On Friday, October 25, 2024 at 4:58:47 PM UTC-6 Brent Meeker wrote:
On 10/25/2024 2:49 PM, Alan Grayson wrote:
On Friday, October 25, 2024 at 11:34:13 AM UTC-6 Jesse Mazer
wrote:
On Fri, Oct 25, 2024 at 5:44 AM Alan Grayson
<[email protected]> wrote:
On Friday, October 25, 2024 at 2:44:06 AM UTC-6
Brent Meeker wrote:
On 10/25/2024 1:36 AM, Alan Grayson wrote:
On Thursday, October 24, 2024 at 11:07:18 PM
UTC-6 Brent Meeker wrote:
On 10/24/2024 5:46 PM, Alan Grayson wrote:
On Thursday, October 24, 2024 at
1:30:32 PM UTC-6 Brent Meeker wrote:
Here's how a light-clock ticks in
when in motion. A light-clock is just
two perfect mirrors a fixed distance
apart with a photon bouncing back an
forth between them. It's a
hypothetical ideal clock for which the
effect of motion is easily visualized.
These are the spacetime diagrams of
three identical light-clocks moving at
_+_c relative to the blue one.
*Three clocks? Black diagram? If only this
was as clear as you claim. TY, AG*
*You can't handle more than two? The left
clock is black with a red photon. Is that
hard to comprehend? Didn't they teach
spacetime diagrams at your kindergarten?
Brent
*
*What makes you think you can teach? *
*That I have taught and my students came back
for more.*
*I can handle dozens of clocks. I know what a
spacetime diagram. It was taught in pre-school.
Why did you introduce a red photon? A joke
perhaps? How can a clock move at light speed? *
*None of the clocks in the diagram are moving at
light speed. The black one and the red one are
moving at 0.5c as the label says. What is it
you don't understand about this diagram?
Brent
*
*One thing among several that I don't understand is
how the LT is applied. For example, if we transform
from one frame to another, say in E&M, IIUC we get
what the fields will actually be measured by an
observer in the target or primed frame. (I assume
we're transferring from frame S to frame S'). But
when we use it to establish time dilation say, we
don't get what's actually measured in the target
frame, but rather how it appears from the pov of the
source or unprimed frame. Presumably, that's why you
say that after a LT, the internal situation in each
transformed frame remains unchanged (or something to
that effect). AG*
Can you give a concrete example? If you some
coordinate-based facts in frame S (source frame) and use
the Lorentz transformation to get to frame S' (target
frame), the result should be exactly what is measured in
the target frame S' using their own system of rulers and
clocks at rest relative to themselves (with their own
clocks synchronized by the Einstein synchronization
convention).
Jesse
*Glad you asked that question. Yes, this is what I expect
when we use the LT. We measure some observable in S, use the
LT to calculate its value in S', and this what an observer
in S' will measure. But notice this, say for length
contraction. Whereas from the pov of S, a moving rod shrinks
as calculated and viewed from S, the observer in S' doesn't
measure the rod as shortened! This is why I claim that the
LT sometimes just tells how things appear in the source
frame S, but not what an observer in S' actually measures. AG*
*Yes, although "appear" can be misleading when you consider
things moving near light speed. More accurate is "measure",
using the invariant speed of light.*
*
*
*On another point concerning time dilation; I demonstrated
that given two inertial frames with relative velocity v < c,
it's easy to synchronize clocks in both frames provided we
know the distance of clocks from the location of
juxtaposition, but I was mistaken in concluding this alone
shows time dilation doesn't exist. It does, because we
insist on using the LT as the only transformation between
these frames, and the reason we do this is because the LT is
presumably the only transformation that guarantees the
invariance of the velocity of light. So time dilation is, so
to speak, the price we pay for imposing the invariance of
the velocity of light on our frame transformation. But I
remain unclear how a breakdown in simultaneity resolves the
apparent paradox of two frames viewing a passing clock in
another frame, as running slower than its own clock. AG*
*Look at the diagram I provided. At the bottom (t=0) the
three clocks are passing by one another. The blue clock sees
the other two as running slower.*
*
*
*Finally, for Brent, a word about "snarky". _You_ get snarky
when I don't understand something, like your "kindergarten"
reference in one of your recent replies. And occasionally I
am correct in my criticisms. Moreover, if you have typos in
your explanation of your graph, you shouldn't be surprised
if they make it hard to understand your graphical
explanation of time dilation. AG*
*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*
