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Refuting Waldyr Rodrigues on "Emergent Gravity"



 
 
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Old November 21st 06, 01:24 AM posted to sci.math,sci.physics.relativity,sci.astro,sci.philosophy.tech,sci.physics.particle
Jack Sarfatti
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Posts: 113
Default Refuting Waldyr Rodrigues on "Emergent Gravity"

Note in my model Kiehn's topological torsion not to be confused with
metric torsion T^a below is

C^ac/\dC^cb = 2(A^a/\dBc - dA^a/\Bc)/\dA^c/\dB^b =
2[A^a/\dBc/\dA^c/\dB^b - dA^a/\Bc/\dA^c/\dB^b]

Is this zero?

Note Minkowski metric raises and lowers indices here.

Is

dBc/\dA^c = 0 ?

Is

Bc/\dA^c - 0?

If it's not then Kiehn's macroscopic spinors may play a role in my
emergent gravity theory that Waldyr still is not able to grasp
physically. But even if it is zero, it does not affect my derivation
below of Einstein's GR from the Goldstone phases of the vacuum ODLRO
inflation field. This is a new way of thinking completely alien to
Waldyr's mind set - and to those of others besides him. Waldyr is not
the only one blinded by the light outside The Cave. ;-)

Meantime note that I get the world hologram result that the quantum
gravity length uncertainty is

deltaL = Lp^2/3L^1/3

automatically. I knew I had seen that before.

That is, we have projected in 3D space only three of the 9 real
Higgs-type vacuum ODLRO components with only 2 effective Goldstone
phases giving stable point topological defects i.e. where all three
Higgs fields vanish at the points of Kleinert's world lattice.


http://mathworld.wolfram.com/CubicLattice.html

The black dots are zeros of the LOCAL vacuum ODLRO parameter in 3D
spacelike slice of 4D space-time where the two Goldstone phases are
undefined i.e. point defects from non-trivial second homotopy group
mapping from 3D space to S2 vacuum manifold as in David Thouless's book
on topology in QM.

Consider a closed surface of area A surrounding N point defects.

Assume ONE BEKENSTEIN BIT PER ENCLOSED NODE WORTH ONE QUANTUM OF AREA
Lp^2 = hG/c^3 = 10^-66 cm^2

Therefore

A = NLp^2

Let n = density of point defects

Therefore

N = nV

Therefore

A = nVLp^2

Therefore

n = (A/V)(1/Lp^2) = (AREA/ENCLOSED VOLUME)1/(QUANTUM OF AREA)

Define 1/L = (AREA/ENCLOSED VOLUME)

Therefore, in analogy with the line vortex lattice in a type II
superconductor for first homotopy one Goldstone phase

Point Defect World Lattice Density = 1/LLp^2

NOW WHERE HAVE WE SEEN THAT BEFORE?

World Lattice Spacing = (LLp^2)^1/3 = L^1/3Lp^2/3

the oft-discussed on archive basic world hologram formula for quantum
gravity metric fluctuation over scale L!

Note this is like a tube of cross section Lp^2 of length L whose cube
root volume maps to a cubic lattice spacing.

Now when you use the measured dark energy curvature /\ = 10^-56cm^-2

World Lattice Spacing ~ 1 fermi = 10^-13 cm, i.e. a micro-nanometer or 1
Gev nucleon mass

On Nov 20, 2006, at 10:04 AM, Jack Sarfatti wrote:

PS the emergent tetrads are on the diagonal of

C^a^b = A^a/\dB^a - dA^a/\B^b

i.e. a = b

Obviously the off-diagonals are essentially the CONNECTION field

where the spin connections are

W^a^b = C^a^b - C^b^a

D = d + W/\

Metric torsion is the diagonal form

T^a = dC^a^a + W^ac/\C^c^c

Curvature is the off-diagonal form

R^a^b = dW^a^b + W^ac/\W^c^b

Therefore, contrary to what Waldyr Rodrigues wrote on the archive, I
have derived Einstein's GR plus the additional structure in Kibble 1961
from vacuum ODLRO


Let me be more specific

Given eight Goldstone 0-forms A^a and B^b

(9 real components to the Higgs field for spontaneous broken ODLRO symmetry)

a,b = 0,1,2,3

C^a^b = A^a/\dB^a - dA^a/\B^b

So things like dA/\dA are really

dA^ac/\dA^c^b

Will this kind of formal system (my model for the cosmic inflation field
and emergent gravity in my archive paper) have your macroscopic spinors
and be "non-equilibrium" as you mean it?

