Greg Egan on Nostr: Many famous experiments have shown the time discrepancies between atomic clocks left ...

Many famous experiments have shown the time discrepancies between atomic clocks left on the ground and those flown around the world.

But the least famous effect is probably this: if you carried a clock all the way east around the equator VERY slowly, at constant altitude, then it would still end up showing 200 nanoseconds less elapsed time than a clock left at home.

To see why, start with a couple of cylinders in ordinary space.

As θ→0, the length of the red helix that wraps around the cylinder approaches the length of the blue line.

But as θ→0, the length of the magenta helix that wraps a bit faster than the green helix, and meets up with it once it has completed one more turn, does NOT approach the length of the green helix. However small θ becomes, magenta is longer, by an amount than depends on α.