Sunday, October 23, 2005

Star Gate Near Earth used by alleged ET JROD & Co?

People who really want to understand how Alien ET Super-Technology really works and not be taken in by Lazar's cargo cult not-even-wrong techno-babble snake oil gibberish drivel will have to raise their IQ's and knowledge of mathematics and advanced physics or else simply become obsolete and extinct and sit on the sidelines.

First of all if you read Tom Friedman's "The World is Flat" you will see that most of you will be "Out Sourced" and have to drive cabs, work at Wal Mart, Kentucky Fried Chicken IF YOU'RE LUCKY - or be on the streets. That's if Usama the Mahdi does not nuke us soon or if the hurricanes, earthquakes, tsumamis do not get worse. Gasoline will reach at least $5 gallon if not more soon. Indeed Wal Mart will close down. Then if that is not enough read
Kurzweil, Ray. The Singularity Is Near and see how your STUPID MINDS clogged with TV Football, Video Games, Lazar idiocies, and other mental transfatty acids are making most of you even less likely to survive the coming Darwinian Struggle of Bladerunner & Mad Max, Escape from LA and all that Terminator, War of the Worlds, Independence Day stuff coming. Wrong physics is dangerous - and not-even-wrong nonsense like Lazar's is even more dangerous. We all make mistakes, but crackpots never admit to a mistake, they never change their tune.

This is a new idea and it may not be correct. I am still thinking about it. The basic idea is a global topological stabilization of a traversable wormhole Star Gate in addition to the local metrical distribution of dark energy with negative pressure. Of course the two concentric spherical surfaces of the Hedgehog defect surrounding the Sun with constant inward anomalous a_g = -cH(t) pointing back toward the vicinity of the Sun cannot be themselves Star Gate portals.

*All boundaries are cycles without boundary, but not all cycles are themselves boundaries. Just as all exact forms are closed with vanishing exterior derivative, but not all closed forms are exact.*

The basic idea is a flux quantization of the geometrodynamic tetrad field from single-valuedness of the local vacuum coherence order parameter

B(x) ~ (hG/c^3)^1/2'd'(Goldstone Phase of Higgs Vacuum Coherence)

The 'd' means singularites such that in the multiply-connected deRham integral d'd'(Goldstone Phase) =/= 0.

The generalized Stoke's theorem is

Integral of a p-form on a bounding p-cycle = Integral of d(p-form) on the bounded p+1 manifold.

A p-cycle has no boundary.

Let & be the boundary operator dual to the exterior derivative operator d

&^2 = 0 i.e. Wheeler's "Boundary of a boundary vanishes"

whose dual is

d^2 = 0

Let '&' be a non-bounding cycle.

That is &'&' = 0 but '&' is not a boundary because the p + 1 manifold is multiply-connected, like in a Star Gate, and there are other disconnected non-bounding cycles needed to complete the boundary. That is the p-boundary of the p + 1 multiply-connected manifold has several disjoint pieces.

Now for a closed p-form, by definition

d(closed p-form) = 0

An exact p-form means

exact p-form = d(p-1 form)

All exact p-forms are closed, but not all closed p-forms are exact.

Dual to the above is

&(p-cycle) = 0

Bounding p-cycle = &(p+1 manifold)

All bounding p-cycles have no boundary, but not all p-cycles are themselves boundaries of p+1 manifolds. Or, in other words, all boundaries are cycles, but not all cycles are boundaries. Just as all exact forms are closed, but not all closed forms are exact.

The non-bounding p-cycle is dual to the closed non-exact p-form,

My idea of "Flux without flux" from singularities is a quasi-Stoke's theorem

Integral of a closed non-exact p-form on a non-bounding cycle =/= 0 is well known.

I set this integral equal to the quasi 'd' of the closed p-form integrated on the multiply-connected p+1 manifold.

Suppose for simplicity there are two p-cycles '&'(p + 1)a and '&'(p + 1)b that when summed make a true bounding cycle. Therefore, think of an annulus in the plane p = 1 outer circle a and inner circle b:

&(p+1) = '&'(p + 1)a + '&'(p + 1)b

Then for sure, Stoke's theorem says

Integral of any p-form on &(p+1) = Integral of d(p-form) on the interior p+1 manifold bounded by &(p+1)

Therefore, breaking this apart into pieces

Integral of any p-form on &(p+1) = Integral of any p-form on '&'(p+1)a + Integral of any p-form on '&'(p+1)b

Specialize the arbitrary p-form to an exact p-form with a singularity that is surrounded by '&'(p+1)b

I call this SINGULAR quasi-exact p-form 'd'(p-1)form

Here is an example, for p = 1

'd'theta = {y d(x) - x d(y)}/{x^2+y^2}

in polar coordinates on the flat plane with

x = rcostheta

y = rsintheta

There is a singularity in the 0-form theta at r = 0

For this special case

Integral of 'd'theta about the total boundary of the annulus excluding the phase singularity at r = 0 vanishes. But the integral of 'd'theta about the outer circle in the CW screw sense will be 2piN where N is the winding number of times we move around the outer circle. The inner circle b must be traversed in the CCW screw sense to give -2piN.

