"What I cannot create. I do not understand." Feynman
"The Question is: What is The Question?" Wheeler
On May 3, 2005, at 7:12 PM, firstname.lastname@example.org wrote:
Jack Sarfatti wrote:
On May 3, 2005, at 2:05 PM, email@example.com wrote:
Jack Sarfatti wrote:
No, you are garbling things there.
A&P are working at the level of the antisymmetric torsion tetradic substratum level. The BILINEAR symmetric curved geometrodynamic level is where Alex is working.
Yes, I know.
But Alex is defining alternate connections (metric-compatible LC and metric-free "affine") on a raw manifold,
and allowing the properties of the connection to define the nature of the manifold -- as is typical in modern
I have Alex's GR17 paper in front of me. I cannot understand his physical picture - what he really means by "FR" (Frame of Reference)?
I think he means what we mean -- roughly, a co-moving array of detectors AKA "moving observer" -- but he doesn't tie this definition *a priori* to spacetime coordinate systems as in Einstein's approach, for reasons I've partly explained.
I do not understand what he means until I see a detailed explanation. I find the following sentences he wrote puzzling:
"the use of the Levi-Civita connection in lieu of the gravitational field in GR leads to a loss of general covariance"
Does he simply mean for the GCT X
(LC) -> (LC)' = XXX(LC) + XY
i.e. when Y =/= 0?
"We show that in the presence of an arbitrary affine connection, the gravitational field in GR may be described as nonmetricity of the affine connection." Huh?
The connections come from the principle of local gauge invariance relative to definite groups!
1916 GR is from locally gauging RIGID GLOBAL T4 down to local GCT Diff(4) with elements Xu'^u to get
Bu^a as the non-trivial part of the Einstein-Cartan tetrad eu^a where
eu^a = Iu^a + Bu^a
Where EEP is
guv(Curved) = eu^a(Flat)abev^b
guv,w (Curved) = (LC)uvw + (LC)vuw
,w = ordinary partial derivative
guv,w = Bu^a,w(Flat)ab(Iv^b + Bv^b) + (Iu^a + Bu^a)(Flat)abBv^b,w
(LC)uvw = Bu^a,w(Flat)ab(Iv^b + Bv^b)
(LC)vuw = (Iu^a + Bu^a)(Flat)abBv^b,w
Bu^a = Bu(LpP^a/ih)arg(Vacuum ODLRO)
Bu = Bu^a(Xa/Lp)arg(Vacuum ODLRO)
Under GCT's Xu'^u
Bu -> Bu' = Xu'^uBu
Under O(1,3)'s /\a^a' in tangent space
Bu^a -> Bu^a' = /\a^a'Bu^a
ea^ueb^vec^wguv,w = 0
Note that this constraint is a Galois solvable polynomial of 4th order in the B-field and is linear in B's first-order partial derivatives.
guv;w = 0
;w = ,w + (LC)^a^bw
That is, we are not free to impose connection fields willy-nilly & higgledy-piggledy & topsy-turvy. They are DYNAMICAL FIELDS! They must come from the principle of local gauge invariance!
Therefore, I do not understand Alex's
"An affine connection can be interpreted as induced by a frame of reference (FR), in which the gravitational field is considered ..."
Many other sentences in Alex's paper I simply do not understand. More on that anon.
I do not see how to relate it to MTW's "LIF" & "LNIF" for which I have a clear and precise measurement epistemology and objective ontology.
I think the key here is to understand that "locality" of coordinate frames arises at a different stage of analysis and interpretation in Alex's model.
In the orthodox theory this has everything to do with the localized nature of coordinate patches on curved manifolds
(there is no such restriction on a flat manifold), and this has to do with the mathematical technicalities of homeomorphisms from opens sets on the manifold to R^4.
Unintelligible. Physical space-time is not flat. It is curved. That is directly observed LOCALLY as geodesic deviation for a pair of test particles at neighboring positions X & X'! Tidal distortion is
D^2(X^u - X'^u)/ds^2 = R^uvwl(Xl - X'l)(dX^v/ds)(dX^w/ds)
Physics is more constrained than pure math. What you write is unintelligible.
Alex's model of observer reference frames -- as I understand it -- comes before all this.
