
A Technically Nice, Historically False “Explanation” of the Displacement Current - itcrowd
http://sudoscience.nl/2016.html
======
bsder
And it doesn't work very well for certain systems. Motors are notoriously
annoying to attempt to use "displacement current" on.

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](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".)

~~~
kkylin
Off-topic (because what's meant by "ether" has evolved over the years), but
still an interesting read:
[http://ctpweb.lns.mit.edu/physics_today/phystoday/Ether.pdf](http://ctpweb.lns.mit.edu/physics_today/phystoday/Ether.pdf)

~~~
gumby
REALLY off topic but I happen to be sitting about 200 yards from Michelson's
childhood home as I read this!

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RichardCA
Forgive me for being a naif, but can someone explain why the derivation
presented in the old Mechanical Universe video from the 80's is problematic?

I'm talking about the part that starts around 19 minutes in.

[https://www.youtube.com/watch?v=SS4tcajTsW8](https://www.youtube.com/watch?v=SS4tcajTsW8)

------
phkahler
I'm left wanting for the real reason...

~~~
mannykannot
Same here. Apparently, it is historically "false" because there is no
documented explanation of how Maxwell found his way to the result. The author
quotes Paul Nahin: "I like the direct, simple (and probably simplistic, I'll
admit) explanation -- Maxwell was a genius and maybe it is a bit too much to
hope to rationalize why he did what he did.", which is not an explanation at
all.

I would be interested to know how likely it is that Maxwell found, and was
influenced by, this derivation.

~~~
itcrowd
Hi! It's true, I did not include the explanation of how Maxwell came to the
displacement current in the post [edit: I mean I didn't include a satisfactory
explanation]. I cannot refer to Nahin's book anymore since I've returned the
book quite some time ago. However, I do have another source:

"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 _d_ E/ _d_ t 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

~~~
mannykannot
Thanks - you have reminded me of it being mentioned in school that Maxwell
came to his four equations through contemplation of a more concrete model that
he later put aside - a sort of Wittgenstein's ladder.

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...](https://plus.google.com/+ChrisReeveOnlineScientificDiscourseIsBroken/posts/7rKJvcyzRjP)

~~~
phkahler
>> Now I am wondering if that was a foretaste of special relativity.

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.

