1,187 karma · joined May 22, 2013
He did indeed use quaternions but it's not easy to find: https://archive.org/details/atreatiseonelec02maxwgoog/page/2...
Unfortunately these equations are not quite without mistakes (I remember a missing dot for a time derivative) compared to the component form. They're correct in the wikipedia article: https://en.wikipedia.org/wiki/History_of_Maxwell's_equations...
If you replace S.∇ with ∇· and V.∇ with ∇× you essentially get the vector calculus version of the equations.
Thank you for extracting the core ideas out of this lengthy text. But I'm still wondering where this very concise present-day formulation with just 4 equations was first written down, even if you can somehow find them scattered around in the book. I found something about Hertz but didn't try to follow up on it, i think he may have only considered a vacuum.
The major difference I found was that Maxwell was expressing things in terms of the scalar and vector potential (which is what you have to do in QED) whereas Heaviside got rid of that and just had an electric and magnetic field instead. I found that you need 7 of Maxwell's equations to derive the 4 Heaviside(?) equations.
If you actually wanted to embrace quaternions you could write the famous 4 equations as just two (using natural units):
∇E + dB/dt = -ρ
∇B - dE/dt = J
Quaternions are about 3D. You need 4 numbers for it, but the space that they operate on is 3D.
On the other hand he did derive the electric and magnetic fields from a scalar and potential field. In that sense Heaviside made a step backwards.
The other person interested in Whirlwind I is Guy Fedorkow and his emulator is here: https://github.com/gfedorkow/Whirlwind-Instruction-Simulator...
Whirlwind I is an absolutely cool and lovely machine. I always call it the first microcontroller (not very micro though, took up a whole building).
That video was not actually very good unfortunately (surprisingly, I might add). I doubt it helped people understand the matter much but just repeated the old "weird incomprehensible 4d number" story.