Also, I do not understand formally his equation
Riemann Curvature = Affine Curvature - (Torsion + Nonmetricity)Curvature
EEP demands (LC) = 0 in an LIF, since in his model
(LC) = (Affine) - (Torsion + Nonmetricity)
(Affine) = (Torsion + Nonmetricity) in the LIF.
I'm not sure this argument is correct. Obviously LC can be a zero matrix at some point in an "LIF" without
ceasing to be defined there.
That it is zero in a particular system of coordinates doesn't change the algebraic
relationship of (LC) with A, S, and Q.
A = (LC) + Q + S
Is this an empty definition of A like
F = ma
is an empty definition by itself? You need more information like
F = GMm/r^2 to break out of the empty definition.
Similarly, t_uv(vacuum) in Yilmaz is an empty definition.
(LC) = 0 in ALL LIF's at P means a critical point for guv,w as a functional of worldlines through intermediate event P. Those world lines for the LOCUS of critical points connecting P(initial) to P(final) are the "straightest" timelike geodesics of MAXIMAL proper time in the curved space-time. This is essentially the action principle for a neutral point test particle applied to geometrodynamics. It is the path of constructive interference of the complex quantum Feynman amplitudes e^iClassical Action/h for the point test particle.
But is this simply an empty tautology like in
F = ma
before one posits a force law like
F_g = GMm/r^2 ?
Alex's torsion is SAME as Shipov's, but totally different from A&P's at the "square root" tetrad level.
For simplicity Alex actually sets torsion to zero for his development in the GR-17 paper -- although he says this is not necessary.
So what? You evade the point.
My analogy with the A&P Weitzenboeck connection has nothing to do with torsion. It has only to do with defining alternate connections over a raw manifold and then writing algebraic relations between them -- which is exactly what Alex and also A&P do in their respective papers.
Look torsion is from locally gauging O(1,3).
Nonmetricity is from locally gauging GL(n) where n = number of extra bosonic space dimensions of hyperspace.
Otherwise, what Alex is doing is empty definitions with no physical meaning.
Then, very much like A&P, he derives algebraic relationships between alternate connections, such as
LC = A - S
which is very similar to what A&P do with the alternate curvature-free Weitzenboeck connection in their paper.
No, you are completely wrong about that.
It's mixing apples & oranges. Severe category error.
Are you saying you can't define a metric-free connection (with a non-zero tensor of non-metricity) on a differentiable manifold?
You can define anything you like, but it has nothing to do with the physics of gravity! You do not seem to understand the difference between theoretical physics and purely formal games.
And, alternately, the metric-compatible LC connection (with a zero non-metricity tensor) on same? Or that you can but you cannot formulate algebraic relationships between them?
That was the point. I thought this comparison would help you to understand Alex's mathematical model.
I have no interest in purely mathematical models if they have no connection to physics.
My interest is VERY NARROW and FOCUSED i.e.
practical low power metric engineering of Warp, Wormhole & Weapon
as seen in the flying saucer evidence!
That is reverse engineering the Kaku Type IV Superior Military Super-Technology of the alleged time travelers - the "Masters of Hyperspaced" visiting Earth for at least the past 10,000 years according to Professor Scott Littleton (Anthropologist) from Claremont Colleges - not a Diploma Mill BTW!
The relationship between the two levels is NONLINEAR
guv = (Iu^a + Bu^a)(Minkowski)ab(Iv^b + Bv^b)
Bu^a = Bu(Pa/ih)(Vacuum ODLRO Goldstone Phase)
Vacuum ODLRO Goldstone Phase emerges from NON-PERTURBATIVE inflation vacuum phase transition
y = (e^1/x)Step Function (-x)
x < 0 is Spontaneous Breakdown of Vacuum Symmetry causing Inflation.
x = 0 is starting point for perturbation theory, which is no good for this problem.
Yes, of course I realize all this. See above.
On May 2, 2005, at 9:02 PM, firstname.lastname@example.org wrote:
Sorry, that's "Arcos & Pereira".
His approach is very similar to that taken in Arcos & Pereirez -- you alternately lay different connections on a raw
manifold, and define the mathematical relationships between them. This is what A&P do with their teleparallel
Weitzenboeck connection. That is also what Alex does with the "affine connection" A in relation to the LC connection.