Reading 2/20/2008: Section 2.13

Okay, so this is rather ashamedly late, but I've been rather wickedly sick the last few days so please do forgive me.

The lead up to (2.254) is simply gorgeous. We start with the general equation of motion, use our previous construction of &Phi, put stuff in terms of kinetic energy, and - Bam! - all of a sudden we have a classical equation of kinetic and potential energy combined with energy flux. As suggested in the book, this is definitely Maxwell-style beauty.

I'm a little puzzled by the comment on p. 124 - why can't we do these calculations in exponential notation? Mathematically, the two are fundamentally equivalent, so it doesn't make sense to me where the difference arises.

My last thought is to wonder if there is some kind of fundamental equivalence (or at least similarity) between EM and P waves. The formulas on the bottom of p. 124 do seem to suggest that if we say

&rho₀ &alpha &omega² -> Sqrt[&epsilon₀/&mu₀]

and

a² -> E₀²

we get some kind of relationship?