On Mon, Oct 28, 2024 at 9:19 AM Alan Grayson <[email protected]> wrote:
> > > On Monday, October 28, 2024 at 5:44:08 AM UTC-6 Jesse Mazer wrote: > > On Mon, Oct 28, 2024 at 2:00 AM Alan Grayson <[email protected]> wrote: > > > > On Sunday, October 27, 2024 at 10:51:23 AM UTC-6 Alan Grayson wrote: > > On Sunday, October 27, 2024 at 4:27:45 AM UTC-6 smitra wrote: > > On 27-10-2024 07:56, Alan Grayson wrote: > > 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 > > > http://insti.physics.sunysb.edu/~siegel/sr.html > > Saibal > > > From link: > > A famous "paradox" is trying to park a relativistic car in a garage: > From the point of view of the car, the garage has "Lorentz contracted", and > the car will no longer fit. But from the point of view of the garage, the > car is now shorter, and so will fit even better. The resolution of the > paradox is that if the front end of the car stops simultaneously to the > back end from one "reference frame", that will not be true in the other. If > both ends do not stop at the same time, the car changes length. (This has > often been observed nonrelativistically, for cars stopped by trees or other > cars.) > > So how exactly is the paradox resolved? Not sure I get it. BTW, I don't > post using all CAPS. AG > > > Is the paradox resolved by assuming that if simultaneity is broken from > the pov of the garage frame, the car length is undefined? AG > > > By "simultaneity is broken" do you just mean the idea from the link that > if both ends of the car stop simultaneously in the car's frame, these > events are non-simultaneous in the garage frame? > > > *The link just says that the apparent paradox is resolved by a breakdown > in simultaneity, but doesn't specify exactly what that means. I notice that > an apparent paradox can be defined for length contraction, whereas I was > trying to resolve it for time dilation, but so far I cannot define the > problem with clarity. Do you have any suggestion in this regard? AG* > > The link doesn't use the word "breakdown", do you use that term just to mean different frames have different definitions of simultaneity, even if they both can make definite statements about which pairs of events on the worldlines of the front and back of the car are simultaneous (and therefore the distance in their frame between any such pair of simultaneous events)? Your comment about the length being "undefined" seemed to suggest you had a different idea in mind. Time dilation and length contraction are not really symmetrical quantities, length contraction depends on having *two* worldlines with identical velocities (the front and back of the object) and looking at the distance between simultaneous points on them, time dilation is based on comparing proper time between two points on a *single* worldline with the coordinate time between those points in some inertial frame. So I don't think you could come up with anything exactly analogous to the garage paradox for time dilation. Jesse -- 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/CAPCWU3KW4z%2BZLO9RQtBF%3DS4jFaoR9PxJL0_OdQitqbO7bzwJXg%40mail.gmail.com.
