On Jan 26, 2005, at 5:21 PM, Jack Sarfatti wrote:
"The Question is: What is The Question?" J.A. Wheeler
Meaning of the Brazilian paper below is the Gestalt Shift
http://www.neurosemantics.com/Stuttering/foreground-background.htm
Thanks Saul-Paul :-)
On Jan 25, 2005, at 10:30 PM, Saul-Paul Sirag wrote:
Jack,
There is a good summary of tests of GR in Clifford M. Will's paper "Relativity at the Century", pp. 27-32, Physics World, Jan. 2005 (a special issue on Einstein). He does not mention the Mercury perihelion advance. [BTW this is covered in great detail in *Gravitation & Inertia* by Ciufolini & Wheeler (1995)]. But the many other tests leave GR looking very good. In particular the Lunar-Laser Ranging measurements (over the last two decades and more) have confirmed not only the weak equivalence principle, but also the strong equivalence principle. To quote from Will's paper:
"Lunar laser-ranging measurements actually test the strong equivalence principle because they are sensitive to both the mass and the gravitational self-energy of the Earth and the Moon. The bottom line of these experiments is that bodies fall with the same acceleration to a few parts in 10^13" (p. 29).
Will also points out that the Brans-Dicke "Scalar-Tensor" theory (and many other alternative theories) are ruled out by these measurements (p. 30).
Cliff told me personally at GR 17 Dublin that he thought Hal Puthoff's PV theory is a non-starter not of interest to serious physicists in the field. So did several others including Matt Visser and Bill Unruh and Professor X. Therefore, Eric Davis, Nick Cook et-al should stop trying to sell Hal's theory to USAF and Aerospace Companies as a serious contender for metric engineering unconventional propulsion systems. That only hurts the field.
BTW( to show the irrelevancy of Paul Zielinski's thesis (LC) = GCT non-tensor inertial force - GCT tensor real gravity force, i .e. inertial forces in inertial frames is the contradiction in Z's proposal!) for the record from Wheeler & Ciufolini "Gravitation and Inertia" Princeton 1995:
Weak equivalence principle "uniqueness of free fall" AKA Galilei equivalence principle "the motion of any freely falling test particle is independent of its composition and structure. A test particle is defined to be electrically neutral, to have negligible gravitational binding energy compared to its rest mass, to have negligible angular momentum, and to be small enough that inhomogeneities of the gravitational field within its volume have negligible effect on its motion. ... the ratio of the inertial mass to the gravitational - passive- mass is the same for all bodies ... in every local, nonrotating, freely falling frame the line followed by a freely falling test particle is a straight line in agreement with special relativity. Einstein generalized the weak equivalence principle to all the laws of special relativity .. that in no local freely falling frame can we detect the existence of a gravitational field, either from the motion of test particles, as in the weak equivalence principle, or from ANY OTHER SPECIAL RELATIVISTIC PHYSICAL PHENOMENON" p. 14
Note that a spinning gyro is not a test particle. Also note that geodesic deviation for TWO test particles is NOT a special relativistic physical phenomenon. *The LIF is taken so small that the geodesic deviation is below the resolution of the stretch-squeeze tidal tensor curvature detector! This restriction would seem to exclude the detection of gravity waves of course.
All viable theories of gravity obey this weak equivalence principle, AKA, "WEP".
Medium strong equivalence principle at the base of METRIC theories of gravity, AKA "EEP" or Einstein Equivalence Principle: "for every POINTLIKE event of spacetime, there exists a sufficiently small neighborhood such that in every local freely falling frame in that neighborhood, all the non-gravitational laws of physics obey the laws of special relativity."
Note EEP restricts itself to "non-gravitational laws of physics".
"If we replace all the nongravitational laws of physics with all the laws of physics we get the very strong equivalence principle" AKA, "SEP" "which is at the base of Einstein's electrodynamics. The medium strong and the very strong form of the equivalence principle differ: the former applies to all phenomena except gravitation itself whereas the latter applies to all phenomena of nature. This means that according to the medium strong form, the existence of a gravitational field might be detected in a freely falling frame by the influence of the gravitational field on local gravitational phenomena. For example, the gravitational binding energy of a body might be imagined to contribute differently to the inertial mass and to the passive gravitational mass ... This is ... the Nordtvedt effect ... However, Lunar Laser Ranging experiment has put strong limits on the existence of any such violation of the very strong equivalence principle."
The EEP (medium strong) with a "locally Minkowski space time" is the physical meaning of the tangent fiber of differential geometry. Therefore, you cannot do differential geometry and also claim to VIOLATE EEP. See Roger Penrose's "The Road to Reality" for more details on that idea. The LOCAL tetrad map
guv(LNIF) = eu^aeu^bnab(LIF)
is part of differential geometry formally AND of EEP informally i.e, interpretively or physically.
