Re: del F = 4pi J ... correspondence between Clifford Algebra and vector formulation of electromagnetism

[Leigh Palmer <palmer@SFU.CA>]

John Denker notes:

> I recently did an amusing exercise.  Starting from
> the equations of electromagnetism in the form
>         del F = 4pi J
> I turned the crank on the Clifford Algebra to confirm
> that it does indeed regenerate the old-fashioned vector
> representation of Maxwell's equations.

I first did this in 1994 when David Hestenes introduced
me to Geometric Algebra while we were both visiting the
in the Cavendish Laboratory. It convinced me that physics
made a wrong turn when it adopted Gibbs's mathematical
notation (including those cross-products John mentions)
instead of the Clifford algebraic approach. Recognizing
that vectors and pseudovectors are very different beasts
is a mystery to students. The latter quantities (called
"bivectors" in GA) are quite obviously different from
vectors in GA; the confusion never arises.

A good source for the Maxwell equation derivation is
section VI of David Hestenes paper "Spacetime Physics
with Geometric Algebra". Go to
http://modelingnts.la.asu.edu/pdf/SpaceTimePhysics.pdf
and download the pdfs.

Leigh