On Friday, October 18, 2024 at 1:12:25 PM UTC-6 Brent Meeker wrote:
On 10/18/2024 4:00 AM, Alan Grayson wrote: > Yes, literally, last night, I had a dream wherein I was describing a > physics problem which puzzles me, to three physicists. It went like > this. First I postulated three inertial frames positioned on a > straight line, with clocks synchronized, and two traveling toward each > other at the same constant velocity v, and the third at rest, located > midway between the moving frames. I didn't explain how these frames > could be constructed, but it's clear that it's possible. Now maybe I > am falling into a Newtonian error, but ISTM that the moving frames > will pass each other at the location of the rest frame, and all > observers will be able to view all three clocks since they're > juxtaposed. Consequently, all three clocks will be seen as indicating > the same time. Note that the stationary frame represents the > stationary train platform in texts which establish the clock rates in > moving frames (represented by moving trains) are slower when compared > to stationary frames. In the model proposed in my dream, it's hard to > claim that the three clocks indicate different times since the moving > clocks are synchronized and their motions are symmetric. So, there > doesn't appear to be any differential rates for these clocks. Maybe > use of the LT will change this situation, since it guarantees the > invariance of the SoL, but it's hard to see why the clock readings for > the moving frames could be different from each other, given the > symmetry of their motion. It's not the an symmetry of their motion, it's the symmetry of how you define "now". When the 3 clocks are together momentarily they can all be set to the same time and there's no ambiguity about it. But once they are apart there is no unambiguous way to compare them. Whether they read the same value "at the same" is ambiguous because "at the same time" depends on the state of motion of whoever is judging the times to be the same. And this is not just because of the relative motion of the clocks. There is the same ambiguity even if the clocks are stationary relative to one another but are at different locations. *I am unclear what "now" means. How is it defined? Can't we use the round-trip light time to establish that the frames which will eventually be moving toward each other, are initially at rest with respect to each other, at a known fixed distance, and use it to synchronize their clocks, and to then apply the same impulse at the same time to both, to get the frames moving symmetrically? This doesn't seem ambiguous. Also, using the third clock, we can establish, as is done in relativity texts, that clocks in moving frames have slower rates than clocks in stationary frames. Using this fact, and the fact that when the moving frames meet, no time contraction is noticed (since these clocks will show the same time), we have another contradiction. AG * > In the dream, the physicists were baffled and couldn't resolve the > issue, which, to repeat, is how the clock rates for the moving frames > could indicate that each clock in a moving frame, was ticking slower > than its symmetric other. AG -- Which I already explained how to prove to yourself. 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 on the web visit https://groups.google.com/d/msgid/everything-list/105f358a-66d1-446d-beb3-d98934e4bfaen%40googlegroups.com.
