Merlyn wrote:
Actually, because the planes fly at equivalent speeds
WRT the Earth, which is a rotating frame of reference,
when they get back to the geographical starting place
(which has moved), they arrive at the same "local"
time
Not right. See below.
and according to Hafele's experimentally obtained
data the clocks do not agree.
But that's right.
The problem with the first item is that the clocks disagree by some tiny
amount -- say, a millionth of a second (I'm guessing but probably
close). So, one of the two planes actually arrived a microsecond before
the other one.
Such a small difference in arrival times of physical aircraft can't be
measured!! At 500 mph the nose of the plane moves 0.009 inches in a
microsecond. Using any earthly measurement system the planes will
_appear_ to arrive back at their starting points simultaneously.
Indeed, the imprecision in the _starting_ locations of the two aircraft
is surely many orders of magnitude larger than the difference in the
location at which they actually met when they came back to home base again.
The only thing which _can_ be measured is the difference in their clock
readings. That's straightforward by comparison -- both planes land, and
you put the clocks next to each other and compare them. Or do it by
radio before they land - either way it's easy.
If you want to actually observe the fact that they don't arrive back at
together at the starting point at the same moment, you need to use
something smaller and more precise than aircraft, like light pulses,
whose arrival time can be measured _precisely_. And when that's done,
you do indeed observe that the arrival times, according to local clocks,
are different. As I've already pointed out, that's the principle on
which ring-laser gyros are based -- if it were not true they would not work.
