I have come up with a thought experiment that really does produce a Twin/Clone Paradox.

Imagine a hyperspherical universe that is sufficiently static in size that
Magellan-style circumnavigation is possible. Set clones off in all directions from earth.

(To keep acceleraction out of the experiment, they can take a running start such that they all pass Earth simultaneously at cruising speed [identical cruising speeds, relative to Earth, speeds that are a substantial fraction of the speed of light] synchronizing their watches to zero as they pass, while an Earth-based clone also synchronizes his watch.)

When the clones reunite, whichever clone has the clock that shows the greatest elapsed time (i.e., whichever clone is oldest) will be the one most nearly at rest absolutely. (My money is on the Earth-bound twin.)

It's too bad that, according to currently popular cosmologies, we can't perform this experiment in our universe. Either the Universe will collapse before circumnavigation can be completed, or (more likely) the runaway expansion of the Universe will thwart circumnavigation. (No matter how much progress our cloned runners make, the receding finish line will make even more progress. Worse than that, the Universe might not even be closed!)

Still, the thought experiment shows that it is logically possible for a meaningfully absolute rest frame (a privileged frame) to coexist with the practical indetectability of same at the local level.

So there you have it, my New, Improved Twin/Clone Paradox!

_________________
John D. Hansen, Jr.
(760) 726-3369

Interesting John,

However, let's assume Earth is just a point in the universe. If you replace "Earth" in your thought experiment with any other point in the universe, the result is the same. Thus the Privileged frame is not really privileged in the big picture. It only appears privileged from its own relative point of view where Earth is the starting and finishing point (the origin). Very elegant experiment just the same even if it does require some grand assumptions (spherical & closed universe)

Tom

What if the "privileged" frame is the one at relativistic speeds? Only from a non-relativistic prespective does speed have meaning, in this sense. Our time and distance perceptions are the result of our non-relativistic motion, or lack of relativistic motion. Perceptually, we recognize differences in time and space between each other's frames, but these differences only seem to exist as long as we are slow (non-fast). From a relativistic vantage, the number of motion/time state variables seems to be 2 or 1 because at relativistic speed the only states are "same" and "different". And this distinction may not exist from that frame's perspective.

To some degree, the constraints of our time, and our space are the result of our "slow" perspective. If I've done my time dialation calculations correctly (and they are relevent), the question of "how how fast are clocks ticking when moving at differing rates from here to there?" would be answered from a relativistic perspective with "what is this fast thing, what is "move", and is there a difference between here and there?" This is a terribly self-centered view of the situation, but I have no other context by which to consider.

I've been wanting to talk about relativity for quite soome time, and I hope I haven't muddied things.