On Saturday, October 26, 2024 at 8:44:51 PM UTC-6 Jesse Mazer wrote:
On Sat, Oct 26, 2024 at 3:06 AM Alan Grayson <[email protected]>
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. WHY DID YOU MODEL IT THIS WAY, INSTEAD OF JUST
USING TWO FRAMES, ONE AT REST, THE OTHER MOVING? 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
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
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
Again, the problem is that you simply haven't clearly laid out what
your procedure is for synchronizing different clocks at rest in the
*same* frame, so your summary of the experiment you want to set up is
too vague without that information. Are all the A clocks synchronized
with one another using the Einstein synchronization procedure in the A
frame, and then the B clocks set with reference to whichever A clock
they are next to at some moment? Or is just one B clock set by
reference to the A clock it's next to, and the other B clocks
synchronized with that first B clock using the Einstein
synchronization procedure in the B frame? Or some other option?
Jesse
I ASSUMED THAT IF THE TWO JUXTAPOSED CLOCKS WERE SET TO T=0, AND I
SPECIFIED HOW ANY OTHER CLOCK IN EITHER FRAME COULD BE SYNCHRONIZED TO
THOSE TWO CLOCKS, ONE CAN INFER HOW TO SYNCHRONIZE ANY OTHER CLOCK, IN
ANY KNOWN DISTANCE TO ANY PREVIOUSLY SYNCHRONIZED CLOCK, AND
SYNCHRONIZE THAT CLOCK. I WAS TRYING TO IMAGINE A SCHEME FOR
SYNCHRONIZING ALL HYPOTHETICAL CLOCKS IN BOTH FRAMES. IF I COULD DO
THIS, I WAS THINKING I'D BE ABLE TO SOLVE THE APPARENT CLOCK PARADOX.
BUT I NOW REALIZE THAT EVEN IF I COULD DO THIS, THE CLOCKS WILL NOT
REMAIN SYNCHRONIZED BECAUSE THE LT WON'T ALLOW IT, AND WE MUST USE THE
LT SINCE IT'S PRESUMABLY THE ONLY FRAME TRANSFORMATION THAT CONSTRAINS
THE SOL TO BE FRAME INDEPENDENT. THEREFORE, I'VE COME TO THE
CONCLUSION THAT THE PROBLEM I'M TRYING TO UNDERSTAND, CAN ONLY BE
SOLVED VIA THE BREAKDOWN OF SIMULTANEITY AFTER MORE CLEARLY DEFINING
THE PROBLEM. AG
FINALLY, I NOTE THAT BRENT WAS CORRECT IN HIS INITIAL RESPONSE, THAT I
FAILED TO DEFINE THE PROBLEM CLEARLY. THIS MIGHT ACCOUNT FOR THE FACT
THAT IMO HIS PLOT FAILS TO OFFER A SOLUTION TO MY INITIALLY ILL-POSED
QUESTION. AFAICT, HIS PLOT JUST SHOWS THAT THE LT IMPLIES A CLOCK IN A
SPATIALLY MOVING FRAME, HIS RED CLOCK, TICS AT A SLOWER RATE THAN THE
CLOCK IN SPATIALLY FIXED FRAME, HIS BLUE CLOCK. THIS WE ALREADY KNEW,
AND THE PROBLEM I SEEK TO UNDERSTAND, IS WHAT HAPPENS WHEN THE RED AND
BLUE CLOCKS BECOME JUXTAPOSED, BUT THERE'S INSUFFICIENT RESOLUTION IN
HIS PLOT, AT THIS POINT OF INTEREST, TO SHED ANY LIGHT ON MY PROBLEM.
I NOW INTEND TO GO BACK ONE OF YOUR PREVIOUS POSTS WHERE YOU ALLEGEDLY
SHOWED THAT THE LT IS, INDEED, A TRANSFORMATION, IN THE SENSE THAT IT
TELLS AN OBSERVER IN THE SPATIALLY FIXED FRAME, THE REST FRAME, WHAT
THE OBSERVER IN THE MOVING FRAME WILL ACTUALLY MEASURE. THIS ISSUE
PUZZLES ME BECAUSE OF THE CONTRACTION OF A MOVING ROD. IN WHICH FRAME
DOES THE SHRINKING ROD RESIDE? TY, AG
