Science > Physics > More on string-wormhole duality in Vacuum ODLRO emergent GR
| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
28 Sep 2005 10:57:13 AM |
| Object: |
More on string-wormhole duality in Vacuum ODLRO emergent GR |
Ex. 1) We need to be careful to distinguish the spontaneously broken
symmetric vacuum manifold G/H for the space of local macro-quantum order
parameters PSI(x) from the physical 3D spacelike slice of 4D spacetime.
For example, if for a given x in 4D spacetime, G/H is a complex plane
fiber at each x, i.e. G/H ~ U(1) ~ S1 (circle in a plane), using the
Bohm polar representation
PSI(x) = R(x)e^iS(x) = RePSI(x) + iImPSI(x)
Looking at the dual vector fields instead of the Cartan forms: define
the ordinary partial derivatives in the fiber space i.e. ,R & ,S
Note that the Lie Bracket for the Cartesian partial derivatives
vanishes, i.e.
[,RePSI,ImPSI] = 0
But the Lie Bracket for the polar partial derivatives does not because
,R = [RePSI,ImPSI + ImPSI,RePSI]/[RePSI^2 + ImPSI^2]^1/2
,S = [RePSI,ImPSI - ImPSI,RePSI]/[RePSI^2 + ImPSI^2]^1/2
Note the coordinate-dependent singularity at the zeros R = Higgs
amplitude of the local vacuum ODLRO order parameter in these partial
derivative vector fields.
In general for any G/H vacuum manifold
PSI = (PSI)ie^i = |Mean Higgs Amplitude|e^i(Mean Goldstone Phase)
B(x) = (hG/c^3)^1/2'd'(Mean Goldstone Phase(x))
The integral of the 1-form B(x) over a closed loop around the z-axis
will be an integer if the order parameter is single-valued.
For example if G/H = SU(2) then i = 1,2,3
If G/H = SU(3) then i = 1,2,3, ... 8
The domain of i is the number of independent elements of the Lie algebra
of the degenerate macro-quantum coherent vacuum manifold G/H, which is
also a quotient group because the unbroken subgroup H of the broken
symmetry group G is always a normal subgroup.
We always need to specify a "metric" in physical spacetime x to define a
Hodge * dual.
3*'d'(Mean Goldstone Phase) is a closed non-exact 2-form (dual to closed
non-exact 1-form B(x)) whose integral over the closed S2 wormhole mouth
is quantized when the vacuum order parameter is single-valued.
Can we generalize this to multivalued order parameters to get anyon
para-statistics? For example a macro-quantum spinor where one has to
rotate 4pi to get back to same order parameter. I suspect that we can
further generalize using the roots of unity to get fractions of the flux
quantum like in the fractional quantum Hall effect.
In the non-rotating wormhole case we ignore the gravimagnetism of the
Kerr metric in a toy model to simply show the idea. Further we restrict
to a spacelike slice 3Geometry.
If 'd'(Mean Goldstone Phase) is a vortex string singularity along the
z-axis from -infinity to 0, then we can associate a point defect on the
string at the origin (x = y = 0) corresponding to one S2 mouth of the
wormhole. The other mouth is for z from 0 to + infinity as shown below
(in physical space not G/H space).
On Sep 27, 2005, at 9:27 PM, Jack Sarfatti wrote:
What is the relation of the shape functions of string and wormhole?
Easy in the toy model below, for the string defect
g -> x^2 + y^2 far from the string
for the wormhole
f -> (x^2 + y^2 + z^2)^1/2
therefore
f^2 = z^2 + g
for a "vortex string" on the z-axis for the Vacuum ODLRO field of the
fabric of space-time.
whose 3D Hodge * dual is a wormhole (Einstein-Rosen Bridge)
On Sep 27, 2005, at 9:07 PM, Jack Sarfatti wrote:
The duality of strings (vortices) and wormholes, heralded as a triumph
in "string theory" is almost trite in my vacuum ODLRO theory of emergent
gravity in which extra dimensions plays no direct role.
Rule of thumb from the nonlinear non-unitary local Landau-Ginzburg type
equations for topological defects when the Goldstone phase goes
singular, the Higgs amplitude drops to zero. It need not be so extreme.
When there is multiple connectivity the Goldstone phase peaks whilst the
Higgs amplitude dips to compensate. This is certainly the case for the
vortex line in a quantum liquid.
OK we have a coherent Goldstone phase field "Theta" 0-form with
singularities so that the 1 form
B ~ 'd'(Theta) is multi-valued.
e.g.
'd'(Theta) = (xdy - ydx)/g[(x^2 + y^2)]
is closed but not exact, i.e, it's closed loop integral need not vanish.
Far from the string (z-axis) where B peaks to a max, the Higgs amplitude
|Psi| for
Psi = |Psi|e^iTheta dips. And if Psi is single valued we get a
quantization (Bohr-Sommerfeld rule).
Asymptotically far from the z-axis (scale is the coherence length) g ->
x^2 + y^2
We then introduce the multiply connected wormhole metric in 3D space
that allows us to define a dual 2-form point defect
3*'d'(Theta) = (xdy/\dz + ydz/\dx + zdx/\dy)/f(r^3)
asymptotically f(r) -> (x^2 + y^2 + z^2)^1/2
df/dr = 0 determines size of wormhole portal with topology S^2
d^2/dr^2 > 0 for stability of the wormhole portal
f(r) = Star Gate Shape function needing a torsioned quintessent
(variable) dark zero point energy field /\zpf(x,y,z) to achieve.
The non-vanishing "Flux without flux" integrals of closed, but
non-exact, forms are always over multiply-connected manifolds and,
therefore, do not vanish. If, in addition the order parameter is
single-valued as it is in a "stationary" equilibrium state, then
integrals are quantized. However one can always force non-integer fluxes
through the holes in an "excited" non-equilibrium state that, if left to
itself, will expel the excess flux out of the core of the defect in the
generalized Meissner effect. The modulation of the vacuum phase for the
fabric of space-time needed for the practical low-power shaping of warp
drive and wormhole portals is such a pumped non-equilibrium process where
Phase of Vacuum Relative to Control ~ 2p(Forced Flux Through
Hole)/(Quantum of Flux)
/\zpf ~ (impedance match)(Surface Density of Vacuum ODLRO)^1/2(Surface
Density of Control ODLRO)^1/2cos(Relative Phase)
Guv(x) + /\zpf(x)guv(x) = 0
On Sep 27, 2005, at 5:57 PM, Jack Sarfatti wrote:
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
Asymptotically
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
where
D = d + W/\ + S/\
d = Cartan's exterior derivative
W = curvature spin-connection where
dB + W/\(1 + B) = 0
T = dS + W/\S + S/\(1 + B + S) = Russian Torsion Field 2-form
where
R = (d + W/\)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)
Note that
d^2 = 0
but
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.
.
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