1. Meaning of the Diff(4) stress-energy current density tensor in
geometrodynamics is

Stress-energy ... Diff(4) tensor = functional derivative of the action
relative to the metric guv.

Therefore, using the standard Einstein-Hilbert action density (-g)^1/2R
you obviously get ZERO in classical vacuum where R = 0 identically.

See Rovelli (2.35) for tetrad definition of the energy tensor

i.e. Einstein field eq.2.34 (typo in Rovelli's text BTW) is the 1-form eq

(IJKL){e^J/\R^K^L - /\zpfe^J/\e^K/\e^L} = kTI

where

TI = TI^u(uvwl)dx^v/\dx^l/\dx^w

TI = &(Scalar Action)/&eI

For classical gravity vacuum, the scalar action is identically zero
everywhere-when.

All we do have in exotic vacuum is

TI(zpf) = /\zpfeI^u(uvwl)dx^v/\dx^l/\dx^w

Note that the completely anti-symmetric symbols (IJKL) & (uvwl) are
Hodge * operators changing p forms to n - p forms. Here in GR n = 4.

Nevertheless (gravity waves & Moon-Earth-Sun near field) there is a
total nonlocal gravity vacuum energy (e.g. Penrose in "The Road to
Reality") therefore, you cannot use global flat idea of simply
integrating a local energy density to get a total energy. This is
because conservation of total energy is only an artifact of T4 symmetry
in global flat space-time WITHOUT ANY GRAVITY at all!

From this POV what Alex tried to do should not even be attempted. Ditto
for Yilmaz. It's not a proper question in GR to ask.

2. You need to use the spin connection for fermion fields in curved
space-time. You cannot use Levi-Civita connection.

3. My language is "base space" - "tangent fiber", Rovelli's is "tangent
vectors" - "Minkowksi space" for same distinction.

4. Holonomy (nonlocal) are the Ken Wilson-Mandelstam loops.

5. Levi-Civita connection (2.81)

(LC)^wuv = eI^w(e^Iv,u + S^IuJe^Ju)

See 2.89 for S^IuJ in terms only of tetrads and its partial derivatives
when the torsion 2-form is identically zero.


On Aug 2, 2005, at 10:09 AM, Jack Sarfatti wrote:

I am listening to K. Dienes in Panofsky Auditorium at SLAC SSI 2005 - he
gives a really plausible argument for extra space dimensions as a way to
get G* ~ 10^40 G at short distances which I need for my model below. Of
course, I knew this but now I give it more weight.
http://www-conf.slac.stanford.edu/ss...rogram.htm#8.3

On Aug 2, 2005, at 9:24 AM, Jack Sarfatti wrote:


http://qedcorp.com/APS/zpf2005.pdf

Succinctly and elegantly

B = (hG/c^3)^1/2d(Goldstone Phase of Higgs Charge-Neutral VEV)

note that SU(2) assignment to the Higgs doublet explains NASA Pioneer
anomaly as a hedgehog topological defect in the Higgs vacuum manifold.
The physics is in the Goldstone phase singularities.

No gravity when h = 0 and c - infinity even when G =/= 0.

e = 1 + B

B is also the compensating local gauge potential from extending T4 to
Diff(4).

One has both spontaneous symmetry breakdown in inflation vacuum phase
transition and local gauging of flat T4 to curved Diff(4) happening
together.

Einstein's curved metric is from the EEP

guv = (1u^I + Bu^I)(Minkowski)IJ(1v^J + Bv^J)

The Shipov dynamical torsion 2-form is

T = De

where the Cartan exterior covariant derivative is

D = d + S/\

S is the spin connection

The Levi-Civita connection is symbolically (suppressing indices)

(LC) ~ eeeS

(not exterior form multiplication but tensor multiplication with
contractions)

S is determined by e when T = 0, i.e. S(e).

T = 0 is when SO(1,3) is not locally gauged.

/\zpf ~ (Cutoff Length)^-2(1 - (Normalization)|Charge-Neutral Higgs VEV|^2)

in

Guv + /\zpfguv = 0

Guv = Ruv - (1/2)Rguv