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

[John Denker <jsd@AV8N.COM>]

RAUBER, JOEL wrote:
> When light is blue shifted, you don't know if the object is moving
> towards you, or if you are moving towards the object.

I completely agree.

My remarks a few minutes ago on this topic are somewhere
between unclear and wrong.  Let me attempt some repairs:

As I said, you can solve the problem by drawing the wavefronts
on a spacetime diagram.  Joe's worldline is the green line in
   http://www.av8n.com/physics/twins.htm
while Moe's wordline is drawn in red then blue.  Messages
sent by Joe follow lightlike lines, i.e. 45 degree lines,
parallel to the dashed black line.

True fact:  on the outbound leg, both parties observe a redshift.
True fact:  on the inbound leg, both parties observe a blueshift.

The principles of relativity tell us that on a moment-by-moment
basis, there is nothing on the inbound leg or the outbound
leg that can tell us which twin stayed behind and which
went travelling.  On the other hand, Joe receives (according
to him) 29+ years of red-shiftes signals (send byMoe during
the outbound leg) followed by a comparatively very short i.e.
30-minute burst of blue-shifted signals (sent by Moe during
the inbound leg).  Moe's experience is very different,
of course;  he receives 30 minutes of red-shifted signals
followed by 30 minutes of blue-shifted signals.

To repeat, observing the redshift and/or blueshift at one or
two moments doesn't give you a complete description of what's
going on.  It's part of the story, but not the crux of the
story.

As always, the crux of the 'twins' scenario is the big turnaround
at the mid-point of Moe's mission.

 From a GR point of view, during the turnaround maneuver Joe's
clocks beat very fast (as seen in Moe's frame) because of
the acceleration, which is the same thing as saying Moe is at
the bottom of a very deep gravitational potential well.  This
is when (according to Moe) Joe ages so much.

Interestingly, if the turnaround is accomplished fairly quickly,
the great aging of Joe does not cause Moe to receive very many
messages during the turnaround.  Most of the message wavefront
lightcones cross Moe's path on the blue (inbound) leg.

You can get the same answer using only SR, using the method of
instanteously comoving frames, as discussed at
   http://www.av8n.com/physics/twins.htm
Somehow, in the interval between the outbound leg and the
inbound leg, there must be a switch in what Moe considers
'his' reference frame.  This switch introduces a huge
non-simultaneity at a distance.
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