A Technically Nice, Historically False “Explanation” of the Displacement Current
sudoscience.nl
sudoscience.nl
Remember, the Heaviside-Hertz pedagogy existed in a time when the "Ether" was assumed to exist.
What works nicely for things that "displacement current" fails badly is a "field based" representation. See "Collective Electrodynamics" for such a pedagogy.
https://mitpress.mit.edu/books/collective-electrodynamics
(Edit: Misspoke a bit: Field based works well for all systems. It just doesn't give nice, textbook, closed-form solutions for certain problems that are "simple".)
I'm talking about the part that starts around 19 minutes in.
I would be interested to know how likely it is that Maxwell found, and was influenced by, this derivation.
"His [Maxwell's] system of equations worked with jeweled precision. Its construction had been an immense feat of sustained creative effort in three staged spread over 9 years. The whole route was paved with inspired innovations but from a historical perspective one crucial step stands out -- the idea that electric current exists in empty space. It is these displacement currents that give the equations their symmetry and make waves possible. Without them, the term dE/dt in [Ampère's law] becomes zero and the whole edifice crumbles.
Some accounts of the theory's origin make no mention of the spinning cell model, or dismiss it as a makeshift contrivance which became irrelevant as soon as the dynamical theory appeared. In doing so they wrongly present Maxwell as a coldly cerebral mathematical genius. One can hardly dispute the epithet 'genius', but his thoughts were firmly rooted in the everyday physical world that all of us experience. The keystone of his beautiful theory, the displacement current, had its origin in the idea that the spinning cells in his construction-kit model could be springy."
Mahon, B., The man who changed everything -- The life of James Clerk Maxwell, 2016 reprint, p.125-126
I searched on "Maxwell spinning cells" and found [1], which includes this:
"Two courses seemed to be open. One was to desert Faraday and fields, and assume that all effects result from action at a distance between magnetic poles and electrical charges or currents...[This] was also the basis of an attempt at a complete theory by Wilhelm Weber, which was mathematically elegant and offered an explanation for most of the known effects. But Weber had made a critical assumption – that the force between two electrical charges depends not only on their distance apart but also on their relative velocity and acceleration along the straight line joining them."
Now I am wondering if that was a foretaste of special relativity.
[1] https://plus.google.com/+ChrisReeveOnlineScientificDiscourse...
I don't know the math, but I have read that the magnetic force is a result of electrostatics in the context of relativity. As such it is also hypothesized that a gravitational equivalent should exist as well, but it will be comparably weaker due to the many orders of magnitude difference between the strength of the electric and gravitational forces.