[Physltest] [Phys-L] Re: Twins on cell phones

[John Denker <jsd@AV8N.COM>]

Rick Tarara wrote:
> During our discussion of the Twins Paradox--my version has one twin rush off
> to Alpha Seti 6  (30 ly) to pick up a pizza and returns an hour later on his
> clock--a student asked, what if they were talking to each other on cell
> phones (intergalactic versions) throughout the trip.  What does each twin
> experience.  I think I can figure out what the earth twin hears, but am
> unsure what is going on with the travelling twin since in his round-trip he
> would receive all 60 years of transmissions from his brother.

Executive summary:  Draw wavefronts on the spacetime diagram.
Keep count of the events where a wavefront crosses the
worldline of the travelling twin.

In more detail:  Suppose the mission begins at the beginning of
New Year's day.  And suppose the stay-at-home twin (Joe) sends
out an annual New Year's greeting every year while the other
twin (Moe) is gone.

An interesting event to consider is the arrival of Moe at the
pizza joint.  The year=0 greeting will have preceded Moe to
this location, but not by much, because the greeting travels
at the speed of light and Moe is only slightly slower.  At
this time in Joe's frame, he has already sent the year=30
greeting, but greetings #1 through #30 inclusive are strung
out in space, in transit.

During the return trip, Moe smashes through the wavefronts
corresponding to greeting #1 through #60 inclusive.

A diagram on which you can draw the wavefronts can be found
at:
   http://www.av8n.com/physics/twins.htm#fig-twins

Here endeth the theory discussion.

As a practical matter, the cell phones wouldn't work, because
the carrier frequency would be waaay outside the band the
cell phone was designed for.

But instead if you encoded the conversations using stone-age
amplitude modulation of a light beam, on the return trip
Moe would hear an extreme version of Alvin and the Chipmunks:
the words would seem to be spoken very quickly in a very
high squeaky voice.
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