Now we imagine the inner circle b shrinking to r = 0 as a limit point. For all practical physical purposes, our detectors only sense the outer circle a. I call this

"Flux without flux" i.e.

Non-vanishing closed loop integral of the 1-form 'd'theta around the non-bounding cycle '&'(2a) BY DEFINITION is the NONLOCAL QUANTIZED FLUX SURFACE INTEGRAL of d'd'theta including the phase singularity at r = 0. That is, the singularity acts AS IF there were "curl" flux present in a kind of Bohm-Aharonov effect since d'd'theta on the closed loop a really vanishes as a simple calculation will show.

Note that any vacuum order parameter in the plane, of the form

Psi(z,r,theta) = |Psi(z,r)|e^iJztheta

with |Psi(z,0)| = 0

where the vacuum manifold is S1 (n = 2) is a vortex core phase singularity along z-axis at r = 0.

Single-valuedness of Psi requires

Jz(Change in theta) = 2piN

where Jz is the "intrinsic quantum angular momentum" of the vortex string.

Note that any stable order parameter topological defect requires a non-trivial homotopy group

PIdim(Surrounding sub-physical manifold)(dim Vacuum Manifold) =/= {Identity Group}

Here dim(Surrounding sub-physical manifold) = 1 i.e. inner circle loop b

dim(Vacuum Manifold) = n = 2

d' = d - n = 3 - 2 = 1 i.e. line vortex defect in the order parameter V manifold.

This is stable because

PI1(S1) = Z i.e. group of integer winding numbers N = +-1, +- 2, ....

On Oct 22, 2005, at 9:54 PM, Jack Sarfatti wrote:

Summary: The NASA Pioneer Anomaly may be a signal that there is a stable Star Gate near the Solar System. The point topological defect stabilizing the Star Gate is near the center of our own Sun according to the NASA data

a_g ~ -cH(t) ~ 1 nanometer per sec^2.

That is, the vacuum broken symmetry is more like that of a "ferromagnet" in internal space V = G/H = S2 than a "superfluid" V = G/H = S1.

Synopsis of the tentative argument (Reference David Thouless, Topological Quantum Numbers (World)):

If V = G/H = Sn-1 for the macro-quantum coherent vacuum order parameter manifold with internal dimension n, e.g. SU(n-1) & O(n) symmetries of V = G/H.

Let m = n - 1

The homotopy groups for the maps of the surround subspace of dim r into the vacuum manifold of dim n are

PIr(Sm) = 0 if r < m

PIm(Sm) = Z are the only stable topological defects, where the integers Z are the stable trapped geometrodynamic fluxes of the gravitational tetrad field

B ~ (hG/c^3)^1/2'd'(Goldstone Phase of Vacuum Coherence)


B^a = (hG/c^3)^1/2'd'(Goldstone Phase of Vacuum Coherence^a)

a = 1, ... n - 1

Here B is an internal 2-component spinor.

n = dimV = dimG/H

Use B = (BaB^a)^1/2 ?

Remember r is the dim of the surrounding space of the defect of dim d' in physical space of dim d with V = G/H of dim n such that

d' = d - n

d' + 1 + r = d

Spacelike slice of space-time has d = 3, space-time has d = 4.

Stargate Wormholes: The mouth has r = 2. d' = 0, d = 3, n = 3, m = 2, PI2(S2) = Z is stable, only if n = 3 i.e. V = 2 i.e. a vector vacuum order parameter. This is consistent with the NASA Pioneer Anomaly!

Note in space-time r = 3, d = 4, d' = 1.

That is, the vacuum manifold has the topology of the unit spherical surface in n = 3 dim with two independent Goldstone Phases (latitude & longitude).

What combination of these 2 Goldstone phases go into the formula for the tetrad B field above?

Development of the argument:

Physical space of 3 dimensions (ignore extra dimensions for now) has a vacuum state that it emerges from and which can support different kinds of local order parameters.

d is the dimension of the physical space. n is the dimension of the vacuum manifold V = G/H of possible order parameters. d' is the dimension of the topological defect or obstruction in the physical space of dimension d. r is the dimension of a subspace S of physical space with which we "surround" or isolate the topological defect of dimension d.

d' + 1 + r = d

Using at first only Galilean relativity, with space split from time

Example 1

d = 3, n = 3 like in a ferromagnet

A point defect has d' = 0, therefore r = 2.

That is we isolate the point defect with a 2D spherical surface S2.

The vacuum manifold is taken as all points in the internal space of dim n beyond physical space of dimension d for which the generalized Higgs intensity is fixed as the unit hypersphere. The Goldstone phases describe the orientations in the internal space of dim n. When n = 2 there is 1 Goldstone phase. There are n - 1 Goldstone phases in V = G/H vacuum manifold of spontaneous broken symmetry SBS.

