On Aug 2, 2005, at 9:00 AM, Jack Sarfatti wrote:
re: http://qedcorp.com/APS/zpf2005.pdf
On Aug 1, 2005, at 10:26 PM, Paul Zielinski wrote:
Yes, maybe he should.
But I'm not sure a tetrad model would easily accommodate his idea of
attributing non-vanishing Riemann curvature to accelerating frames (even
in the absence of actual gravitational fields).
In fact this is completely WRONG and misconceived! Riemann curvature is
geodesic deviation, i.e. a property of the relative acceleration between
two closely spaced (relative to radii of curvature) point test particles
(no spin) each on timelike geodesics.
Accelerating frames play NO essential role at all. Of course you can
express the curvature tensor Ruvwl in any local frame you like LNIF or LIF.
In terms of tetrads as Cartan 1-forms e, the curvature is a 2-form R
exterior covariant derivative of the spin connection S with itself.
R = DS = dS + S/\S
S is completely determined by e if Shipov's torsion 2-form vanishes
T = De = de + S/\e = 0
i.e. solve for S in terms of e = 1 + B
where in my new theory the essential equation is simply
B ~ (Lp)d(Goldstone Phase)
with PHASE SINGULARITIES
Lp^2 = hG/c^3
of the charge-neutral VEV of the standard model. Note that is
phenomenological so that my virtual electron-positron condensate model
can explain it. The additional component in the flavor doublet can come
from weak and strong forces - it does not develop the spontaneous broken
symmetry VEV BTW - so this seems a plausible consistent idea!
PS the non-trivial topology explaining Pioneer anomaly for example as a
Hedgehog defect is in the multiple-connectivity of the VACUUM MANIFOLD
G/H(unbroken) of macro-quantum coherent order parameters that have
winding numbers when a closed loop in space-time is considered. In
Landau-Ginzburg this multiple-connectivity in the vacuum manifold
happens when the closed loop in space-time goes around a ZERO of the
order parameter.
Z.
Jack Sarfatti wrote:
Yes, I think Alex Poltorak should take a new look at what he has done
from the POV of tetrads. On Aug 1, 2005, at 6:46 PM, Mcmahon, David M wrote:
Orthonormal tetrads correspond to what is used by "physical observers".
The method is also far superior to using coordinates in my opinion.
I like Sean Carroll's book a great deal, but as I recall while he
discussed tetrads in the appendix, throughout the text he uses
coordinate methods (you see him stating Christoffel symbols for a given
metric, blah blah) which I find distasteful and cumbersome.
Yes.
Carroll's choice is probably a result of his training as a particle
physicist (I believe). Someone trained as a relativist would probably
use tetrad methods.
I would definitely say Cartan's equations are elegant, computing
Christoffel symbols and the like using coordinates is a nightmare best
delegated to the computer.
From: Jack Sarfatti [mailto:sarfatti@pacbell.net]
Sent: Mon 8/1/2005 7:34 PM
To: Paul Zielinski
Subject: Re: Note to Zielinski
The tetrad model is the only way to go because
1. It is simple
2. It is elegant
3. Everything is manifestly objectively locally frame-invariant for ALL
observers.
4. Rovelli says the best definition of the gravitational field IS the
non-trivial part of the tetrad field that you can think of as the 4D
elastic-plastic distortion field of Hagen Kleinert's "world crystal
Planck lattice".
Note the world-crystal distortion field is
B^I = e^I - 1^I
it is a Diff(4) scalar invariant.
B^I is also the local gauge potential of T4 -> Diff(4) expressed as a
Diff(4) invariant field.
And
B^I = LpGrad^I(Phase of the charge neutral vacuum ODLRO field in the
SU(2)weak sector of Standard Model)
That at a deeper level is my virtual electron-positron condensate at
least as the dominant component.
Any change in this MACRO-QUANTUM PHASE is PHYSICAL - because of "More
is different" phase rigidity.
It's the phase singularities that are important and they are "strings"
in an important sense!
