On Friday, October 18, 2024 at 4:09:18 PM UTC-6 Brent Meeker
wrote:
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
*
*Haven't you seen in texts the case of a train (the moving
frame) and the station (the fixed or stationary frame) used
to develop some of the basic concepts of relativity? Maybe
the LT or maybe time dilation. I distinctly recall this. I
didn't pull it out of the proverbial hat. Anyway, suppose we
have two frames in SR and each frame sees time dilation
manifested in the other frame. If they occurred at the same
time, this would be a paradox, *
