 Quote by ronirvol
In the twin paradox, the twin that experiences the most acceleration does not age as much.
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It's not really a matter of "the most acceleration", the basic principle of the twin paradox is that if one twin doesn't accelerate at all between meetings while the other does at some point, the twin who accelerated will be younger. If both twins accelerate the problem will be more complicated and will depend on the particulars of when and where they accelerate as well as the magnitude of the acceleration they experience.
 Quote by ronirvol
If I synchronize two digital watches, then put one in a centrifuge for a long time, one watch will experience much more acceleration than the other. If they remain synchronized, why is the acceleration inside a centrifuge different from the acceleration if one watch had been in a space ship?
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Suppose one watch doesn't accelerate at all between meetings with the other watch, which is placed on a centrifuge. In this case, just as in the twin paradox the watch that was accelerated on the centrifuge will show less time elapsed when it reunites with the watch that didn't accelerate--they will
not remain synchronized.