Dept. of Physics & Astronomy, University of Missouri - StL, St. Louis MO.
If you consider motion unfolding on a map of
landmarks fixed with respect to a single inertial reference frame,
the map-frame choice defines both distances and
simultaneity! The two times in the metric equation (map and
traveler) then give rise to two useful velocities (coordinate and
proper), two accelerations (coordinate and invariant -- only the
latter connects to the physics directly), and two time-integrals of
the equations of motion (a vector momentum equation associated
with action-reaction, and an ``oriented-scalar'' impulse equation
associated with the force "felt" by the traveler).
As a result, invariance in relativity as it differs from Newtonian
physics can be described clearly, and tons of problems including
constant acceleration can be worked, before inertial frames
in relative motion (with length-contraction, velocity-addition,
and frame-dependent simultaneity) need be considered quantitatively.
The study of relative motion also simplifies when the
variables defined above are put to use.
While at it, should you consider accelerated motion of a
traveler on the map using clocks in a chase-plane not quite
keeping up with the traveler, one can also find a context
in which Galileo's 1-D constant acceleration equations provide
relativistically correct predictions as well. In fact, Galileo
discovered the simplest set of equations for describing
relativistic constant acceleration in 1-D, although at high
speed it deals only with the behavior of a rather special subset
This page contains original work, so if you choose to echo on paper, in application,
or on the web, a citation would be appreciated. ( Thanks. /philf :)
For source, cite URL at http://www.umsl.edu/~fraundor/mbrsynop.html Version release date: 12 Apr 2005.