E&M felt more like … [a] condensed matter theory than something that said much about nature.

*uncomfortable cough* … egad … oh dear…that’s not very nice, now is it? If you’re looking for theories that “say much about nature”, I would recommend you give condensed matter physics a closer look.

Cheers,

-cvj

-cvj

Maxwell’s original papers on this from 1861 are online at http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf

It’s all about “theory of molecular vortices” and pressures in the aether; see page 38 (on your PDF reader) for Maxwell’s graphical illustration of the “displacement current” mechanism. Page 49 on the PDF reader (labelled page 22 on the document) gives Maxwell’s claim to have predicted the velocity of light; using the formula for transverse waves in an elastic solid he gets the right answer and immediately declares in his own italics:

“… we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

That 1861 quotation is quote common, but Maxwell rebuilt the mathematics of the theory in 1965 in a more abstract way and that averts some of the physically suspect theorizing (aetherial gear cogs and idler wheels in space) that the 1861 papers contains. Nowadays, the mathematics is all that is important.

It is curious that a lot of Maxwell’s problems seem related to the Dirac sea issues of quantum field theory, for example if the vacuum is polarizable without any limits, it would be able to polarize around an charge just enough to completely cancel it’s electric field completely.

This is clearly one reason for assuming lower limit electric field strength for polarization in quantum electrodynamics. What amazes me from studying lecture notes like http://arxiv.org/abs/hep-th/0510040 is that there are no vacuum loop effects beyond 1 fm from a fermion. The field below the IR cutoff is qualitatively different and more classical in nature than the close-in field which is affected by loops of charges appearing and annihilating. This isn’t made clear in popular accounts, which always seem to say that the vacuum is filled with pairs appearing and annihilating everywhere. Clearly the IR cutoff, requiring an intense field strength or frequency to create loops, prohibits any polarization of the vacuum and thus “displacement current” in radio or light waves, which don’t contain strong enough fields to polarize the vacuum.

Instead, a time-varying electric field is a curling magnetic field (4th Maxwell equation) just as a moving electric field (relative to observer!) is a straight magnetic field; the Lorentz force law, which assumes E = v x B, is literally to be interpreted as saying that “an magnetic field is a moving electric field”. (Maxwell’s detailed mechanism by which the electric field polarizes vacuum charge inducing “displacement current”, to create a magnetic field, is just complex and superfluous. You simply don’t need moving charge to create a curling magnetic field, because a varying electric field will do the job directly.)

This is a reversion from Maxwell’s aether to Faraday’s 1846 paper Thoughts on Ray Vibrations which argued how that oscillations of electric and magnetic fields could constitute light.

-cvj

Bernhard Riemann once claimed: “The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean.” His prophesy was realized later with Einstein’s general theory of relativity. It is futile to expect one “correct geometry” as is evident in the dispute as to whether elliptical, Euclidean or hyperbolic geometry is the “best” model for our universe. Henri Poincaré, in Science and Hypothesis (New York: Dover, 1952, pp. 49-50) expressed it this way.

I am going to try and take it take it to a “whole…nother…..level.”

The story of physics is that one can go very far with linear or first order approximations, but nature herself is highly nonlinear. If QM were linear, twice a state vector would correspond to a state with twice the number of particles or twice of something. E&M is truly linear (in vacuum), and that shows that it is that much farther away from nature. It is a simplification, a fable, a story for undergraduates, an approximation that works only for very tenuous situations.

And I should mention that in the density matrix / operator formalism of quantum mechanics, the fundamental equation is the simplest non linear equation, . This expresses perfectly the difference between the easy linearity of E&M and the difficult non linearity of the real world.

Good Luck with the E&M fun-ness!

-cvj

Then recently I found Carver Mead’s ‘Collective Electrodynamics,’ which works through this point of view. It’s really a big improvement.

-cvj

Cheers,

-cvj