On 10/18/2024 5:50 PM, Alan Grayson wrote:
On Friday, October 18, 2024 at 5:19:58 PM UTC-6 Brent Meeker wrote:
On 10/18/2024 3:27 PM, Alan Grayson wrote:
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, *
*Are these frames moving relative to one another? *
*
*
*Well, the station obviously wasn't moving, but there were other
examples. It was a good text, but I can't recall its name. If I get
the energy, I'll try to find it on Amazon if it's still in print. AG *
*Then they will see time dilation in one another as they pass by
AT THE SAME TIME AND PLACE.
*
*Then, IMO, we have a paradox. How can an observer see another's
observer's clock running slower, and vice-versa, at the same time and
place? Years ago when we discussed this, you seemed to take the
position that breakdown in simultaneity could resolve the issue. Now
you seem to be backing off from this explanation. AG
*
*Because years ago it was not assumed they were at the same place, in
which case there can be no motion-independent assessment of their
relative rates.
Brent*
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