NASA Pioneer Anomaly as Dark Energy Point Defect in Vacuum Higgs Field
Basic idea is gravity & inertia emerge TOGETHER in order to obey equivalence principle.
Inertia of leptons & quarks come from macro-quantum Higgs vacuum amplitude.
Gravity comes from complementary Goldstone phase of Higgs vacuum amplitude.
The selection of a spontaneous symmetry breaking scheme is not unique, though it is more restrictive than the solutions to string theory.
The NASA Pioneer anomaly (2 actual probes, and apparently their rotation about their centers of mass distinguishes them from other probes that do not sense the anomaly) suggests a monopole-like point defect at center of sun in the hedgehog configuration with wrapping number -1.
i.e. use the adjoint 3 irrep of SU(2)weak analogous to isospin 1 in nuclear physics. This corresponds to R in SO(3). 2 SU(2) elements U & -U in the 2-rep map to the same R in SO(3). The multiply-connected parameter manifold of SO(3) is S^3 with antipodal points identified.
We then have 3 real Higgs fields in this adjoint 3-rep of SU(2)weak. Use a Mexican Hat quartic potential and choose a vacuum that is (0,0,|(0|phi|0)|) i.e. the real reference vacuum order parameter points along z-axis in group space. Rotations about this z-axis in the SO(3) group parameter space annihilate the real order parameter. Consequently an SO(2) subspace or rotations R = exp-ithetaT3 leaves |(0|phi|0)| invariant. Therefore, H = U(1) and the Vacuum Manifold is G/H = SU(2)weak/U(1) ~ S^2
That is the dim n = 3 of the vacuum manifold S^n-1 in 3-space d = 3.
The stable defect here is d' = d - n = 0
1 + r + d' = d
r = 2 is dim of surrounding subspace of the defect in physical space.
But if you look at the simplest model of the Higgs potential, the Goldstone phase variation in the minimum circle happens at constant |(0|phi|0)|, therefore in this 3 adjoint IRREP of SU(2)weak, the theta in the U(1) = H does exactly that, so that this is our Goldstone phase, in this scheme, in which to get emergent gravity.
B(curved at P) = (effective lattice coarse-graining)'d'(theta)
in the large scale.
Note that the choice of irrep of SU(2)weak to use for the Higgs mechanism may be different at different scales in the geometry of spacetime. We can only go by empirical results.
The Pioneer anomaly does suggest and adjoint 3 irreducible representation of the weak force SU(2)weak group with a Higgs field vacuum manifold ~ S^2 on scale of tens of AUs with a point hedgehog defect N = -1 for a_g = -cH(t) constant in magnitude in space directed radially from roughly center of Sun. This starts at 20AU from the Sun.
There is a small amount of dark energy between these two spherical boundaries making a blue shift of signals from the two Pioneers back to Earth. This blue shift modulating the motional Doppler red shift makes the deceleration 1 nanometer per sec^2. The periodic rotation of the Pioneer space probes about their centers of mass obviously makes such a small blue shift easier to detect. That's why it is not seen in the other probes, but it's there I guarantee it.
On Nov 1, 2005, at 7:49 PM, Jack Sarfatti wrote:
The Higgs mechanism for the spontaneous breaking of SU(2)weak in the post-inflationary vacuum explains the origin of inertia for the leptons and quarks that make ordinary matter whose Omega is only 0.04 of course. Omega ~ 0.96 is all virtual nonlocally coherent but locally incoherent ZPF of which Omega ~ 0.23 is negative ZPF energy density and Omega ~ 0.73 is positive zero point density where
Total density of Omega = 1.00 (large scale) is
Omega(Total) = Omega(ZPF) + Omega(Higgs)
So Omega Higgs Condensate is only ~ 0.04.
Omega = density/(critical density)
Note that the "Omega" Higgs condensate analog in superfluid helium is also quite small. Most of the superfluid helium ground state is nonlocally phase locked ZPF that is locally completely random same idea seen in the EPR real 2-photon pair state of Clauser --> Aspect experiments on violations of Bell's locality inequality for polarization correlations.
|1,2> = (2)^-1/2[|1+>|2-> + |1->|1+>]
Now for SU(2) I took case of 3 independent conjugate phases for the Paul spin matrix algebra T1, T2, T3. However, in the standard theory there is actually only ONE independent phase theta needed. That is, a = 1,2,3
U(n,theta) = e^i(theta)n^aT^a = cos(theta/2) + 2in^aTasin(theta/2)
This is for a physical rotation of theta about a space axis with unit vector n = (na) whose effect in the fundamental irrep 2-component complex spinor space is given by U(n,theta). The two hidden angles of latitude & longitude are in the n unit vector.
OK it is this theta(P) that is the relevant Goldstone phase for the emergence of gravity in
B(P) = (Effective Lattice Length)'d'(theta)