4 ms·

A Technically Nice, Historically False “Explanation” of the Displacement Current

20 points by itcrowd 9y ago

phkahler 9y ago
I'm left wanting for the real reason...
- c3534l 9y ago
  Sounds to me like he was just playing around with the equations until he saw something that might be true.
- mannykannot 9y ago
  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 9y ago
    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 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
    - mannykannot 9y ago
      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/+ChrisReeveOnlineScientificDiscourseIsBroken/posts/7rKJvcyzRjP https://plus.google.com/+ChrisReeveOnlineScientificDiscourse...
      - phkahler 9y ago
        >> 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.
bsder 9y ago
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 9y ago
  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 9y ago
    REALLY off topic but I happen to be sitting about 200 yards from Michelson's childhood home as I read this!
RichardCA 9y ago
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

20 points by itcrowd 9y ago

phkahler 9y ago

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

c3534l 9y ago
Sounds to me like he was just playing around with the equations until he saw something that might be true.
mannykannot 9y ago
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 9y ago
  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 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
  - mannykannot 9y ago
    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/+ChrisReeveOnlineScientificDiscourseIsBroken/posts/7rKJvcyzRjP https://plus.google.com/+ChrisReeveOnlineScientificDiscourse...
    - phkahler 9y ago
      >> 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.

bsder 9y ago

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 9y ago
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 9y ago
  REALLY off topic but I happen to be sitting about 200 yards from Michelson's childhood home as I read this!

RichardCA 9y ago

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