On 10/18/2024 4:00 AM, Alan Grayson wrote:
Yes, literally, last night, I had a dream wherein I was describing a
physics problem which puzzles me, to three physicists. It went like
this. First I postulated three inertial frames positioned on a
straight line, with clocks synchronized, and two traveling toward each
other at the same constant velocity v, and the third at rest, located
midway between the moving frames. I didn't explain how these frames
could be constructed, but it's clear that it's possible. Now maybe I
am falling into a Newtonian error, but ISTM that the moving frames
will pass each other at the location of the rest frame, and all
observers will be able to view all three clocks since they're
juxtaposed. Consequently, all three clocks will be seen as indicating
the same time. Note that the stationary frame represents the
stationary train platform in texts which establish the clock rates in
moving frames (represented by moving trains) are slower when compared
to stationary frames. In the model proposed in my dream, it's hard to
claim that the three clocks indicate different times since the moving
clocks are synchronized and their motions are symmetric. So, there
doesn't appear to be any differential rates for these clocks. Maybe
use of the LT will change this situation, since it guarantees the
invariance of the SoL, but it's hard to see why the clock readings for
the moving frames could be different from each other, given the
symmetry of their motion.
It's not the an symmetry of their motion, it's the symmetry of how you
define "now". When the 3 clocks are together momentarily they can all
be set to the same time and there's no ambiguity about it. But once they
are apart there is no unambiguous way to compare them. Whether they
read the same value "at the same" is ambiguous because "at the same
time" depends on the state of motion of whoever is judging the times to
be the same. And this is not just because of the relative motion of the
clocks. There is the same ambiguity even if the clocks are stationary
relative to one another but are at different locations.
In the dream, the physicists were baffled and couldn't resolve the
issue, which, to repeat, is how the clock rates for the moving frames
could indicate that each clock in a moving frame, was ticking slower
than its symmetric other. AG --
Which I already explained how to prove to yourself.
Brent
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