Peter is at rest in a frame travelling at 0.9c with respect to Jane and other
observers stationary in her frame. Peter is at the origin of his coordinates in
his frame and Jane is at the origin of coordinates in her frame. They each note
the time as they pass one another. Later, Peter passes Sam, another observer in
Jane's frame. One minute has elapsed on Peter's clock. What is the elapsed time
difference on the clocks of Sam and Jane?
To me, the issue is comparing a single clock to a pair of clocks separated in
another frame.
If we measure muon speed and flux at the top of a mountain, and have previously
learned their lifetime (in the muon's rest frame), we may venture to predict the
muon flux at ground level. If we base this prediction on the elapsed time on Earth
clocks (one on the top of the mountain and one on the ground) we underestimate the
flux at ground level, because a single muon, passing the mountaintop and then
reaching the Earth's surface elapses less time than on the two spatially separated
Earth clocks.
--
Mike Moloney, Physics & Applied Optics Department
Rose-Hulman Inst of Tech, 812 877 8302
moloney@rose-hulman.edu http://www.rose-hulman.edu/~moloney