[Phys-L] Re: "moving clock runs slower" (yes)

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Bob Sciamanda wrote:

> 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.

I don't know what it means to say that the space points are
"different" any more than I know what it means to say that they are
the "same."  For causally connected events such as the two you
describe, there is always an inertial frame for which the two events
occur at the same spatial position.  You can then compare the elapsed
time in that special (proper) frame with the elapsed time experienced
by others who are present at both events and you will find that the
proper time is always maximal.

Indeed, the paper that I referred to earlier in the current issue of
AJP ["Differential aging from acceleration: An explicit formula,"
AJP, V73, p.876] makes clever use of this fact.  It suggests that we
consider assigning a standard time to EVERY instant of an arbitrary
trip's worldline.  That standard time is simply the proper time in an
inertial reference frame that is spatially coincident at the start of
the trip (when both clocks were "zeroed") and the current instant of
interest.  Of course, the inertial reference frame used to assign the
standard time at any given instant along the worldline of the trip
will be (infinitesimally) different from the inertial reference frame
used a moment before or after.  It is easy to show that the standard
time defined in this manner will never advance at a lesser rate than
the time shown on the traveler's clock.  Moreover, one can compare
the rate at which the standard time advances to that at which the
traveler's clock advances to define a very defensible instantaneous
rate of differential aging.

--
John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>
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