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Refutation of Waldyr Rodrigues's Archive Remarks on "Emergent Gravity"



 
 
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  #1  
Old November 20th 06, 07:04 PM posted to sci.math,sci.physics.relativity,sci.astro,sci.physics.particle,sci.philosophy.tech
Jack Sarfatti
external usenet poster
 
Posts: 113
Default Refutation of Waldyr Rodrigues's Archive Remarks on "Emergent Gravity"

see discussion forum at http://stardrive.org

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 the CONNECTION

where the spin connections are

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

D = d + W/\

Metric torsion is

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

Curvature is

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

On Nov 20, 2006, at 9:54 AM, Jack Sarfatti wrote:

Hi Robert

Given two 0-forms A and B (Goldstone phases of a vacuum ODLRO inflation
field)

Construct the 1-forms (emergent tetrads that also come from localizing
T4 as in Kibble 1961)

C = A/\dB - dA/\B

dC = 2dA/\dB

So what is C/\dC?

Is it zero or not?

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
  #2  
Old November 21st 06, 01:51 AM posted to sci.math,sci.physics.relativity,sci.astro,sci.physics.particle,sci.philosophy.tech
Ken S. Tucker
external usenet poster
 
Posts: 740
Default Refutation of Waldyr Rodrigues's Archive Remarks on "Emergent Gravity"

To Happy Jack,

Jack Sarfatti wrote:
see discussion forum at http://stardrive.org

PS the emergent tetrads are on the diagonal of

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


I know ascii notation sucks, but it takes time
to work what you meant to equationalize,
probably I'm just bitchin on a typo.
Ken
....

 




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