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Science Forum Index » Military Forum » Finsler Geometry? Who ordered that?
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| Jack Sarfatti |
 Posted: Sun Feb 06, 2005 3:23 pm |
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Begin forwarded message:
From: Jack Sarfatti <sarfatti@pacbell.net>
Date: February 6, 2005 12:16:08 PM PST
To: Doc Savage <adastra1@mac.com>
Subject: Re: Non-holonomy and anisotropy of metrics: NASA Pioneer,
preferred frames
bcc: Invisible College
Mathematicians and Theoretical Physicists have opposing tendencies. We
theoretical physicists (at least in the tradition of Hans Bethe where I
was at Cornell in late 50's and early 60's) aim to interpret the most
phenomena with the simplest possible mathematics even if the latter is
ugly - Morse and Feshbach not Witten and Greene. 
We are not into "Math for math's sake." The beautiful math is slain by
the ugly fact - and all that. Physics today has many observational
anomalies to be explained. I have drawn the line in the sand. I say only
two battle tested ideas are needed to explain everything:
1. Local gauging of symmetries (both internal and spacetime) connecting
reference frames introducing compensating gauge connection dynamical fields.
2. Spontaneous breakdown of selected vacuum (virtual quanta) and ground
(real quanta) states of selected symmetries yielding preferred frames of
reference. (AKA "More is different" in soft-condensed matter physics and
"Higgs mechanism" in high-energy physics where the vacuum coherence is
Frank Wilczek's "multi-layered multi-colored" cosmic superconducting
vacuum field.)
How to apply the above is completely pragmatic, i.e. data-driven.
For example, selection of a preferred direction (angular orientation) in
space under the space-space rotation group O(3) in the ferromagnet is
the same idea as in the selection of a preferred inertial frame
(absolute rest) for the set of Lorentz boosts (space-time rotations
rather than space-space rotations i.e. "rapidity" rather than "angle" -
hyperbolic sinh(rapidity)/cosh(rapidity) in O(1,1) rather than
trigonometric sin(orientation)/cos(orientation) in O(2). The hyperbolic
case is what R. Cahill and the Sicilians are claiming empirically. It is
the space-time rotation vacuum spontaneous breakdown of Lorentz boost
symmetry analog to the space-space rotation ferromagnetic spontaneous
breakdown of ground state orientational symmetry. The systems are
different, the groups are different, but the idea is the same! Preferred
space orientation in the ferromagnetic ground state. Preferred
space-time orientation (selected rapidity) in the local space-time
region allegedly detected with Michelson interferometers and He-Ne
lasers. The physical dynamics is unchanged. There is no dynamical
breaking of Lorentz boost symmetry in the Cahill effect anymore than
there is dynamical breaking of rotational symmetry in the ferromagnet.
Dynamical breaking of symmetry i.e. a new term in the Hamiltonian (or
Lagrangian) is NOT what I am talking about with "More is
different"/"Higgs Mechanism" spontaneous breakdown of vacuum/ground
state symmetry. The distinction is "dynamical" vs "spontaneous". Local
gauging is still another form of symmetry breaking. The global symmetry
is broken down to a local symmetry, but is restored in a way by the
compensating gauge potential connection field relative to a now larger
dynamical system. General relativity is an example of local gauging just
as the electro-weak/strong force theory is. Only the groups are
different. The idea is the same! Spontaneous breakdown of vacuum
symmetry is independent of local gauging of global to local symmetries.
In 1916 GR the translation group T4xO(1,3) global symmetry is broken
down to local O(1,3) Lorentz group symmetry in the tangent bundle. The
compensating gauge-potential connection field is most easily seen in the
Cartan tetrad formulation of 1916 GR (e.g. Brazilian paper) that clearly
distinguishes appearance (GCT effect) from intrinsic (gauge force
without force) effects. The gauge transformations on the non-trivial
part of the tetrad correspond to the GCT (Diff(4)) transformation in the
geometrodynamic picture. The gauge force without force and
geometrodynamic picture/formalisms are physically equivalent - merely a
Young Woman/Old Hag Gestalt Shift - a simple two-way mathematical map
from one picture to another. That is,
eu^a = (Kronecker Delta)u^a + Bu^a dimensionless Cartan tetrad, Bu^a is
the non-trivial intrinsic part
u in base, a in tangent fiber - this is the EEP missing in Hal Puthoff's
PV without PV.
Bu = Bu^aPa/h dimension (Length)^-1 = gauge force-without-force
compensating potential breaking GLOBAL T4 to LOCAL GCT.
{Pa} = Lie algebra ("mom-energy" of Wheeler) of T4
Bu = (Higgs-Goldstone Macro-Quantum Phase from spontaneous broken U(1)
in PV virtual electron-positron pairs),u
,u = ordinary partial derivative
The map from gauge force-without-force picture to Einstein
geometrodynamical picture is
guv(LNIF) = [Minkowski(LIF)]uv + Lp^2[Bu,v + Bv,u] (dimensionless)
the above is the elastic Bohm giant pilot-wave hidden variable guidance
constraint
expect non-holonomic "Dirac string" phase singularities where
Bu,v - Bv,u =/= 0
(mixed second order ordinary partial derivatives of the Goldstone Vacuum
Coherence Phase do not commute)
Note Lp^2 = hG/c^3 quantum of area
Gravity is zero when Lp^2 shrinks to zero for whatever reason i.e. h ->
0, or G -> 0, or c -> infinity.
