> Andrew Clough wrote:
> > This is an interesting question to ask: Just what frame of reference
> > results in the fastest possible passage of time?
> That depends on your frame of reference. The "fastest possible passage of
> time" is always in the frame of reference identical to your own, at least
> as you measure time. If you're on a ship travelling at .99c and we orient
> the frame of reference so that you're motionless, then someone who leaves
> the ship in a pod, decelerates to be at rest with reference to the fixed
> stars, stays that way for a week in his reference frame, and then
> accelerates to catch back up with the ship he left, will experience less
> total subjective time than someone on board ship who didn't experience any
This is correct, but I don't think it is quite right to say that
the answer depends on the frame of reference. The right answer,
consistent with your example, is that the path between two points in
spacetime which maximizes the perceived elapsed time is that which
experiences no acceleration; that is, a geodesic curve, the equivalent
of a straight line in spacetime. This optimal path can be considered
to be observer-independent.
Now, in general relativity there may be multiple geodesics which go
from one point to another; for example, throwing a ball into orbit and
letting it come back, versus throwing a ball straight up and letting it
fall back. You can arrange for these to take exactly the same amount of
time and both are geodesics. But in principle the elapsed time along
the two paths may be different.
Each of the geodesics is a local extremum in distance and in elapsed
proper time along the path. If there are multiple geodesics, one of
them will be the maximum. In the case of the ball example, I would
guess that the orbiting observer will experience less proper time,
because it is lower in the gravitational field.
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