Example: The Metric Equation
A classical “deep” simplification involves the use of Minkowski’s metric equation to view special relativity, prior to tackling the formidable obstacles presented by multiple inertial frames.
ds2 = dx2 + dy2 + dz2; (c d?)2 = (c dt)2 - ds2
This equation precipitated thinking that lead to even deeper simplifications in our understanding of gravity, at the same time extending Pythagoras’ theorem to allow study: (i) of relativistic acceleration with simple algebra, and (ii) of curved spacetime problems with simple calculus.
Edwin Taylor won the Oerstead medal of the American Association of Physics Teachers, earlier this year, and is now co-authoring a book on Scouting Black Holes with John Wheeler, with hopes for “a second course” in physics directed in part to this end.