I wrote:
If you start with 2 atomic clocks synchronized together, and you move one up 10 m to another floor, that causes it speed up slightly . . .
. . . distance is now a function of time (1 m = distance light travels in a vacuum during the interval of 1/299,792,458 s).
<ahem> This leads to the quandary: How do you know you have gone up 10 m? As you go up, time dilation decreases and the definition of a meter keeps changing.
I suppose: move horizontally, measure 10 m on a stick, and then raise the stick vertically. But -- aha! -- gravity will shorten the stick (not just by mechanical compression but also by Lorentz transformation). Same problem.
All units of measure are defined by some other unit, in a mobius strip configuration. Pin down one and another slides away.
- Jed
