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A comment on Why is Maxwell's theory so hard to understand? (2007) [pdf]. Parent comment

Re:Why is Maxwell's theory so hard to understand? (2007) [pdf] by kurthr on Monday January 29, 2024 @07:02AM (#39175322)
True, but he did use quaternions (by 1873), which allow the field properties to be written as a single equation. It's kind of sad that more physicists don't use or teach quaternions, while math and CS have fully adopted them.

I really liked Kathy Joseph's historical reviews of vector physics and the people who developed it, which explain some of the reason's for how it's taught. Most texts don't even develop electrodynamics from relativistic electrostatics as a demonstration.

https://youtu.be/CdwxpSInhvU

I think I fell down the rabbit hole from Freya Holmer's "why you can't multiply vectors".

https://youtu.be/htYh-Tq7ZBI

The key being that all of the Hamiltonian fields can be found in a single quaternion equation, which is just what happens when you start multiplying vectors together.

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Re:Why is Maxwell's theory so hard to understand? (2007) [pdf] by aap_ on Monday January 29, 2024 @10:09AM (#39177095)
Unfortunately he didn't use quaternions in his initial formulation (that was all split into xyz coordinates) and in his later revision he took apart the quaternions into scalar and vectors parts. It could have been so much prettier....but luckily we have geometric algebra for that today.

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.

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