"First, the equivalence between a gravitational field and an accelerated frame in the absence of gravity, and the equivalence between a flat region of spacetime an a freely falling frame in a gravity field, has to be considered valid only locally and not globally."
Note that universal inertial forces (independent of mass) like the Coriolis and the centrifugal forces only are detected in NON-INERTIAL FRAMES.
It is meaningless in Einstein's GR to claim that in a Local Inertial Frame (LIF) that a real gravity force (a GCT tensor) is cancelled by an inertial force (GCT non-tensor). This is what Zielinski claims and it is false.
You CAN make such a claim in Newton's force picture because Newton's idea of "inertial frame" is not the same as Einstein's idea of "inertial frame".
In Newton's paradigm you CAN think of a gravity force field in a global inertial frame. This force is cancelled by an inertial force in the free-falling frame that is a NON-INERTIAL frame in Newton's picture! That is, the distinction "inertial/non-inertial" is SWITCHED in the transition from Newton to Einstein. This is Zielinski's error. He tries to force Newton's picture INTO Einstein's. The Brazilians have shown that there is a kind of Bohr complementarity between the two pictures so long as one does not try to force the square peg of one picture into the small round hole of the dual alternative picture.
Wheeler address's the issue of tidal curvature that Zielinski misinterprets as some kind of violation of Einstein's key idea for GR. Zielinski then gets conspiratorial and psychoceramic that Wheeler & Co are somehow trying to pull the wool over our eyes. Wheeler addresses the long line of wrong critics of Einstein of which Zielinski is the latest: (p. 15)
Note the EEP is immune from the spherical drop issue below. What is at stake is the SEP.
The SEP "has been the subject of ... criticisms over the years ... the content of the strong equivalence principle has been criticized even 'locally'/ It has been argued that if one puts a spherical drop of liquid in a gravity field, after some time one would observe a tidal deformation from sphericity of the drop. Of course, this deformation does not arise in a flat region of spacetime ... No matter if we are freely falling or not, the gradiometer will eventually detect the gravity field and thus allow us to distinguish between the freely falling cabin of a spacecraft in the gravity field of a central mass and the cabin of a spacedraft away from any mass, in a region of spacetime essentially flat. Then, may we still consider the STRONG EQUIVALENCE PRINCIPLE (SEP) to be valid?"
Wheeler then gives the Taylor expansion of the metric in the NEIGHBORHOOD {P'} of a spacetime event P that I have given many times before. The simple solution to the problem that Zielinski has magnified to excess is "The Riemann curvature tensor represents at each point, the INTRINSIC CURVATURE of the manifold, and, since it is a tensor, one cannon transform it to zero in one coordinate system if it is non-zero in some other coordinate system. ... The metric tensor can indeed be written using the Riemann tensor Rijkl, in a NEIGHBORHOOD of a spacetime event, in a freely falling, nonrotating, local inertial frame to SECOND ORDER in the separation" (P' - P)
goo ~ - 1 - R0i0j(P'-P)^i(P'-P)^j
Note that in the weak curvature slow speed Newtonian force limit of GR
goo ~ -[ 1 + V(Newton)/c^2]
V(Newton) = Universal Newtonian Gravity Potential Energy per unit mass of test particle)
Therefore in the LIF:
V(Newton)/c^2 ~ R0i0j(P'-P)^i(P'-P)^j
Note Rijkl has dimension 1/Area
(P' - P) has dimension Length
Furthermore, the post-Newtonian GRAVIMAGNETIC FIELD g0k of Lense-Thirring FRAME-DRAG not found in Puthoff's PV theory but found in NASA experiments and used by Ray Chiao of UCB in his "gravity radio" idea for submarine warfare C^3 and efficent superconducting gravity wave detectors, is in Fermi Normal Coordinates
g0k = -(2/3)Roikj(P'-P)^i(P'-P)^j
k = 1,2,3
with electro-gravitic coupling
~ g0kA^k
A^k is EM vector potential in
p = mv - (e/c)A (3-vector)
In NEAR FIELD this may allow a geodesic glider WEIGHTLESS WARP DRIVE for metric engineering! Ray Chiao only uses FAR FIELD.
And finally, i,j,k,l = 1,2,3
gkl = (Kronecker Delta)kl - (1/3)Rkilj(P'-P)^i(P'-P)^j
Zielinski ignores the levels of approximation of perturbation theory and, therefore, formulates a pseudo-problem.
