🚀 go-pugleaf

  The metric equation in special relativity, as it  
is often written, has two times and one displacement 
in it, e.g. (c dT)^2 = (c dt)^2 - (dx)^2 where c is 
the speed of light.  This equation is more widely 
useful in general relativity, and probably in the 
study of arbitrary hyperspaces, than are the familiar 
Lorentz equations for transforming between two frames 
(which of course can be derived therefrom).

  This suggests that a strategy for introducing 
special relativity from the metric equation might 
have some advantages.  One might even see the same
benefits that prompt us to discuss single-frame 
kinematics in classical introductory physics, before 
we hit kids with the complexities of multiple 
(i.e. primed and unprimed) frames.  

  Work here suggests these advantages are real, 
although the language usually used to introduce 
relativity may need some updating.  Take the 
assertion, for example, from a popular modern- 
day text that the "principle of relativity means 
that any kind of experiment (measuring the speed 
of light for example), performed in a laboratory 
at rest, must give the same result when performed 
in a laboratory moving a constant velocity past the 
first one."  While students are wondering how this 
can possibly be true say for the speed of an object 
NOT moving at the speed of light (like the origin 
of the second laboratory, which has a finite 
velocity as measured by an observer in the first 
laboratory and a zero velocity when measured in the 
second), they are not being told that the rate of 
momentum change in special relativity (something we 
are classically used to thinking of as frame-
independent) becomes frame-dependent at high speeds 
(as the rate of energy change is even classically).

  Hence, when one first considers an approach 
based on the metric equation (we refer to it as 
the 1-map 2-clock strategy), a bit of cognitive 
dissonance as well as a bit of jargon might be 
expected.  The good news is that once over the 
hump, the mathematics of map-based relativity 
focussed on physical clocks which monitor the two 
times found in the metric equation, may win you
over (as it has me) with one pleasant surprise 
after another.

  You can find more on the surprises we've had, and
some suggestions for classroom implementation,  
at <http://www.umsl.edu/~fraundor/a1toc.html>.

			Cheers   /philf    :)


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//P.Fraundorf Phys&Astr/CME 3145165044 philf@newton.umsl.edu
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