John Denker wrote:
| . . . 2b) The simplest and IMHO most satisfactory explanation is that
elapsed
| time is path-dependent for the same reason that path-length is
| path-dependent.
I like this description (it is not, however, a physical "explanation").
Just a comment:
It seems obvious that we are talking about a *comparison* of two clock
readings and not some absolute or intrinsic time dependence upon path. If
the traveler left (and returned to) an uninhabited (and un-instrumented)
earth, he would not notice this effect. While traveling, his passengers are
oblivious to their space-time trajectory - they merely read their clocks.
Even if they knew that their clock-time is path-dependent, how do they
correct it - to agree with what standard?
The path-dependence has utility only with respect to the path of a second
(standard?) clock. When the second clock stays fixed on earth it seems
natural to consider its proper time as the really useful variable
(standard?).
What do we say when the departure and re-uniting space points are different?
Suppose Joe and Moe leave Earth and meet on Io, taking very different
space-time trajectories. Can we choose a clock? Why do we need to? Each
generates its own time base variable for doing physics from its proper
frame - including an analysis of events on the other's world line.