Consider a merry go round with a radius of 1 light year and a tangential velocity of 0.9c. The rider is in a capsule on the edge of the merry go round. The observer is just a guy who is the same age as the rider but just floating in space. The merry go round start's spinning. The rider is in a couch in the capsule and at 0.9 c experiences a very tolerable 7.6 m/s^2 centrifugal acceleration.
From the rider's point of view, the observer is like an orbiting planet with an eccentric orbit, albeit at relativistic speed. So the rider will calculate that the observer will age more slowly.
But the observer will see the rider rotating very fast and will calculate the she will age more slowly.
When the merry go round runs for a few days and then stops, who is the one who experienced time dilation?
I read these recent threads:
Clearly, we humans continue to be puzzled at this hundred year old story. From reading the threads above, PM2ring's comment is enlightening:
"In Special Relativity, speed causes time dilation, but with constant speed the situation is symmetrical. If observers A & B have a constant relative velocity then A measures B's clock to be running slow by a factor of γ, and B measures A's clock to be running slow by a factor of γ.
To break the symmetry, (at least) one of the observers needs to make one or more changes of reference frame. It's not so much that the acceleration causes time dilation, it's merely the mechanism whereby the reference frame is changed."
This tells me that in my model above, the rider will age more slowly since she is not in an inertial frame of reference. But consider if the observer is on an identical merry go round, just shifted a little in the z direction. If both merry go rounds are spinning in the same direction, they are covariant. Each rider will see the other as stationary. Each will calculate that Neither rider will age slower.
But if the merry go rounds spin in opposite directions, each rider will see the other moving very fast and will calculate that the other should age more slowly. When the merry go rounds stop, they will be surprised to see they are the same age, even though each saw the other whipping by.
These two situations put the riders in symmetrical reference frames. Yet in one direction they see each other age similarly, and when spinning opposite, they see each other age differently.
And it doesn't require a merry go round. If both riders are on rocket sleds light years apart and travel towards each other at 0.9c, each will see the other age more slowly. Yet when they meet, they should be the same age since their reference frames are symmetrical.
I guess it would be nice to have a mechanistic explanation of what is going on. How is it that traveling fast changes the fundamental nature of aging.