In a message dated 8/31/2004 4:58:13 PM Central Daylight Time, email@example.com writes:
[Jack] I do not understand what you mean by Coulomb pressure? Do
you compute the electric field E(a) at the shell at radius a, i.e. E(a)
~ (Ne)^2/a^2 and then compute the electrostatic energy density ~
E(a)^2/8pi? Is that what you mean?
[Jack] Even if that is what you mean, I do
not see how anything gets "balanced" here? You have a "classical"
electrostatic energy density and a micro-quantum ZPF virtual photon
density. Both are positive. In what sense do they balance?
[Hal] "Force balance. The ZPE pressure (as in Milonni et al.'s paper "Radiation pressure from the vacuum: Physical interpretation of the Casimir force", Phys. Rev. A, Vol. 38, No. 3, pp. 1621-1623, 1988) outside the sphere presses inward, and there being no pressure from within the ZPE-depleted sphere - - at least from below the Compton freq - - pressing outward, so the net ZPE pressure is inward. This is what balances (with stability) the outward Coulomb pressure. This is specifically displayed in http://arxiv.org/abs/physics/0408114 ."
[Jack now] Oh! So you assume that there is "no pressure from within the ZPE-depleted sphere". OK at least that makes sense logically although I think the model is false - now at least I see what the idea was, which I did not see before. In my view the effective spherical cavity of N electrons, each of area ~ (h/mc)^2, tiled around the spherical surface at radius a ~ N^1/2(h/mc) supports all spherical virtual photon mode eigenfunctions of wavelength approximately 2a or maybe 4a down to some short wave cutoff - maybe h/mc maybe smaller. That is, I think of the interior of the spherical cavity as a band-pass filter with a long wave cut-off of ~ a and and short wave cutoff that is not really known - maybe h/mc. The outside would not have the long wave cutoff at all - or it would be something like the Hubble horizon at ~ 10^28 cm. I suppose you call this Casimir Type I model. Of course, Casimir had no concept of my /\zpf field. Note that
/\zpf ~ (short wavelength cut-off)^-2[(short wavelength cut-off)^3|Vacuum Coherence|^2 - 1]
Where Vacuum Coherence is a LOCAL "ODLRO" smooth c-number complex scalar field obeying an Einstein GCT covariant nonlinear partial differential equation with essentially the "inflation"/"Higgs" type "Mexican Hat Potential".
Einstein's LOCAL metric tensor guv field (there is a self-creating bootstrap here) comes from the robust macro-quantum phase of the Vacuum Coherence via the LOCAL GCT first rank world distortion tensor at event P
du = (short wavelength cut-off)^2(phase of Vacuum Coherence),u
,u is ordinary partial derivative relative to x^u(P) a local coordinate chart at event P
guv = nuv + (du,v + dv,u)/2
nuv is the globally flat constant Minkowski metric tensor WITHOUT ANY GRAVITY!
When Vacuum Coherence = 0 we are back to the unstable globally flat pre-inflationary FALSE VACUUM!
This is where the virtual electron-positron pairs fail to bind into a vacuum condensate like a superconductor above critical temperature.
The GCT tensor transformations derive from the U(1) local gauge transformations on the Vacuum Coherence.
Physics is simple when it's local. Macro-quantum physics is local because ODLRO order parameters are local and also they are of lower relative entropy which solves Roger Penrose's dilemma of the origin of the Arrow of Time for the Second Law of Thermodynamics in the inflation theory. The Vacuum Coherence at large-scale is the post-inflationary field and at small-scale is the Higgs field for the rest mass inertia of the lepto-quarks not from random virtual photon acceleration friction, but from vacuum coherence.
The DYNAMICAL BACKGROUND INDEPENDENT world elasticity tensor (du,v + dv,u)/2 is NOT SMALL! This is not perturbation theory. guv is a smooth c-number function and you can also in addition must add a spin 2 GCT tensor huv "graviton" quantum field to it that is like its "normal fluid" source-sink.
Defining the Levi-Civita connection from first partial derivatives of guv in usual way without torsion (added later perhaps along with other conformal gauge fields) gives
Guv + /\zpfguv = 0
The exotic vacuum equation where Tuv is not fundamental, but emerges from micro-geon exotic vacuum solutions.
/\zpf > 0 is dark energy with negative pressure causing STRONG short-scale anti-gravity.
/\zpf < 0 is dark matter with positive pressure causing STRONG short-scale gravity
In fact Ken Shoulders EVO's need dark energy cores! The N-poly-electron "shell" or cavity of radius
a ~ N^1/2(h/mc) is a "Dark Energy Bottle".
Mike Turner said it couldn't be done! (April 2003, Physics Today Op/Ed) Well Ken Shoulders seems to have done it anyway!
Break the bottle and the Dark Energy Genie escapes as anomalous "Cold Fusion".
Dark Energy is the exotic stuff of weightless warps, wide wormholes and weird weapons.