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 Originally Posted by Eric
Right, it is starting to make sense.
If we take the http://www.einstein-online.info/spotlights/Twins traveling twins example to an extreme then we can say that I age slower than people on earth because I'm moving closer to the speed of light.
As such, I could take a measurement at 59 seconds while someone on earth does it at 60.
Still trying to get my head around this.
That link offers a poor explanation that ignores the fact that we can take out the acceleration entirely and still predict the time dilation.
Assume we have 3 clocks. One on Earth, the inertial frame. Another is already moving at speed past Earth, and happens to be perfectly synchronized with Earth as it passes. The third clock is going in the opposite direction of the 2nd. It passes the 2nd some distance away, and at that time, those 2 clocks happen to be perfectly synchronized.
Now, the 3nd clock passes the first clock on Earth some time later and we STILL note that the clocks are not synchronized, even though we have completely eliminated any accelerating reference frames.
The actual answer to unravel the paradox is to understand that spacetime paths have different lengths, and that's enough to desynchronize the clocks. The "inertial" clock on Earth has a theoretical spacetime path which moves only in time, but not in space. The other clocks move in both time and space. The magnitude of the length of the spacetime path is what determines a clock's tickrate.
(And again, we're talking about the imaginary, internal clocks which mediate all interactions. Yes, slowing down all the interactions slows down the macroscopic clock, but it's literally that time flows at a different rate, and nothing to do with clocks, as such.)
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