Norman Albers

How does this come about in your theoretics?

I have been successfully solving the Kerr metric vacuum solution for the electron as a strong angular momentum source. As distinct from my representations of inhomogeneous possibilities, this is a clean application of General Relativity to an object of spin [math]\hbar/2[/math], and the mass of the electron. The Kerr metric characterizes angular momentum (AM) by the parameter 'a' = J/Mc, which has dimensions of length as does the Schwarzschild geometric mass 'm'. For this value of AM, 'a' is about 2 E-13 meters. On the other hand, 'm' is roughly E-57 meters. My first attempt ignored terms in m since they seem miniscule compared to changes in radius larger than Planck length. However there is a very interesting joker in this deck. In the Schwarzschild solution, the first metric term: [math]g_{00}= 1 - 2m/r [/math] is well-behaved except at the origin of r=0, and in this case the scale is set by m. In the Kerr electron case, however, the coordinates have been put through four or five transforms and usually presented in terms of the final set of variables which present an axially symmetric form. I have tracked the transforms backward to express physics in the original 'lab' Cartesian coordinates. There is a degeneracy in the radial transform, such that [math]\rho[/math] goes strictly to zero in the flat disc region of z=0 and [math] r \le a[/math]. This causes asymptotic behavior where permittivity goes to zero, at least near r=0 and r=a, just as it does at the center singularity in the massive Schwarzschild solution. This behavior characterizes a thin layer, of dimension m, about those regions of the disc. I will be writing up this study and welcome comments from anyone who might have read such an interpretation elsewhere. Other near regions seem generally to have higher permittivity, shading off into the far-field, greater than unity and more like the mass source solution. This might even be the case between r=0 and r=a on the disc of z=0. Thus the singularity itself is a thin torus at a, as well as the small center Schwarzschild singularity. (More later...) When I say "permittivity" of a region, I have solved the null geodesic case and associated lightspeed measured in Cartesian coordinates with what I see as local permittivity, as in my paper on gravitation, and the Polarizable Vacuum interpretation as I am investigating it. This is a mathematician's paradise and possibly a physicist's hell, we'll see. There is a stunning discontinuity between interior behavior approaching the point z=0, r=a, and exterior metrics. I hope to post a paper within a few days.

In a difficult encounter on a faraway forum in a distant galaxy, ruled by the Evil King X, when my inhomogeneous electron model with circular currents was dismissed as garbage, I re-entered in under Electrodynamics, "Possible Solution for Ball Lightning". I was partly serious, though the vacuum fluctuation field is not the same as ionized atoms. I do claim that if the field structure described is established in an ionizable medium, it will have self-sustaining dynamics.

I have come to an interesting and useful realization about the relation between Compton electron wavelength, and what I call 'geometric angular momentum radius' from the Kerr GR metric solution. Here, we multiply the 'geometric mass' of the Schwarzschild solution, [math] m=\kappa M/c^2 [/math], with a parameter also of length dimension, so the product [math] ma= -\frac{\kappa J}{ c^3 }[/math] may be called 'geometric angular momentum'. Substituting for m, [math]a=\frac J {Mc} [/math]. I kept going back and forth with my friend solidspin about this being E-12 or E-13 meters. Compton radius is closer to the first figure, where my geometric radius came out a magnitude smaller. I see Compton length as that defined by considering the mass of the particle to be equated to a photon of such energy. This is a spin-1 object, and we say "it's like [math]Mc^2=h\nu=hc/\lambda[/math]". On the other hand, we may think of the Kerr AM issue as though a linear momentum of Mc had a moment radius of a, yielding the AM of the electron, which is Planck's constant divided by [math]4\pi[/math]. This [math]4\pi[/math] is the factor between the two parameters. I started by throwing out terms in [math] m/\rho [/math] or even m/a. However at E-13 meters or so, [math]\rho[/math] becomes strictly zero if also z=0. So these terms must be retained and worked with.

To Swansont's statement, yes, but that does not take away from a good statement such as Weyl's.

Stochastic knowledge!!!

Once in the gym locker room a clearly conservative sort of young man tried to corner me as to "Are you a liberal or a conservative?" I just kept tweaking his head, saying, well get to specifics. I am this, or that, depending. He could not handle this and I was amused. Nice statement from Martin about not copping attitudes.

Whoa, thank you Swansont. The plot is thick and I hope to see further. So are all these possibilities expressed in a Lagrangian expression such as I read about the Standard Model? I didn't know how things are structured at this level. You speak of a lower energy of the virtuals; may I call them vacuum fluctuations?

What cannot be "destroyed" is mass-energy. When an electron encounters a positron, which happens frequently, they "disappear" yielding two gammas going off in opposite directions, balancing momentum and energy. Our local space gives production of "particle-antiparticle" pairs given sufficient energy sloshing around. Each cosmic "ray" in the upper atmosphere creates a large shower of such as it plays pinball with quite a few atmosphere atoms. What is weird is the virtual field, which most of us agree, in some degree, must characterize the "vacuum". Here lie great questions and further theory.

After annihilation of mass states there is present the same total energy. ajb, is the space necessarily curved? The Schwarzschild solution is of the vacuum with a source. The curvature tensor is set to zero. I think the opposite! You can recreate the GR solution by considering the whole thing to be a thickening of the polarizability of the vacuum. Locally one always measures permittivity of [math]\epsilon_0[/math], but you can apply dielectric theory (as in my paper) which has the same weird behavior, only there it's called "dielectric runaway". Maybe the harder question is being approached by ajb who notes that we need to bend our ideas. It seems now that I have had the wrong idea of the word "curvature" so I must apologize to ajb. Checking my sources, one can speak of the rank-4 Riemann tensor. If all its terms are zero then it is a flat, Lorentz space. The Einstein equations use the rank-2 contraction or the Ricci curvature tensor. So the vacuum space outside of a massive source is correctly described as curved. Sorry.

