On 10/18/2024 1:11 PM, Alan Grayson wrote:
On Friday, October 18, 2024 at 1:12:25 PM UTC-6 Brent Meeker wrote:
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.
*I am unclear what "now" means. How is it defined? Can't we use the
round-trip light time to establish that the frames which will
eventually be moving toward each other, are initially at rest with
respect to each other, at a known fixed distance, and use it to
synchronize their clocks, *
*So what? They won't be synchronized in any reference frame moving
relative to them. You can arbitrarily foliate flat space time to define
comparisons as "now", but it has no physical significance. You're
unclear on what "now" means because it doesn't mean anything.
*
*and to then apply the same impulse at the same time to both, to get
the frames moving symmetrically? This doesn't seem ambiguous. Also,
using the third clock, we can establish, as is done in relativity
texts, that clocks in moving frames have slower rates than clocks in
stationary frames.*
*I don't know where you get this stuff. No relativity text I know even
recognizes the concept of "stationary". It's called "relativity" for a
reason!
Brent
*
*Using this fact, and the fact that when the moving frames meet, no
time contraction is noticed (since these clocks will show the same
time), we have another contradiction. AG *
> 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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