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? Then they will see
time dilation in one another as they pass by AT THE SAME TIME AND PLACE.
Brent
*
*so the solution must be that the observations are at different times.
How can this be established? AG *
**
*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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