5th March 2007 - 08:11 PM
Dr. Albers -
Some excellent steps forward - I'm very impressed. If you want an outstanding treatment of current which seems like it will help you, I urge you to (re)read Bamberg, Sternberg. A Course in Mathematics for Students of Physics, Vol. 2, p 476. ISBN: 0-521-33245-1
Further, you state:
Here there is not a net charge field so I can say there may not be divergence in the vacuum polarization density. I have just come to see my homogeneous r^-2 as also polarization "dipoles"; why not? Such a distribution will have zero divergence and thus charge density, yet manifest electric field. Thus my electron has a non-diverging (homogeneous) polarization balanced by the near field inhomogeneous (diverging) population.
I see nothing wrong at all w/ your conclusion. But if you draw a schematic that conforms a potential falling off as r^-2, what n-space shape does one get (it's not spherical, which is why I mentioned this before)? Aamof, I have a schematic that I would like to share w/ you which may solve your query regarding your statement above, as "polarization dipoles" - I believe this is a perfect
example of dipoles, but in a sense that treats your proposal in a QM manner. I will send you a msg, giving you my email address, so I can send you the pdf...
So appropriate you place such weight on polarizability (which I, again, believe correct). Please see Bonin, Kresin. Electric-dipole Polarizabilities of Atoms, Molecules and Clusters. ISBN: 981-022-4931 p. 11. As you correctly mention, dielectrics are directly related to polarizabilities by the Debye eq:
alpha = 3/4pi*n(eta^2 - 1/eta^2 + 2) - musub0^2/3kT where the first term of the eq. is the Lorentz-Lorenz relation.
So, as strange as this sounds, could you think about eta^2 (i.e., permittivity), but as a lim rho->some upper limit defined by the density of some regular object? The second term above will end up having a fractional coefficient in front of it, making it less relevant (but not zero). The reason why I ask is b/z there must be a weak dependence on kT, as in the case of regular matter, such that vacuum density is greater inside massive objects. Further, there will definitely be a difference in vacuum density in an object w/ mass, as compared to free spacetime.
Let me send you a msg. w/ my email address and I can explain in more detail why there are physically reasonable, QM grounds for this.