This might belong here, or in astronomy/cosmo, but: I read of the possible radiation from event horizon limits of virtual particles, one of which is going outward and the other of which is going in. This may be seen as radiation from the outside but something is gained by the black hole, so it seems to me this cannot be seen as a mechanism for loss of BH mass/energy. What is claimed here? If we have interrupted what was a virtual process. this is serious business, but accounting should go both ways.

I am working to write these coordinate transforms and would appreciate comments on working to interpret physical phenomenology. Starting with the Eddington transform, [math] \bar x^0= x^0 +2m~log |r/2m -1| [/math], we use a time coordinate displaced from the original by a logarithmic term in the radial variable. [More later.] Now that I remembered to use the transpose of the coordinate transform matrix to get to the metric transform: [math] \hat {g_{ab}}= \bar T g_{cd} T [/math], I am expressing the Eddington transform to another symmetric tensor. My question to all is, what is the meaning of the Kerr metric after something like five coordinate transforms, which we need to get to the axially symmetric expression satisfying the field equations, with only the cross-term, [math]d\phi cdt[/math]? I am starting by asking what is the appearance of nearfield physics to a farfield observer, which is expressed in the original Cartesian coordinates. Every perspective is useful, if you know what you are talking about.

I see the SOL as implied from a differential null geodesic to be decreasing in the tangential direction, but increasing in the radial sense. In the Schwarzschild metric solution they both decrease, as if the vacuum were thickening. This is quite different and speaks to me of some sort of quadrupole moment, some way of seeing angular momentum interactions.

I read the concept as saying that we can tie energy to frequency even in massive objects. Then further, we connect momentum to wavelength. Thus we describe a phase velocity which is E/p and thus has speed of light as a lower limit. Group velocity gives us behavior of mass.

There is a trade-off here between some characteristic on the plane or on the pole (so-called z-pole, + or - ) of an angular momentum vector. I would appreciate input from those who might know of previous investigations here. This is not like the gravitational rotating mass, a different regime, and it has to do with the basic relation between General Relativity and angular momemtum on the quantum level.

The construction is of a wavefield where momentum is represented by wavelength and energy is represented by frequency, according to massive possibilities in special relativity.

When you set up equations for conservation of energy and conservation of momentum for the incompressible case, you get that pressure is potential energy and velocity is kinetic energy. When a flow diameter is reduced, an exchange between the two forms is created. Friction is a certain rate of loss of these energies.

Conservation of mass is thus clear, but further sciencefisfun asks about pressure tradeoffs in changing flows. These are what happens in situations of changing diameters of pipe. If you analyze energy content of what goes in and then comes out, acknowledging that velocity manifests energy, as does pressure, they trade off, given no other inputs or losses.

There is metric physics implied at roughly the classical radius of the electron, as the General Relativistic definition involved in angular momentum of the electron yields a "geometric angular momentum" of ma where a is determined by the angular momentum of the source, and m is the geometric mass, or [math] \kappa M/c^2 [/math]. Both m and a have dimensions of length. I am working to complete my study of gravitation in the small by considering the electron as an object of angular momentum [math]\hbar/2 [/math], and of charge e-, and surprisingly not so important here, mass of about 10^-30 kg. In general relativity theory I get a value for characteristic angular momentum radius of roughly 10^-13 m. This is defined: [math]a=J/Mc[/math]. People often talk of the 'geometric angular momentum' and this is the product am, where m is the 'geometric mass' or Schwarzschild radius. Without assuming anything further about interior field structure, or saying the source is "small", the vacuum Kerr metric can be interpreted is this regime, [math] 1>>a>>m [/math] , as: [math] (ds)^2~= (dx^0)^2 - (d\sigma)^2~+\frac {a^2 sin\theta^2} {\rho^2 + a^2} d\rho^2 - a^2 cos\theta^2 d\theta^2 - ...[/math] 'Sigma' is the three-space differential, with radial variable [math] \rho[/math]. In this realm of the solution space, there are no "null surfaces" such as we encounter in the massive rotating system. We may investigate null geodesics however, asking about light propagation radially and transversely, by setting [math](ds)^2[/math] equal to zero and looking at the spatial displacement of interest. The results are fascinating. Maybe we can get away with speaking of naked singularities.

So also AlphaNumeric states a limit process. This is intriguing to me, Severian, what are the infra-red divergences?

Eric 5, I figure we define 'space' as wherever physics of light and massive entities happens. This is one of the best of questions.

Nature certainly does away with embarassing infinities. There is no Rules Manual, and we move forward with experimental poking around, and with mathematic insights to further representations.

B-b-bingo! Here in Feynman Lectures, Vol. I, p. 30-7, a section on thin films. "...some of the light is reflected both on entering and leaving a refracting medium. Then, if we look at the reflection of a light source in a thin film, we see the sum of two waves; if the thicknesses are small enough, these two waves will produce an interference, either constructive or destructive, depending on the signs of the phases. It might be, for instance, that for red light, we get an enhanced reflection, but for blue light... destructive interfering reflection, so we see a bright red reflection. If we change the thickness..." Here is a good industrial sort of reference: http://www.winrepco.com/Low-e%20Glass.htm THEY ARE SAYING, "METALLIC COATING", but I don't yet know how-so. Pure metals manifest an imaginary index...

Cool. I am guessing. All these materials are dielectrics.

Thanks, scalbers. I know the problem is "just pathlengths projected into angles" and I am now getting a feel for it. Bear in mind that this manifests in such different scales and situations. I see Feynman has a whole chapter on diffraction that I've not ever read. I'm glad the winter rains just came.