For example, if the order parameter is a real scalar field n = 1 the vacuum manifold is simply 2 isolated points +1 & -1 i.e. S0 = V = G/H the unit sphere of zero dimension.

If, the order parameter is a complex scalar field with U(1) internal symmetry, then n = 2 & G/H = S1.

If d' = 1 in d = 3, we have a string line vortex defect with r = 1. That is we surround the line vortex with a closed loop S1 = surrounding subspace S.

If d' = 2 in d = 3 we have a wall defect and r = 0, i.e. S0 the two isolated points of S0 for surrounding subspace S.

Example 2 Thin film anyon condensates.

d = 2. If d' = 0 a point defect in the thin film, then r = 1, i.e. a loop S1 surrounds the point defect in the film.

If d' = 1, a line defect in the film then r = 0, then S0 again.

*Also we must have d' = d - n

The only possible Galilean order parameters in 3D space have dim n = 0,1,2,3.

Special relativity allows dim n = 0,1,2,3,4.

The NASA Pioneer anomaly suggests the vacuum order parameter with n = 4 allowing a Hedgehog point defect d' = 0 where d = 4 for space-time rather than space alone. This suggests SU(2)weak = G/H.

Given the internal group SU(N) it is in 2N real dimensions with hypersphere of dim 2N - 1 = S(2N-1) so that n = 2N as the dimension of the Vacuum Manifold G/H. On the other hand, O(N) as internal symmetry group has n = N.

The SU(2) internal group has 3 independent parameters S3, i.e., n = 4 for its vacuum manifold of coherent order parameters.

The U(1) group has N = 1 independent parameter, i.e. n = 2, i.e. S1 vacuum manifold (closed loop circle in a plane with one phase angle & n = 2, S2 = sphere in space with 2 phase angles & n = 3, S3 = hypersphere in 4D with 3 phase angles & n = 4.

Therefore, when d = 3, d' = d - n

Point defect d' = 0 has n = 3, which does not allow SU(2). It allows O(3). But d = 4 & d' = 0 allows SU(2).

Each point in the surrounding subspace S of dim r in physical space of dim d is a point in the vacuum manifold V = G/H of dim n.


d' + 1 + r = d


Dim of defect + 1 + Dim of surrounding subspace S = Dim of physical space


d' = d - n

Dim of defect = Dim of physical space - dim of Vacuum Manifold internal space G/H of order parameters

So that

d - n + 1 + r = d

n = 1 + r

The MAPs of surround subspace S into G/H Vacuum Manifold divide into non-overlapping homotopy equivalence classes in G/H internal order parameter space. G = initial symmetry group spontaneously broken in vacuum down to normal subgroup H. Two maps are equivalent if they continuously deform into each other. This gives for dim r of the surround space S, the rth homotopy group PIr(G/H) where dim(G/H) = n.

Remember for U(1) superfluid in 3D space d = 3, dimG/H = 2 therefore

d' = 3 - 2, i.e. ONLY STRING LINE VORTEX is allowed.

However, in space-time, d = 4

If U(1), i.e. S1 = G/H so that n = 2, therefore r = 1, i.e. a closed loop and

d' = d - n = 4 - 2 = 2, i.e. a wall in space-time i.e. the space-time swept out by a string.

If n = 3 for V = G/H.

Examples of Homotopy groups PIr(V)

For U(1) order parameter n = 2 & d = 3

PI0(S1) = 0 i.e. identity group of 1 element i.e. S0 surrounding space 2-points of a wall defect in 3D space.

PI1(S1) = Z all integers i.e. line vortices r = 1 closed loops surrounding d' = 1, where n = 2 in d = 3.

PI2(S1) = 0.

i.e. r = 2 means surrounding spherical shell of a point defect in 3D space.

Theorem: The Homotopy Group PIr(V) of a defect must not be the trivial group 0 if the defect is STABLE.

Therefore, in 3D space with V = G/H = S1 i.e. U(1) complex scalar order parameter there are no stable point defects and no stable wall defects. There are only stable string line vortex defects.

If V = G/H = Sn-1 for an order parameter with internal dimension n, e.g. SU(n-1) & O(n) symmetries of V = G/H

Let m = n - 1

PIr(Sm) = 0 if r < m

PIm(Sm) = Z are the only stable topological defects.

Remember r is the dim of the surrounding space of the defect of dim d' in physical space of dim d with V = G/H of dim n such that

d' = d - n for topological stability

d' + 1 + r = d

Spacelike slice of space-time has d = 3, space-time has d = 4.

Stargate Wormholes: The mouth has r = 2. d' = 0, d = 3, n = 3, m = 2, PI2(S2) = Z is stable, only if n = 3 i.e. V = 2 i.e. a vector vacuum order parameter. This is consistent with the NASA Pioneer Anomaly!

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