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. 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
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