I'm trying to understand tetrads. I'm particularly interested in Rovelli's and others' explanations of the relationship between the Einstein-Cartan tetrad model and the 1916 metric field model for GR.

Good! Remember my basic idea here that seems to be completely original compared to Visser's, Chapline's, Volovik's et-al approaches. The key idea is in superfluid helium

v = (h/m)(dTheta)

v = coherent velocity field (here a closed 1-form in 3D Euclidean space)

Theta = single macro-quantum ground state ODLRO Goldstone phase

PSI = (Higgs Field)e^i(Goldstone Phase)

in this simplest of "More is different" emergence from Sid Coleman's "hidden symmetry" (goes back to Brout-Englert - PW Anderson). PS Robert Brout was one of my tutors at Cornell (in group theory) I saw him again in Brussels when Jagdish Mehra invited me to Prigogine's institute when I was with Abdus Salam in Trieste 1973-4. That's when I suggested

Hadronic Resonance Spin = (1Gev)^-2(Energy)^2 + Jo

as a strong short-range gravity G* - 10^40G(Newton) as a kind of Kerr "black hole" - decay by Hawking radiation. Also wrote about making miniblack holes in accelerators & baby universes in ICTP internal memos 1973-4. Also did a paper on Dirac Eq in curved spacetime David Finkelstein I think published it? - or maybe it was Foundations in Physics? I forget which.

in any case the vorticity vanishes locally:

dv = 0 means irrotational curl-free flow (2-form)

nevertheless first homotopy group is non trivial for stable string (line vortex) quantized circulation defects where the two real Higgs scalars making single-valued complex order parameter vanish, so that THETA is undefined on the string vortex (healing coherence length with string at center - random zero point energy self-trapped inside the core!).

Effective integral of dv on singular area surrounded by closed non-bounding cycle enclosing a stable string defect i.e. circulation integral of v = N(h/m), N = 0, +-1, +-2 .... first homotopy group

OK for the world crystal lattice on 3D spacelike slice we have 2 Goldstone phases THETA & PHI with three real Higgs fields giving stable point "monopole defects" of the EMERGENT GeoMetroDynamic GMD field.

LENGTH 1-FORM is not closed

L = Lp[(dTHETA)(PHI) - (THETA)(dPhi)]

Define closed AREA 2-FORM A

A = LpdL ~ 2Lp^2(dTHETA)/\(dPHI)

dA = 0 is WORLD HOLOGRAPHY of

Volume without volume.

Integral of A over closed surrounding non-bounding 2-surface enclosing N stable elementary GMD monopole point defects is ~ NLp^2 i.e. Bekenstein area quantization from non trivial 2nd homotopy group.

N area quanta (HOLOGRAM) project to N interior volume-without-volume quanta (HOLOGRAM IMAGE)

consistent with Jack Ng's

&L = (Lp^2L)^1/3 = N^1/6Lp

&L is lattice spacing of Kleinert World Crystal Lattice = quantum foam bubble size

L is scale of a null horizon

1-1 map of horizon area bit quanta to volume-without-volume bit quanta = HOLOGRAM PRINCIPLE

OK now to TETRADS

THETA^2 = (THETA)^a(THETA)a

PHI^2 = (PHI)^b(PHI)b

e^a = I^a + @A^a = Einstein-Cartan emergent gravity tetrad field

@ = dimensionless string coupling field - environmentally dependent probability to cut and fuse strings.

I had in one model

@ = N^-1/3

ranges from 0 to 1 like a probability N = 1 is min out to infinity.

ds^2 = guvdx^udx^v = e^aea

A^a = M^a^a

M^a^b = (dTHETA)^a/\(PHI)^b - (THETA)^a/\(dPhi)^b

Spin connection is

S^a^b = - S^b^a = M^[a,b]

This requires 9 real Higgs scalars. Stable defects needs one space dimension for each Higgs fields.

This give branes with 6 extra space dimensions (e.g. Shipov's oriented point -> Calabi-Yau).

Basically one HYPERSPACE dimension for each generator in the Lie algebra of the space-time symmetry group - this would be 15D for Conformal Penrose Twistor Group! 10 for Lorentz group.

Supersymmetry is trivial from Penrose map of nth rank Poincare group tensors to 2nth rank spinors.

This becomes TWISTORS for Conformal Group!

Z: "Considering this relationship with reference to both the inertial compensation and Einstein equivalence paradigms could be very illuminating."

I don't think so. "Inertial compensation" is a Newtonian idea making no sense at all in Einstein's GMD theory. It's an inappropriate concept taken out of its proper context. There is no loose string in Einstein's equivalence principle, which in fundamental for is SIMPLY

ds^2 = guv(LNIF)dx^udx^v = e^aea(LIF)

with universal minimal coupling to source matter fields Psi

Du = e^auPa + S^a^bPab

{Pa,Pab} is Lie algebra of Poincare( to Conformal Group)

in a matrix representation in which the source matter field components forms a basis

e.g. 2-component Weyl spinors

4-component Dirac spinors

spin 0 Poincare group scalars

spin 1 Poincare group vectors ...

Pa generate T4 (total momentum 4-vector)

On 10/29/07, Jack Sarfatti

The problems of interest are:

1. Dark energy

2. Dark matter

3. Multiverse? WAP as explanation for the arbitrary parameters of the standard models of both quarks, leptons & gauge bosons and the precision cosmology of the accelerating universe.

4. Extra dimensions?

5. Practical warp drive & time travel to past seen in UFOs - I take that as established fact for sake of argument at least.