In the twin paradox the clocks are biological and there is no preferred frame of reference according to special relativity.Not really, from the perspective of both, no one's clocks are moving any faster or slower, but if you took a round trip in a spacecraft (with a clock on board) and you were traveling faster than most everything else around you through the fabric of spacetime the whole time, when you got back, your clock would be shown to have been experiencing the passage of time slower than the ones back on earth the entire time, etc. (Leaving gravitational time dilation effects out of it for the moment of course). But, from the perspective of both looking at their own clocks the entire time, no one's own clock was going any faster or slower the entire time, but that's only because in the ship, both the clock, and the one's looking at the clock on board, were experiencing the passage of time slower the entire time. And, because of this, also when they looked out of their window, or whatever, at everything else outside of them, including the clock on earth, etc, they think they would see them as having been experiencing the passage of time slower the entire time, but it was just only because they were the entire time, etc. (or even slower as they were headed away from Earth, and just a little bit faster as they were headed back) (but that might take a little bit more explaining, and will just only further complicate the issue, so let's just leave that out of it for now) but, point being, when the craft got back to earth, their clock on board would always be behind the one on earth, and that's because they experienced the passage of time slower than those on Earth just simply because of their velocity, or faster movement/travel through spacetime, etc. And while it may have appeared to them that everything else was experiencing the passage of time slower for a time, it actually wasn't, but was just only them experiencing the passage of time slower the entire time, just simply due to their faster velocity, or faster movement/travel through spacetime, etc.
Take Care.
Mary travels away from and returns to Frank's location who is stationary is equivalent to Mary being stationary and Frank the travelling twin.
The paradox is that each twin should be young relative to each other on completion of the round trip as there is no preferred frame of reference.
In fact Mary turns out to being the younger twin as during the round trip she changes direction (and undergoes acceleration in the process) which destroys the symmetry of the argument.
The Minkowski space-time diagram for the twin paradox also serves to illustrate the point.
In this case Mary does a 20 year round trip of proper time travelling at v = 0.8c.
Each year Frank sends a signal to Mary who on receiving the signal sends a signal back to Frank.
During this 20 year round trip Frank sends out 20 signals but only receives 12 signals from Mary.
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