## Saturday, October 22, 2005

Star Gate near Earth used by ETs?

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)

i.e.

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.

Remember

d' + 1 + r = d

i.e.,

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

And

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

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!