gravitation and vacuum polarizability

[Norman Albers]

The Polarizable-Vacuum Theory uses the GR metric coupled with a 'scalar field'. I am trying to show the GR metric as a result of vacuum mechanics of 'massive' entities (or of radiation densities). It just depends on what you theoretically start with.

 

People like Robert Dicke and Hal Puthoff accept the GR metric, either Schwarzschild, or the isotropic 'dark gray holes' discussed by the latter, and then 'put in' a scalar field. I hope to show the same essences as coming from an understanding of the fundamental fields of photons and of matter (and of whatever further fields) producing such metric behavior in the small. It seems that quantum field theory precludes any such 'constructionist' approach. I think this is an unnecessary part of our confusion, and that further development will include this as well as a new four-dimensional acknowledgement of the quantum field in the large.

Edited August 26, 2008 by Norman Albers
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[Norman Albers]

Scalbers, here is the punchline, I think of the reference you gave (Schwinger): "The vacuum states with definite chiral charge and zero electric charge have the form (R,L~L,R) O, ~2~-n = N exp ]/.~ mg KC~ (30) where n = 0, 1 .... and N is a normalization constant. We see that the zero mode is present not only in the Hamiltonian of the system (21) but also in the ground-state wave function. It follows from (27) and (28) that the vacuum condensate is a chiral condensate. This circumstance ensures screening (bosonization) of the system if its chirality is nonzero. Indeed, the physical vacuum is one of the linear combinations of the ground states (30) and does not have definite chirality. Therefore, the chirality of the physical system goes over in the case of screening to the vacuum." (Boldface my emphasis.) I appreciate the statement on vacuum degeneracy (accepting of either matter or antimatter) as well as hints to "screening" which I seek to understand, as I make my own models of these things.

[Norman Albers]

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.

Edited November 14, 2008 by Norman Albers
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[Norman Albers]

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.

[Norman Albers]

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.

[Norman Albers]

As I build my understanding of the mathematics here, I am impressed by the importance of the many coordinate transforms used at the drop of a simplifying hat. One must keep track of these or be lost! My work today indicates this is true of the degenerate metric form which is quite useful in getting the Kerr rotational solution. Having this form depends upon the coordinate choice, and so one must use caution in finding physical theoretics. To get the axially symmetric Kerr form, one abandons this simplicity.

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.

Edited December 3, 2008 by Norman Albers
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[Norman Albers]

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.

Edited December 9, 2008 by Norman Albers

[Norman Albers]

This discussion is moving, as per current developments, to the 'reissner-nordstrom..' thread.

[Norman Albers]

Thanks for the suggestion.

 

First of all, the terms matter and anti-matter are sort of misleading. The mass aspects are essentially the same. The only difference is within which mass gets which charge. If we assume charges are equal but opposite, and with mass essentially the same, the interaction is based on charge.

Another observation, is although protons within nuclei are matter and the positron is anti-matter, this interaction is not destructive, with the positron able to get involved in the nuclei and act just like it is matter.

 

Simple mass preference can explain all at the same time.

pioneer I feel you have no hook on which to hang your "simple mass preference". I do like your statement about positrons being massive. Any localization of energy is. I feel you are ignoring a great deal of physical truth in symmetries. The mystery is of symmetry breakdown. Energetic encounters, whether of accelerator or "cosmic ray" nature, give particle pair production.

Edited March 8, 2009 by Norman Albers

[Norman Albers]

I am reading in Feynman Lectures Vol. II, chapter 31 on polarizability tensors. He offers here the machinery which I say is applicable to the vacuum per se. I am seeking a clear expression of the implications of the Schwarzschild and also rotating Kerr metrics, in such a parallel statement. There is a rich realm of implications between strongly rotating large masses, and then again, particles as strongly rotating tiny masses.

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I am feeling my way to a unified field consistent with all we can now comprehend, and maybe there is something for me to express between the differential relations of GR and the interpretations of quantum vacuum physics.

Edited March 17, 2009 by Norman Albers

[Norman Albers]

The metric tensor produced in GR for rotating masses is real-valued. I am looking at null light-speeds, which may be complex-valued. They are expressed as the square root of the ratio of two metric terms, and so must be complex, just because the ratios may be negative. If I can connect my reasoning on gravitational vacuum polarizability with these theoretics, there ought to be a complex tensor expresson for polarizability of the vacuum.

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I must make an important qualification about the metric tensor terms being real. The point of my recent study of the Kerr electron angular momentum object is that we must acknowledge and understand the coordinate system used to solve and express the metric. The fully axially symmetric representation is entirely real but this is coordinate-dependent. Transformed back to Cartesian coordinates there is a singular ring where the metric term itself, and not just its square root, is complex.

[Norman Albers]

Situations like inside a black hole event horizon produce expressions where the quantity [math]ds^2[/math] can be negative. Therefore we might think, as I offered previously on another thread, that these modes may be fundamentally absorbing, which is to way, not happening. Beyond that I am thinking on what solidspin calls 'spassitude', and you can laugh all you want until you get with the program, namely representation of [math]ds[/math]. To fulfill my Polarizable Vacuum visions this must be a complex field. Doing General Relativity I have always dealt with [math]ds^2[/math] as a bilinear mathematic form. Now it's time to look further.

Edited March 28, 2009 by Norman Albers

[solidspin]

so,

 

I, unfortunately, did NOT coin the term spassitude. That said, Norman and I appear to be correct that, provided the proper basis set is selected, Clifford-style 4-space rotations of the photon-coupled graviton vector should be perfectly reasonable. If one re-examines the Maxwell equations in their Hodge dual/anti-self dual forms...the Stepper operators naturally fall out: F(+/-) = 1/2(F +/- i*F).

 

Hoult and Bhakar in Conc. Mag. Res. 9 (1996) lay out the framework. Although strictly in an NMR context, it doesn't matter, as far as I can tell, provided the modifications I'm thinking of are consistent...

[Norman Albers]

In post #36 I made a statement about the implications of the Kerr low-mass AM solution that I now see as incorrect. The GR metric terms do not become imaginary. They do become negative; furthermore, if you solve for null geodesics, they have terms stirred by the AM to complex nullspeeds, but is not a property of the original metric tensor.

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The singular ring analyzed in the original coordinates introduces a quadratic equation when you look at radial displacements. Thus, when we set ds=0, there is not yet a direct relation between cdt and dr.

Edited April 7, 2009 by Norman Albers
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[Norman Albers]

I will try to bring my offerings into focus, but much is being accomplished in the Mathematics section, linear algebra, where I am trying to develop a first-order substructure encompassing polarizability: http://www.scienceforums.net/forum/showthread.php?p=489673#post489673

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I can no longer be part of this forum.