On 10/25/2024 2:44 AM, Alan Grayson 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. *
The set of points (t,x) representing a stationary light clock, two
vertical lines with 45deg "photon" lines bouncing between them, is
generated. This is the blue one. Then a Lorentz transform is applied
to the that set of points. Here's the LISP code I used:
*(defun gammma (v) (/ (sqrt (- 1.0 (* v v)))))
(defun lorentz-2d (v)
"Returns a function that takes a point (t,x) and
returns the transformed point (t',x')"
(lambda (p)
(let ((t0 (car p))
(x0 (cadr p))
(g (gammma v)))
(list (+ (* g t0) (* g (/ x0 v))) ;this is t'
(+ (* g x0) (* g v t0)))))) ;this is x'
(defun lorentz-trans (v points)
"Transform a set of points, e.g. a world-line"
(translate (mapcar (lorentz-2d v) points) (car points)))*
I don't know if you read LISP but in this case it's very simple. The
first line is just defining the gamma value for a given speed, in this
case v=0.5. The second function *lorentz-2d(v)* takes a speed and
returns a function *lambda(p)* that takes a point and returns the
point's coordinates in the frame moving at speed v. The third function
just applies that transform to every point on the given list *points*.
The *translate* function just moves the graph timewise so it lines up
with a given starting point.
*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. *
Right.
*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*
Right. A coordinate transform shouldn't change anything local. In this
case it is just distances and times that are different than one expects
from Euclidean space+time. Everyone in their own local inertial is /ex
hypothesi/ looking at an identical perfect clock.
Brent*
*
*
*
**
*It's a real muddle. I think you meant well, but you don't have
the maturity to contain your temper. Nonetheless, the photon
clock gave me a good idea, which I just wrote about. AG *
**
Because the speed of light is invariant the photon paths
are at unit slope inside all three clocks, so it is
easily seen why the relative motion makes the clock seem
slow although each clock is ticking at the same rate in
it's own reference frame. The red diagram is just the
blue diagram Lorentz transformed as it would be seen in
a frame moving the left at 0.5c, and the black diagram
as it would be seen from a frame moving to the right.
Brent
--
You received this message because you are subscribed to the
Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To view this discussion visit
https://groups.google.com/d/msgid/everything-list/12f98ce1-58fb-4dd9-b432-780991b177a6n%40googlegroups.com
<https://groups.google.com/d/msgid/everything-list/12f98ce1-58fb-4dd9-b432-780991b177a6n%40googlegroups.com?utm_medium=email&utm_source=footer>.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send
an email to [email protected].
To view this discussion visit
https://groups.google.com/d/msgid/everything-list/2435cf31-5053-4c30-90fc-5ebad44a3787n%40googlegroups.com
<https://groups.google.com/d/msgid/everything-list/2435cf31-5053-4c30-90fc-5ebad44a3787n%40googlegroups.com?utm_medium=email&utm_source=footer>.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion visit
https://groups.google.com/d/msgid/everything-list/b14922bd-9fa2-4fb7-9e2f-bc09dafdfea2%40gmail.com.
