Science > Physics > F. Hehl vs S. Weinberg in Physics Today torsion & Witten's M Theory
| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
27 Apr 2007 01:00:02 PM |
| Object: |
F. Hehl vs S. Weinberg in Physics Today torsion & Witten's M Theory |
Ed Witten & Lenny Susskind lament on absence of an "organizing idea" for
M Theory (equivalence principle was the organizing idea for Einstein's
1915 GR). They need lament no more - it's the same organizing idea!
There has been a recent flurry in letters in Physics Today - a bit odd
in that Weinberg seems unfamiliar with Hehl's work, yet Hehl gave famous
lectures on torsion theory at Institute of Advanced Study in Princeton
published in Rev. Mod. Phys. 1976.
Hehl lectures on Einstein's GR as a limiting case of a local Poincare
group theory. Utiyama's & Kibble's work on that done in ~ 1961. However,
Hehl makes IMHO the incorrect assumption that the torsion field is
generated only by the micro-quantum spins hence it does not propagate as
a far field wave. Richard Hammond has shown that this assumption is not
necessary and indeed there is experimental evidence against it. The
coupling should be to the total 4D angular momentum field tensor of all
sources including orbital (for 3D part) both real and virtual - the
latter includes IMHO both repulsive dark energy and attractive dark
matter as negative and positive quantum pressure exotic vacuum phases
respectively of a quintessent /\zpf locally variable microscopic ->
macroscopic field.
96% of our possibly pocket Hubble bubble universe on the overpopulated
cosmic landscape of eternal chaotic inflation (self-created Gott-Li?) is
random incoherent off-shell virtual quanta acting as the external "wood"
source pump of the "marble" Higgs-Goldstone coherent vacuum condensate
field whose Goldstone phase(s) modulation is the smooth c-number
emergent warped Einstein-Cartan fabric of spacetime. The Calabi-Yau
extra-dimensions are from the 6 "angle parameters" from locally gauging
the Lorentz-group whose implied full 4D rotation tensor is the torsion
source in the same way that the full 4D translational group's implied
"matter" stress-energy tensor is the curvature source. Why only choose
the quantum spins of on-shell quanta in the former?
That all non-gravity fields, both real and virtual, participate as
sources is part of the equivalence principle.
To be a bit more precise
The 4-parameter translational group's Lie algebra of "observable
charges" forms the global total energy-momentum 4-vector of all the
source fields. These global integrals are over local stress-energy
tensors of the non-gravity fields whose dynamical actions are gauge
invariant with respect to the localized Poincare group where curvature
and torsion are derived from more fundamental compensating gauge
potentials at the square root tetrad + spin connection Cartan 1-form
"substratum" level. Supersymmetry is natural in the substratum as is the
coupling to spinor field sources. Difficulties in properly defining the
integrals at the derived quadratic geometrodynamical level and in trying
to include the gravity field itself requiring asymptotic flatness are
not relevant to the more fundamental point here. As Penrose et-al point
out the pure gravity vacuum field does not have a local self-source
stress-energy tensor even though there is total energy-momentum in the
vacuum gravity field.
Similarly, the 6-parameter space-time translation group is generated by
integrals of the 4D rotational source field tensors of all the
non-gravity fields. These 6 parameters are the dimensions of the local
Calabi-Yau fiber.
J = L + S
S = quantum spin
L = orbital angular momentum
is only for the 3 space rotations of the Lorentz group's Lie algebra.
Hehl, oddly only takes S as the source of the torsion field. This is not
even a covariant choice IMHO.
In addition there are the 3 boosts (spacetime rotations) that will
contribute to the torsion field.
Gennady Shipov has the germ of this idea in his concept of the "oriented
point" needing 2 metrics 4D translation and 6D rotational - the latter
years before string theory's construct of the Calabi-Yau fiber space.
http://qedcorp.com/APS/Shipov.jpg
The Calabi-Yau space fiber is compactified in a anisotropic way in
general so that the above simple spheres look more like
http://www.futura-sciences.com/comprendre/d/images/510/CalabiYauSpace.jpg
But the idea is clearly similar. Shipov had years before M theory was a
glimmer in Witten's eye.
The Kaluza-Klein radii are Ri i = 1 ... 6
Kaluza-Klein charges are ei ~ G*^1/2h/cRi
G* is running gravity coupling constant of the secondary spin-2
geometrodynamic field.
Note that the renormalizable spin-1 vector tetrad fields have
dimensionless couplings
(G*h/\zpf/c^3)^1/2 for each vertex in the Feynman diagrams where /\zpf
is the quintessent field -> Einstein's cosmological constant in large
space scale limit.
The reciprocal of this is the Bekenstein BIT number of deSitter future
horizons i.e.
Wheeler's IT FROM BIT
.
|
|
| User: "Rock Brentwood" |
|
| Title: Re: F. Hehl vs S. Weinberg in Physics Today torsion & Witten's M Theory |
29 Apr 2007 05:20:35 PM |
|
|
On Apr 27, 1:00 pm, Jack Sarfatti <sarfa...@pacbell.net> wrote:
Hehl lectures on Einstein's GR as a limiting case of a local Poincare
group theory.
GR is not a Poincare' gauge theory, nor can it be. I spelled out the
reasons why not in a reply (posted in s.p.r.) to an article you
earlier wrote; there are fundamental problems with the conception of a
Poincare' gauge theory.
If you really want to get technical, the gravity field in GR, itself,
is a GA(4) gauge field (general affine group on 4-manifolds). Formally
it has some similarity to Poincare, which becomes especially apparent
when you work out the generators for GA(4). You can already see this
by simply looking at the indexes on the various objects. The indexes
on the connection coefficients
Gamma_{mu nu}^{rho}
are arranged with {mu} being the 1-form index associated with any
connection, and (_{nu}^{rho}) being the GL(4) index associated with
the GL(4) group
[e^{mu}_{nu}, e^{rho}_{sigma}] = delta^{rho}_{nu} e^{mu}_{sigma} -
delta^{mu}_{sigma} e^{rho}_{nu}.
not SO(3,1).
The total connection would thus read
Gamma_{mu} = Gamma_{mu nu}^{rho} e^{nu}_{rho} + delta_{mu}^{nu}
e_{nu}
where e_{nu} comprise the affine part of the generators for GA(4),
[e^{mu}_{nu}, e_{sigma}] = -delta^{mu}_{sigma} e_{nu}.
In effect, this is what is already well-known as the Cartan
Connection.
It's out of this that you get the Riemann curvature and torsion as the
field strengths.
Once you put on the fermion fields (or any fields with non-integer
spin), this global symmetry is broken and reduces to the local SO(3,1)
symmetry associated with fermions -- NOT Poincare' symmetry. Fermions
do not transform under GA(4), nor GL(4) nor even the ISO(3,1) of
Poincare', but only under a local SO(3,1) symmetry or its covering
group.
The "Poincare'" vierbein coefficients are associated with the group
quotient GL(4)/SO(3,1), not with the affine part of ISO(3,1). This is
a 10-dimensional group whose underlying manifold is isomorphic to S_3
x R^7. The 10 dimensions correspond to the 10 components of the metric
from which the vierbein are extracted.
.
|
|
|
|
|
Related Articles |
|
|
