Electron Field Soln. w/ Circular Currents

[Albers]

I have extended the Maxwell current eq. to construct an electron model as inhomogeneous charge cloud with a singular but integrable, and thus finite, center. A solution containing the Euler integral is obtained and it is clear this is a model of superconducting circular flow. DO NOT BE PUT OFF BY THE FIRST FEW EQUATIONS. They are just the full current eq which I narrow down to a kindergarten level with frequency set to zero. This tends to make wave theorists turn pale, which is hugely satisfying. I have a URL in the profile. The suspended superconducting ring has a DC skin current. Quantum mechanics adds to this the constraint that there is an underlying wave function which must be integer multiples of 2pi so it "comes around to the same phase". Also in QM, the square of the wave function is interpretable as charge density. I am not doing QM.

[Albers]

If I can show you why a half-million MEV of light is caught dancing on the point of a pin, and why it has fields like a curled-up porcupine electrically and a magnetic moment as if something was moving around, then you could not tell these angels dancing from an electron or positron. One hundred years ago we learned that energy content is proportional to mass. We think, "ah, somehow light turns into mass". We should stop thinking. Nothing turns into anything else. What does happen is a phase change as literal as water to ice. Pick at ice on a cold bench and you will look in vain for water, until you remember that angled molecules have very different states of relation at different states of temperature and pressure. I solve the electron as a "wave" field of zero frequency, and can claim to have the only reasonable solution in the realm of possible guesses to represent physics. There is no feature of change around the circle but energy does flow, as we solve for vector potential A-sub-phi given a RHS to the current eq. of (1/r)e(-r). The singularity is quite piqued but quite integrable as all observables of squared fields go as the inverse square of radius. Again we just assume that the not-vacuum is whatever it is to make this happen! Then we can ask further questions...

[Albers]

In the photon section I observe that Planck's constant is somewhat irrelevant to the photon field. Having set that stage, the only major question is why does the electron such as I depict have the angular momentum it does, and why is this one-half of all orbital angular momenta? I believe the second part is already answered by our present mathematics of fields of fermions and bosons. I suspect the answer to the first is that the size of this entity is determined by the fundamental constants including the fine structure constant. I need to think further on what fundamental constraints are being elucidated here. One needs to come out of such a calculable geometric model with the correct relation between 'e', 'h', and 'alpha'. It is possible, though I need to work here, that something comes out because there is really a length scale in the exponential of a dimensionalized model. We should have gained something by our geometric construction, on a purely logical level. I will work the dimensions through and say something in a day or two.

[Albers]

The first thing I can say is that fine structure constant is a dimensionless ratio. In a geometric model such as I offer it is produced as the ratio of two volume integrals. The FSC goes as the square of charge, over 'hc', and both these have dimensions of energy-length. So in my model: charge is simply four-pi as it is for any workable distribution. Planck's constant I set equal to twice my volume integral of angular momentum density, declaring spin one-half. Thus I am really comparing the different radial distributions of charge density and ang. mom. density and issuing a total FSC. If we ask about interactions, we are just now poking into the near-field, last I heard. It depends what energy photon you use to poke what you will experience. Last year I read of high-energy interaction manifesting an FSC of 1/126, rather than 1/137.

[Albers]

nutcracking

GIven a magnetic vector potential field in A_phi such as in my electron model, I have shown, by integration by parts, that the total magnetic moment of the field may be read simply as: (8/3pi)Lim(r^2A(r)) at large radius. So long as the near field has been shaded to any higher-order dependence in r there is no singular contribution at the center. . . . . . . . . My paper completing the magnetic moment calcs is now available as PART III of the electron paper: http://laps.noaa.gov/albers/physics/na