Jack Sarfatti

"If we knew what it was we were doing, it would not be called research,
would it?"
- Albert Einstein


On Nov 20, 2006, at 7:34 AM,
wrote:

Dear sirs.
I recently was told about your article
http://xxx.lanl.gov/abs/quant-ph/0208068
in which you referred to my remarks in Bohmplus.pdf
http://www22.pair.com/csdc/pdf/bohmplus.pdf
*
Let me inform you that that this article was conceived 30 years ago (1976),
and is now published, in an updated version, as chapter 5 in
volume 3 of a series of monographs on
Non-Equilibrium Systems and Irreversible Processes,
Vol 3
"Wakes, Coherent Structure, and Turbulence"
R. M. Kiehn
ISBN 978-1-84728-195-1
This and my other monographs can be obtained from
http://www/lulu/com/kiehn
in paperback form.
I would appreciate if you would reference my works as they appear in
these monographs,
even though they appear as downloadable files on the internet.
*
The original article made note of the fact that there was an exact map
between the
Schroedinger equation in 2D + time (for an electron in an EM field) and
the viscous compressible Navier-Stokes fluid,
where the square of the Wave-Function was proportional to the square of
the vorticity in the viscous fluid.
Hydrodynamicists call this function "Enstrophy"
*
I was always interested in extending the ideas to a 4D system, but the
solution was not found when the first draft of the monograph was
published (2004)
The topic was included in the second draft (early 2005)
*
Since that time I have realized that macroscopic Spinors are to
associated with all non-equilibrium systems.
Such objects (macroscopic Spinors) are eigendirection fields of
anti-symmetric matrices.
AS thermodynamics systems can be encoded in terms of a 1-form of action, A,
the derived 2-form, F=dA always leads to an antisymmetric matrix
describing the possibility
of continuous topological (not necessarily geometrical) evolution.
If the system satisfies A^dA = 0 , then the system is in a state of
isolated equilibrium.
If A^dA is not zero, then the system is not uniquely integrable, the
thermodynamic system is not in equilibrium,
and here is where the macroscopic Spinor pairs arise.
There is a remarkable relationship between macroscopic Spinors, Surfaces
of zero mean curvature, and Harmonic vector fields
*
The bottom line is that Spinors are NOT necessarily artifacts of
microscales or relativity theory,
but are artifacts of certain topological structures
*
In another representation, consider a set of basis vectors (or verbeins)
as matrices that
will map linear systems of perfect (exact) differentials into (perhaps)
non-exact combinations
of differentials, or a vector of 1-forms. Then it is possible to
compute the Cartan connection matrix, which will be
anti-symmetric if the basis set is orthonormalized. The anti-symmetry
leads to the concept of Affine Torsion.
However, if the system of 1-forms is integrable, then the Affine torsion
can be mapped away.
But, if the systems of 1-forms is not integrable, the Affine torsion can
not be mapped away,
and therefore Macroscopic Spinors will enter the solution set.
*
I am now inspired to address the Bohm-Arahanov fluid problem in 4D as a
global Symplectic structure
that can decay by means of dissipative processes into emergent compact
domains (topological defects)
with a Contact structure. Both systems are far from equilibrium for the
Symplectic structure is of Pfaff topological dimension 4
and the Contact structures is of Pfaff topological dimension 3. This
work will appear in Vol 5 of the monograph series.
*
"Topological Torsion and Macroscopic Spinors"
R. M. Kiehn

*
I know that the Contact structure admits one conjugate pair of
macroscopic Spinors, and the Symplectic structure admits
two conjugate pairs of macroscopic spinors.
*
Regards,
R.M.Kiehn
http://www.cartan.pair.com




 




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