5. The connection to quantum theory is almost obvious in the tetrad
field formulation.
On Aug 1, 2005, at 3:57 PM, Paul Zielinski wrote:
Sean Carroll is great. I've been using his PDF "Lecture Notes on
General Relativity" for some time.
I haven't seen his book -- I'll look out for it.
Jack Sarfatti wrote:
Paul Sean Carroll is here at SLAC. He has a new GR text book that >>
looks good. You should get it. He has a clear appendix J on tetrads >>
that clearly answers one of your main concerns on the proper relation
of local frames to local coordinates. It's basically a convention
and is not necessary.
OK, I'll see what he says about that.
The point is that tetrads are abstract objects can be used and
interpreted in different ways.
More than one way to skin a cat.
"we made a decision to choose bases for our tangent spaces that were
adapted to the coordinates"
OK. For convenience only?
The tetrads generalize this without any necessary connection to any
local coordinate patch. Indeed, everything I do below is manifestly
local frame invariant. Changing the vacuum ODLRO Goldstone phase is
a PHYSICAL CHANGE that is a LOCAL DIFF(4) OBJECTIVE INVARIANT.
OK.
I think it's important to get a really tight grip on the tetrad model,
which I think may depart in certain respects
from the 1915 coordinate frame approach -- depending on
interpretation, of course.
Z.
On Aug 1, 2005, at 11:14 AM, Jack Sarfatti wrote:
Note that in my theory http://qedcorp.com/APS/zpf2005.pdf , the >>>
linear elastic piece of the metric tensor looks like a simple free >>>
field spin 1 gauge theory in the "square root" subspace >>>
representation, while still spin 2 in the bilinear geometrodynamic >>>
representation.
e.g. the basic local frame-invariant OBSERVABLE of Einstein's 1915
GR is
ds^2 = guv(curved)dx^udx^v = eI(x)e^I(x)
eI(x) is the subspace "spin 1" gauge tetrad field.
(Math details Ch 2 of Rovelli's "Quantum Gravity")
e^I(x) = 1^I + Lparg(VacuumODLROPhase)^,I = 1^I + B^I
Lp = (hG/c^3)^1/2
The charge neutral component VEV of Higgs field is what I call >>>
VacuumODLRO.
No classical gravity if h = 0 and c = infinity even when G =/= 0
B^I is the intrinsic warp subspace field from the charge neutral
component of the Higgs internal symmetry multiplet of SM or its GUT
... that is in the Yukawa couplings. Then in the timelike geodesic
LIF basis
ds^2 = (1I + BI(x))(1^I + B^I(x)) = (Flat Space-Time) + 1IB^I(x) +
BI(x)1^I + BI(x)B^I(x)
Everything here is INDEPENDENT OF LOCAL COORDINATES!
The subspace Brazilian "torsion field" is
F = dB + B/\B
The Lagrangian density in subspace is ~ F/\*F, this will give a >>>
local Yang-Mills energy tensor in the subspace.
Do NOT CONFUSE THIS with Einstein's SPIN CONNECTION out of which
Levi-Civita connection and tidal curvature spring when Shipov >>>
geometrodynamic level torsion = 0. The geometrodynamical TOTAL >>>
gravity energy is still nonlocal and the classical local gravity >>>
energy tensor is still ~ /\zpfguv whose invariant is
t(gravity) = (c^4/8piG)/\zpfguv(dx^u/ds)(dx^v/ds)
t(gravity) > 0 is dark energy
t(gravity) < 0 is dark matter
On Aug 1, 2005, at 9:36 AM, Jack Sarfatti wrote:
My neutral VEV that generates Einstein's 1915 gravity field >>>>
equations is simply the charge neutral component of the flavor >>>>
doublet of the standard model. It gives the inertia of the >>>> fermions
via the Yukawa couplings that are simply a lumped-
parameter phenomenology for micro-geons with induced ZPF V/c^2 ~ 1
on scale of 1 fermi.
.