That is, we cannot then perform the local gauging of T4's global linear
transformations down to GCT's local nonlinear transformations in a
physically correct way if Lp^2 = 0.
The Ricci rotation coefficients Aa^b^c are global phases in 1916 GR
since O(1,3) is not locally gauged.
That is,
Tu = eu^aAa^b^cSbc
Where {Sbc} is the Lie algebra (boosts & rotations) of O(1,3)
is not a dynamically independent torsion field at this stage but is
totally dependent in its variation from the T4 derived tetrad eu^a.
Locally gauge O(1,3) to get Shipov's torsion field theory!
There is NO conformal group here yet. However, we can easily extend the
Brazilian gauge formalism of GR to include it, i.e. to locally gauge
full conformal group and to spontaneously break it in the vacuum only if
data so demands!
*However I see no experimental necessity, so far, to go to the conformal
group or to Finsler geometries.
i. R. Cahill & the Sicilians report data that requires spontaneous
breakdown of O(1,3) vacuum symmetry in space of Earth's neighborhood. No
local gauging to get torsion fields is needed.
ii. NASA Pioneer anomaly does not require any new mathematics to explain.
iii. Shipov & Akimov report data that would require local gauging of
O(1,3) to get torsion fields with propagation. Richard Hammond also
reported data to that effect.
We now have a battle-tested computational paradigm to deal with ALL
observational anomalies - is my conjecture. including UFOs as a military
threat e.g. ABC's Peter Jennings in
http://abcnews.go.com/Primetime/story?id=468496&page=1
Finsler geometries et-al? Who ordered that? However, in case I am wrong
in my sweeping conjecture, it's good to keep one eye on these exotic
mathematical flora and fauna. :-)
I have tried to edit the typos here so that I could better understand
the message. Please correct any of my edits if they change the meaning.
I also make some comments. Thanks.
On Feb 6, 2005, at 7:37 AM, Sergiu Vacaru wrote:
Dear Colleagues,
Thanks for your kind e-mails and information on your duscussions. I hope
I could participate in the future.
Here I have some remarks on Finsler geometry:
It is considered to be a generalization of Riemnannian geometry, on
tangent bundles, with anisotropies of metric (depending on direction),
which is more sophisticated and with less experimental evidence for such
extensions.
Anisotropies of metric? Meaning what? Off-diagonal guv? Solutions need
not be spherically symmetric nor isotropic.
The most surprising thing is that Finsler-like structures can be
modelled on (pseudo) Riemannian spaces (in a more general context of
string theory with nontrivial torsion, on Rieman--Cartan manifolds) by
generic off--diagonal metrics which can not be diagonalized by
coordinate transforms but effectively diagonalized with respect to
certain nonholonomic frames (vielbeinds) with associated nonlinear
connection structure. The off--diagonal terms define just the
coefficients of nonlinear connection (N-connection) and inversely. On a
such manifold, a part of the degrees of freedom (coordinates) are
holonomic and another ones are nonholonomic (subjected to certain
constraints) which is distinguished by the nonlinear connection
structure and creates a specific anisotropy of gravitational
interactions even in the framework of general relativity. We found a
number of exact solutions of the Einstein equations modeling such
configurations (deformed black holes, spinor and solitonic
configurations, cosmological type solutions). In a particular case, we
can take state that the off-diagonal terms are related to the Cartan
N-connection from Finsler geometry and the diagonal terms are some
Finsler metric coefficients. This allows us to model Finsler structures
just on a (pseudo) Riemannian space.
I will need to see the actual math. Sounds interesting.
The conclusion is that we can not avoid Finsler geometry even in the
usual (Einstein) gravity if the generic off-diagonal metrics and
nonholonomic frames are considered. By the way, Riemann in his 1854
hability thesis considered already Finsler metrics. He had not
investigated them considering the constructions to be of higher order
sophistications. It was necessary in the elaboration of E. Cartan's
moving frame method in order to understand that by nonholonomic frames
it is possible to model Finsler structures even by quadratic (metric)
forms but with additional nonholonomic structures.
Interesting.
The main problem is that the bulk of monographs on Finsler geometry were
written to emphasize more general constructions than the the Riemannian
ones, just on tangent bundles. It is realy difficult to see the point on
modeling of Finsler structures on the usual Riemannian manifolds. The
bulk of discussions and pessimistic conclusions for physics (even of
Berstein and C. Will) had been taken with respect to physical models on
tangent bundles and without a deep analysis of the N-connection
structure. I hope soon to elaborate an e-preprint with details.
My credo is: we can not understand deeply the Einstein's gravity without
Finsler geometry.
Finally, I note that Clifford-Finsler spaces result trivially from the
Clifford spaces if nonholonomic frames and off-diagonal metrics are
considered.
I'm grateful for your time.
SV.
This has piqued my interest in looking at the math. :-)
Carlos Castro escribió:
Dear Sergiu ( Jack and Tony ) : I included Sergiu Vacaru in this e-mail
because he is the expert on non-holonomic and anisotropic deformations
of ordinary Riemann-Cartan geometry. He is an expert on Finsler
geometries that are far more fundamental than Riemannian geometries. You
may understand the recent work by Cahill on anisotropic propagation of
light signals within the context of Sergius' more findamental work. This
is very common in Finsler geometries. I wish Sergiu the best in his
immigration to Quebec.
Sergiu gave me the website
http://www.icca7.ups-tlse.fr
where you can register for the Int. Congr. of Clifford Algebras to be
hold in Toulouse, France.
In case you wish to attend.
I have to see.
All the best
Carlos |
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