Sunday, January 08, 2006

Warp Drive Equations

Forget the Heim-Hauser nonsense from AIAA. You all saw what Nobel Laureate G. 't-Hooft thinks of it. The following is mainstream and is much more likely to point in the correct direction to understand anomalous observed UFO/Skinwalker phenomena of interest to CIA, DIA, NDI et-al. See remark on rotating conducting plates at end.

On Jan 8, 2006, at 5:06 PM, Jack Sarfatti wrote:

1. We take the condensed matter approach that "More is different" (P.W. Anderson) and so Einstein's 1915 theory of gravity as smooth curved spacetime is an emergent collective low energy effective c-number local field theory very much like superfluid helium and the BCS theory of superconductivity using the Landau-Ginzburg local order parameter. The latter systems are for the ground states of real on-mass-shell particles. In our problem we are dealing only with the vacuum states of virtual off-mass-shell particles.

2. What is new about this paper is the idea that Einstein's field equations are a trivial consequence of the modulation of the Goldstone phases in the inflation Higgs field in the first 10^-44 seconds of the chaotic creation of our pocket universe.

3. This is prior to the splitting off of the electroweak Higgs that gives the leptons and quarks mass at ~ 10^-17cm. It is prior to the heating of the Big Bang whose surface of last scattering is seen in the WMAP NASA data.

4. Guided by

4a. Hawking-Bekenstein conjecture

Entropy of black hole/k = (Area of Event Horizon)/4Lp^2

4b. 't-Hooft/Susskind world hologram conjecture

i.e. the geometrodynamic field is fundamentally 2 + 1 with the 3 + 1 Einstein theory as a kind of "holographic image"

we are led to a simple toy model of three real Higgs scalar fields that Bose-Einstein condense in the first 10^-44 sec causing inflation.

This is V(Planck 10^-33 cm) = G(False Vacuum)/H(True Vacuum) = S2

with 2 0-form Goldstone phases theta & phi defining the locus of minima in the effective Higgs potential at 10^-33 cm. We leave open the possibility that Lp* >> Lp = 10^-33 cm from extra space dimensions of brane theory.

5. The pre-inflation false vacuum is not a pre-geometry, it is not a spin-foam, it is simply the globally flat standard model U(1)xSU(2)xSU(3) or its GUT or maybe string theory type extensions. The details of that do not matter. It is of course sans gravity and sans mass in the unstable false vacuum.

6. We also make an analogy with the Bohm pilot-wave guidance constraint

v(IT particle) = (h/m)grad(phase of pilot BIT wave)

becomes (I change notation)

L/Lp = (dtheta)(phi) - (theta)(dphi) = Geometrodynamic LINE FLUX DENSITY 1-FORM

7. V(Planck) = G/H = S2

8. Equation of the locus of minima for 3 real Higgs scalar field h1, h2, h3 is

cos^2theta + cos^2phi + cos^2chi = 1

taking theta & phi as the 2 independent Goldstone phases where the Higgs potential

U(h1, h2, h3) has a stable locus of degenerate minima on the unit spherical surface in a fiber space.

9. Therefore, the geometrodynamic area flux density 2-form is

A/Lp^2 = dL/Lp^2 = 2(dtheta)/\(dphi)

10. Obviously the geometrodynamic volume flux density 3-form is locally zero

V = dA/Lp^3 = 0 This is "volume without volume" i.e. 't-hooft/Susskind hologram

Think Bohm-Aharonov effect where

curlvs = 0 locally but loop integral of vs round a line vortex defect is quantized Nh/m

Similarly for magnetic flux.

Closed (nonbounding) surface integral of A is quantized to integer x Lp^2

from second homtopy group(S2) = Z

11. Finally derivation of 1915 GR in a few lines directly from EEP

guv(curved) = eu^anab(flat)ev^b

eu^a = 1u^a + Lu^a

ds^2 = guvdx^udx^v

e = 1 + L

e = eu^adx^u&a

dx^u is a local 1-form basis in base space

&a is a local 1-coform basis in tangent space fiber

Symbolically in local frame invariant form

ds^2 = (1 + L)n(1 + L)

L = 0 is globally flat special relativity, but with no gravity and NO masses!

12. It's Bohm hidden-variable Wheeler micro-geon "Mass without mass", but only when the electroweak Higgs field splits off from the Planck Higgs field to give the lepton-quark plasma masses before confinement as the hot Big Bang cools down to the surface of last scattering seen in WMAP.

13. The effective G for the lepton & quark micro-geons is strong at short-range because the cosmological constant /\ is itself a local scalar field /\zpf that is both + and - at short scales.

For example, for a thin weakly rotating spherical shell of effective charge Q, angular momentum J, the effective Newtonian limit potential energy per unit mass M is V, where dimensionless V/c^2 is

V/c^2 = -(1/2)/\zpfr^2 + (hc + Q^2)/Mc^2r + (J/Mc)^2(1/r^2)

The force per unit mass is

F/M = - dV/dr = +c^2/\zpfr + (hc + Q^2)/Mr^2 + 2(J/M)^2(1/r^3)

Equilibrium happens for /\zpf < 0 and

F/M = 0

Stability is

dV/dr^2 > 0


-c^2/\zpf + 2(hc + Q^2)/Mr^r + 6(J/M)^2(1/r^3) > 0

This is trivially true since /\zpf < 0 i.e. negative zero point energy density with positive pressure. In this spherically symmetric problem w = (pressure)/(energy density) = - 1 (unlike anisotropic QED Casimir plates for effective ).

14. Note for Casimir plates, the longitudinal pressure perpendicular to the plates is negative. This gives simultaneously an attractive electrical force, but a repulsive gravity "force" on the plates, of different strengths of course. The transverse pressure is positive giving a repulsive electrical force and an attractive gravity "force" all assuming a positive energy density of course.

The GR equation is for plates separated by a

Guv + (8piG/c^4)Tuv = 0

Where approximately (weak curvature perturbation of flat space-time)

Tuv ~ (pi^2/720)(h/2pi)a^-4[-1,+1,+1,-3}

only diagonal elements shown. All off-diagonal source stress-energy density components are zero.

This will change if the plates rotate!

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