Some intuitive wormhole math
Some math intuitions (under construction)
Given a "multi-valued" 1-form
B = Lp'd'(Theta)
Lp^2 = hG/c^3
Theta = Mean Goldstone Phase corresponding to Vacuum Manifold G/H
Probably G = SU(2)hypercharge, H = U(1)
Restricting to the 3-geometry metric of a space-like slice of 4-D space-time to define the Hodge 3* operation
3*B is a 2-form.
Given a R1 1D string Goldstone phase singularity for the vacuum ODLRO field the along z-axis
B/Lp = (xdy - ydx)/(x^2 + y^2)
We have the 2D S2 dual multi-valued 2-form "Flux without flux"
3*B = 3*Lp'd'(Theta) = (xdy/\dz + ydz/\dx + zdx/\dy)/f(r)^3
with the wormhole space-metric with topology R1xS2
3g = dr^2 + f(r)^2(dtheta^2 + sin^2thetadphi^2)
f(r) is the wormhole shape function
f(r) -> r = (x^2 + y^2 + z^2)^1/2
<3|'d'3*B> = |<'&'3|3*B> = 4piN' (2D Brane Flux without flux quanta for 3*B 2-forms)
N', N = 0, +-1, +-2, ...
<'&'2|B> = <2|dB> = 2piN (1D Brane (AKA string) Flux without flux for B 1-forms)
Now extend this to a Kerr-Newman metric in which the interior of the wormhole between the two S2 2D wormhole mouths is filled with positive dark zero point energy density and negative pressure - sort of like George Chapline's "Dark Star" on micro-scale.
On Sep 27, 2005, at 9:17 AM, Jack Sarfatti wrote:
Memorandum for the Record
Subject: Advanced Space Flight Technology
No more Space Shuttles ever needed again.
I have been asked
"Ok Jack , I read it. Assuming its true, then pray tell how do we get some and bottle it as fuel?"
Forget fuel. There is no fuel! This is not a rocket ejecting mass. Also that is what is wrong with Hal's approach and Woodward's approach and even Gennady Shipov's torsion field drive. Even though they are PROPELLANTLESS, i.e. not ejecting mass, nevertheless they change mass M (by one alleged means or other, torsion for Shipov, Mach's principle for Woodward so there is a vdM/dt term just like in a rocket but without any ejected mass. This is intrinsically unstable and is a BOMB if they change e/m too much! Also it is a non-geodesic drive, i.e. they feel inertial g-forces! Mine is different. I have little LC oscillator loops embedded on nanoscale in thin very high Tc 2D layer anyon films "painted" on the fuselage. Forcing different non-integer continuously varying magnetic fluxes through the little Josephson "super-conducting loops" modifies the Goldstone phase of the Higgs vacuum phase that controls the curvature and the torsion of the local space-time geometrodynamic field. The trick is how to lock the phase of the vacuum to the magnetic fields (currents through the loops). I don't know enough solid state physics yet to do that, but obviously the alien ETs do because their ships fly.
Note that Maxwell's EM field equations in the curved space-time with Shipov's torsion field look like in invariant Cartan notation:
F = DA
DF = 0
D*F = *J
D = d + W/\ + S/
d = Cartan's exterior derivative
W = curvature spin-connection where
dB + W/\(1 + B) = 0
T = dS + W/\S + S/\(1 + B + S) = Russian Torsion Field 2-form
R = (d + W/\)W = Einstein's curvature 2-form from 1915 theory (not done this post-modern way of course)
R/\(1 + B) + /\zpf(1 + B)/\(1 + B)/\(1 + B) = 0
is 1915 Einstein vacuum equation with cosmological constant.
This all generalizes to include torsion to
R' = (d + W/\ + S/\)(W + S)
(d + W/\ + S/\)R' = 0
(d + W/\ + S/\)*R' = *J'
(d + W/\ + S/\)^2*R' = (d + W/\ + S/\)*J' = 0
this is key equation for local stress-energy current density conservation for practical low-power metric engineering of Weightless Warp Drive and Wormhole.
B is the curvature field gauge potential from locally gauging T4 -> Diff(4) of GCTs.
S is the torsion field gauge potential from locally gauging the Lorentz group O(1,3).
A is the electromagnetic gauge potential from locally gauging the internal U(1) group.
This local frame-invariant theory is easily extended to the standard model of quarks and leptons using
the SU(2) and SU(3) internal symmetry groups.
From the standard model SU(2)hypercharge spontaneous symmetry breakdown in pre -> post inflation of false to true vacuum I get (consistent with both standard particle model and standard cosmological model of mainstream physics)
B = (hG/c^3)^1/2'd'(Goldstone Phase of Higgs Field)
T = (hG/c^3)d'd'(Goldstone Phase of Higgs Field)
d^2 = 0
d'd' =/= 0
from PHASE SINGULARITIES
e.g. string vortex phase singularity along z-axis in 3D space
'd'(Phase) = (xdy - ydx)/(x^2 + y^2) 1-form
Note that the 1-form is infinite on the z-axis string.
<&2|'d'(Phase)> = <2|d'd'(Phase)> = 2piN
N = integer winding number
This is Bohm-Aharonov nonlocal "Flux without flux".
The Bohm hidden variable single electron (quark) is an extended microgeon with a strong dark zero point energy uniform core and a thin shell of charge in a "point defect" in the LOCAL vacuum order parameter ODLRO Higgs field manifold G/H.
On Sep 26, 2005, at 9:44 PM, Jack Sarfatti wrote:
Is the discovery of dark energy the key to warp drive?
Dark energy is positive zero point energy density with negative pressure. Einstein showed that the pressure is 3 times as powerful as the energy density in bending space-time. Therefore, dark energy anti-gravitates repelling everything and expanding space beyond its normal Hubble expansion. This is the accelerating universe in which ~ 73% of the large-scale stuff is this dark energy with negative pressure. In addition the Russians (Gennady Shipov in Moscow) are extending Einstein's theory to include torsion fields as well as curvature fields. In that case we can have quintessent fields in which the zero point energy density is not simply a cosmological constant, but is a variable local scalar field. We can now build a Weightless Warp Drive (WWD) like Alcubierre's by a kind of Josephson wave interference effect. We live in a Higgs Ocean vacuum field. The Higgs Ocean has vacuum waves. We use a local high Tc coherent wave like in the thin film anyon condensates that locks into the local phase of the vacuum wave. This is similar to a heterodyne radio receiver. By modulating the local vacuum wave's phase we can make both positive and negative zero point quantum pressures in different parts of the star ship's fuselage and, therefore, shape the weightless free float geodesic glide path of the ship. This does not take a lot of power. It's like Tao Chi. For more details see the new book Super Cosmos by Jack Sarfatti (2005) ISBN:1-4184-7663-3.