On Friday, October 18, 2024 at 7:30:05 PM UTC-6 Brent Meeker wrote:
On 10/18/2024 5:50 PM, Alan Grayson wrote: On Friday, October 18, 2024 at 5:19:58 PM UTC-6 Brent Meeker wrote: On 10/18/2024 3:27 PM, Alan Grayson wrote: On Friday, October 18, 2024 at 4:09:18 PM UTC-6 Brent Meeker wrote: On 10/18/2024 1:11 PM, Alan Grayson wrote: 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, * *So what? They won't be synchronized in any reference frame moving relative to them. You can arbitrarily foliate flat space time to define comparisons as "now", but it has no physical significance. You're unclear on what "now" means because it doesn't mean anything. * *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.* *I don't know where you get this stuff. No relativity text I know even recognizes the concept of "stationary". It's called "relativity" for a reason! Brent * *Haven't you seen in texts the case of a train (the moving frame) and the station (the fixed or stationary frame) used to develop some of the basic concepts of relativity? Maybe the LT or maybe time dilation. I distinctly recall this. I didn't pull it out of the proverbial hat. Anyway, suppose we have two frames in SR and each frame sees time dilation manifested in the other frame. If they occurred at the same time, this would be a paradox, * *Are these frames moving relative to one another? * *Well, the station obviously wasn't moving, but there were other examples. It was a good text, but I can't recall its name. If I get the energy, I'll try to find it on Amazon if it's still in print. AG * * Then they will see time dilation in one another as they pass by AT THE SAME TIME AND PLACE. * *Then, IMO, we have a paradox. How can an observer see another's observer's clock running slower, and vice-versa, at the same time and place? Years ago when we discussed this, you seemed to take the position that breakdown in simultaneity could resolve the issue. Now you seem to be backing off from this explanation. AG * *Because years ago it was not assumed they were at the same place, in which case there can be no motion-independent assessment of their relative rates. Brent* *Maybe this will help. In the text which I recall, it was not assumed that both frames were in motion. Whereas the train was moving, the station was not, and could not be imagined as moving. So maybe, the idea that time dilation occurs only applies when one frame cannot be assumed to be moving. When both frames are moving, the only way to determine time dilation is to have synched clocks and determine if one falls behind the other. In this situation, due to symmetry, each clock will fall behind the other at the same time and place -- actually at every time and place -- which IMO is impossible and paradoxical. 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