On 10/26/2024 12:06 AM, Alan Grayson wrote:
*So that one typo, which was correct elsewhere made it
muddled for you?
*
*In part yes. When I think an author doesn't know what he's
expounding about, I lose interest. Also, although I was a
software engineer at JPL, I don't know LISP, so it would be
hard to see what assumptions you made in generating the
plot. And the plot is claimed to establish time dilation,
and I'm not sure how you developed the width of the blue
path say, to show time passes more rapidly compared to the
other plots. AG*
*I just assumed a width for the blue path. All that
determines is how fast the light clock ticks. Then the other
two light clock world lines were generated by point-by-point
application of the given Lorentz transform. So I showed the
two clocks moving relative to blue ticked more slowly, not
the other way around. Do you not see that the bouncing
photon hits the mirror less often in red's clock as measured
in blue's frame.
*
*Yes, so that implies tics are less frequent in red's clock,
compared to blue's clock, so the time rate for red is less than
blue, which is what I in effect posted -- that blue clock tics
more rapidly than red clock. Why do you fail to understand what I
wrote? AG
*
*I understood it, but it read as if you didn't realize red was
just the transform of blue and it is in the clock's own frame it
runs fastest. You wrote as though I "developed the width of the
blue path say, to show time passes more rapidly" whereas I chose
it arbitrarily and derived the other two.
Brent
*
*Are you saying the red clock is in the same frame as the blue clock?
I missed that point. *
No, it's obviously moving relative to the blue clock.
*Why did you model it this way, instead of just using two frames, one
at rest, the other moving? *
Because I was addressing a different question. I didn't create it just
for you.
*Why does the red clock's photon cross at right angles, but this isn't
so for the blue clock? Were they arbitrary choices? AG*
*All the photon lines are at 45deg because the speed of light is
invariant; its 1.0c in the diagram for blue. If I transformed to red's
frame then red would look just like blue does in this diagram.
Brent
*
*
*
*This discussion began with my claim that there could be a clock
paradox, defined by two clocks, each running slower than the other. If
such a paradox existed, it would be impossible to produce a plot which
would show it. So, what exactly does your plot show; that the LT
establishes that a moving clock runs slower than a stationary clock?
This is not something I disputed.** I don't see how your plot resolves
a possible paradox. **AG*
*A failure of imagination. As drawn in blues frame, red is obviously
running slower than blue. But suppose we transform to red's frame.
Then red would go straight up the diagram taking the place of blue. We
know this because red was generated from blue by the inverse transform.
Then blue will be transformed to black. And in that picture blue will
obviously be slower than red.
Brent
*
*
*
*I thought that if I could synchronize clocks in two inertial frames
without the LT, I could establish the paradox. But now I don't think
this is true. What is true, is that the LT causes time dilation, and
is, so to speak, the price we pay to guarantee frame invariance of the
SoL. AG*
*
*
*For Jesse; I looked up Einstein's method for determining simultaneous
events. IIUC, it involves two clocks and a light source midway between
them to produce simultaneous events, with the conclusion that
simultaneity exists in the rest frame of the clocks, but not in a
moving frame. I didn't use it to establish that clocks in two inertial
frames can be synchronized. Neither did I deny it. I don't see why you
think there's something awry that I didn't use it. AG*
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