can use a similar clock to the earth clock to keep track
of his local time.
As the traveler closes the distance to earth on the return trip,
fewer photons are in flight with passing time. Assuming the
traveler's on board clock was not affected by his acceleration, his
"earth time" clock and local clock will come back in
synchronization. Further, his earth time clock and earth's clock
will be in perfect synchronization upon arrival. If not, the number
of photons sent and the number received can not match, which is
nonsense. The only other way for the traveler's clock to not agree
with the earth clock, or his own "earth time" clock for that matter,
is for the traveler's clock to have been affected by the acceleration.
Horace Heffner
