On Nov 1, 2005, at 9:20 PM, Jack Sarfatti wrote:
Basic idea is that gravity & inertia must emerge together in order to obey the Einstein equivalence principle (AKA EEP).
Note that stability of the universe's carbon life forms, rigidity of common materials, atomic physics & chemistry, i.e. fine tuned e/m ratios etc are for late cosmological epochs when TCCB << 250Gev
The rest inertia of leptons & quarks must come from the macro-quantum Higgs vacuum amplitude in the spontaneous symmetry-breaking of SU(2)weak (in standard model effective field theory in sense of the renormalization group scaling of coarse-graining out finer scales, i.e. sliding short-distance cutoff L^2 - hG*/c^3. Also note
&r ~ h/&p + L' ^2&p/h ?
Use analogy with computer graphics. &r is pixel size as &p increases pixel size decreases up to a minimum then increases again.
&r/&p = -h/&p^2 + L'^2/h = 0
&p = h/L'
is L' an absolute scale-independent constant?
Note that L' = (hG/c^3)^1/2 ~ 10^-33 cm at large scales - starting at millimeters at least up to current Hubble scale c/H(t) ~ 14 x 10^9 light years.
However, it is possible that effective L' cutoff is much larger by 20 powers of 10 on the scale of a fermi.
Gravity comes from complementary Goldstone phase modulation complementary to the 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.
N = number of Lie algebra generators for unstable incoherent false vacuum symmetry group G.
N - K = number of Lie algebra generators for metastable coherent vacuum symmetry subgroup H.
n = dimension of REAL representation of G
Then for G Yang-Mills field coupled to n-component real scalar field.
The number of real massive Higgs boson small oscillations in the Higgs vacuum amplitude is n - K.
The number of Meissner effect massive gauge bosons is K.
The number of massless gauge bosons is N - K = dimH
Topological defect stability is
d' = d - n
d = dim of physical spacelike slice (AKA physical space)
d' = dimension of stable defect in physical space
i.e. the homotopy group mapping of
1 + d' + r = d
r = dim in physical space that surrounds the defect of dim d'
SSB in SU(2)weak models
1. global SU(2) in 2-irrep i.e. 2 complex fields, T^a = 2x2 Pauli spin matrix/2, a = 1,2,3 na is unit 3-vector axis of rotation in group parameter space through angle THETA. The 3-parameter (@,#,%) manifold of SU(2) is the simply-connected unit S3. For now we are in an abstract fiber space of 2 complex dimensions over physical space-time base space. Unitary 2x2 matrix element in this 2-IRREP is
U(THETA,na) = e^iTHETAnaT^a = cos(THETA/2) + 2inaT^asin(THETA/2)
Since na is a unit vector, we can use the 3-direction cosines
n1 = cos@
n2 = cos#
n3 = cos%
n^2 = n1^2 + n2^2 + n3^2 = 1 i.e. unit S3
Therefore the 3 conjugate phases to T^a are (THETA)na.
The Higgs mechanism here is
SU(2) -2-> I with a single complex VEV local order parameter (0,(0|phi|0)) in a Mexican Hat quartic potential. H is the trivial identity group I.
The Vacuum Manifold V = G/H = SU(2)/I = SU(2) = S3
N = 3
N - K = 0
K = 3
n = 4
Therefore, there are 3 massive gauge fields, 1 massive Higgs field
no massless gauge fields.
There are no stable topological defects in this scheme of using the fundamental 2-irrep of SU(2)weak.
2. Adjoint 3-irrep of SU(2) T^a given by the structure constants of SU(2) in 3x3 matrix rep. n = 3 real scalar fields. This is a 2 -> 1 homomorphism of SU(2) to SO(3) whose multiply-connected 3-parameter manifold is S3 with antipodes identified.
G = SU(2)
If only VEV is along T3 axis in group space
H = U(1)
i.e. S1 circle about T3 axis.
SU(2) -3-> U(1)
R = e^-i(THETA)T3 leaves real(0|phi|0) invariant. Therefore, THETA is the effective Goldstone phase here.
B(P) ~ L''d'THETA(P)
G/H = SU(2)/U(1) ~ S2 = Sn-1
n = 3 = dimS2
N = 3 for G = SU(2)weak
N - K = 3 - K = 1
K = 2
n - K = 3 - 2 = 1 Massive Higgs
2 Massive gauge bosons
1 Massless gauge boson.
d' = d - n = 0
i.e. point defect singularity where (0|phi(x)|0) -> 0 in physical 3D space surrounded by
r = 2 i.e. S2 2-cycle that is not a boundary.
This is quantized geometrodynamic "flux without flux" N = -1 is a Hedgehog.
3. Next consider G = U(1)hyperchargexSU(2)weak -1x3-> H = U(1)EM
n = 4
Now N = 4
N - K = 1
K = 3 massive gauge bosons i.e. W+,W0,W-
N - K = 1 i.e. photon
n - K = 4 - 3 = 1 Massive Higgs
d' = d - n
Where d = 4 for complete space-time
d' = 0
1 + r + d' = d
r = 3 surrounding subspace in 4-D space-time with space-like slice S2.
This surrounding space for wrapping number N = -1 (hedgehog) are two concentric spherical surfaces in physical 3D space with point defect at center, and the 3-vector real vacuum order parameter oriented along the radial direction with CONSTANT MAGNITUDE
a_g = -cH(t)
V = G/H = U(1)hyperchargeSU(2)weak/U(1)em ~ S2
e^-i(Goldstone Phase)T3 leaves the one non-vanishing REAL VEV INVARIANT like in simplest Higgs model.
There is only ONE Goldstone phase here for the T3(weak generator) and it seems to give gravity via
B(P) = (hG/c^3)^1/2'd'(Goldstone Phase)
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)