On Jan 26, 2005, at 2:46 PM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
On Jan 25, 2005, at 3:08 PM, iksnileiz@earthlink.net wrote:
They do point out that the gauge representation is able to handle theories in which certain aspects of EP are violated i.e. mg =/= mi,
[Z] That is not the point. They allude to the dissident literature on the equivalence principle in support of their teleparallel alternative to the standard theory. This amounts to a critical argument against the orthodox view. So you still don't understand what is meant by a mathematical decomposition of the LC connection into tensor and non-tensor parts?
[S] I understand what it means. It is false in Einstein's 1916 GR geometrodynamic representation where
{LC} = non-GCT tensor
It has no tensor part at all.
[Z] I have simply pointed out that the Einstein equivalence hypothesis, as classically stated by Einstein himself, is not necessary for Einstein geometrodynamics.
[S] Be specific. What words by Einstein?
[Z] I have given you direct quotes from Einstein any number of times.
[S] All you do is cite a possibly BAD English translation. You do not read the original German and you do not know what Einstein really said here at all! Have you checked with a German speaking physicist in the field? NO!
Your theory is based on quicksand.
[Z] Except that the Brazilian paper shows how, mathematically, you can do exactly what I have been proposing within the teleparallel framework.
[S] I deny that, nor do the Brazilians claim there is any conclusive experimental evidence for such theories that violate SEP.
[Z] But at least the differences are testable in principle.
[S] Yes, but they have all so far been falsified as mentioned by Sirag above. Puthoff's "PV" is such a theory and it does not agree with experiment beyond the 3 trivial weak field limit "classic tests". PV fails to predict gravimagnetism now observed, it has no event horizons pretty much now observed, it fails to give correct 1913-16 pulsar curve off by what 1/3? When 1916 GR is on target to 10^-14 for which a Nobel Prize was given. At least Hal has a real theory. It happens to be wrong and confused in its foundations, but at least it is definite enough to be falsified and it has. Hal can at least calculate as you so far have not been able to do.
[Z] So you wanted to talk about the Schwarzschild solution instead?
[S] Yes, until you can solve that you have nothing of interest. Vilenken's vacuum wall has nothing to do with your claims. It is an entirely different problem. It has to do with a NONLOCAL Bohm-Aharonov closed non-exact 1-form in the connection from non-trivial topology of the vacuum coherence order parameter that is the fabric of spacetime. This also explains the NASA Pioneer 10&11 anomaly a_g = - cH as a hedgehog defect centered on Sun (and maybe ALL STARS). What is important in the Brazilian model for me, so far, is that their gauge potential theory representation is close to my macro-quantum theory for emergence of gravity from the COHERING of the ZPF of the false pre-inflation vacuum. They map their gauge force freedom into GCTs, which is key to what I do.
[Z] This gauge freedom is intimately tied up with general covariance -- which is closely parallel to what I have been saying.
[S] Really? Where? Show your equations for that. They do not seem to claim a LOCAL gravity energy tensor in the geometrodynamic representation.
[Z] In the geometric model. They say only that there "seems" to be no such decomposition in the standard formalism, based on curvature. The reason they say this is because they are aware that there is no proof.
[S] It's like p & x in Heisenberg. A sharp local energy density in the gauge force Newtonian rep is NONLOCAL in the geometrodynamic rep - like wave packet Fourier transforms
[Z] That is not the Brazilians' theory -- it's your gloss.
[S] Yes.
[Z] You are trying to do complementarity -- but they are talking *replacement* of curved-vacuum geometrodynamics
with a Newtonian-type force described by contortion.
[S] Paul you do not seem to know that the Brazilians write
GCT tidal stretch-squeeze geometrodynamic 1916 GR curvature tensor ~ teleparallel contortion type term
which translates to teleparallel curvature = 0
The Brazilians do not claim that Riemann curvature is zero.
The Brazilian gauge potential Bu^a is the non-trivial part of the dimensionless TETRAD
eu^a = (Kronecker Delta)u^a + Bu^a
that I call
Bu ~ Lp^2(Goldstone Phase),u
Bu = Bu^adx^a
Bu has dimensions of length.
[Z] OK.
[S] But this is very important and very new. Indeed it's completely original. No one has done this before me I am pretty certain. Sakharov in 1967 did not realize that it is the cohering of the random ZPF that gives emergent gravity. PW Anderson was getting the needed idea of "More is different" simultaneously also in 1967 and they did not know of each other's work or how they might be connected.
Note that when Lp^2 = hG/c^3 -> 0 MACRO-QUANTUM GRAVITY VANISHES!
guv(LNIF) = eu^aeu^bnab
Note that guv(LNIF) is the Einstein geometrodynamic representation where nab is the metric in the gauge force rep.
[Z] OK.
[S] Bu^a is the Newtonian non-geometrical gauge force representation.
guv(LNIF) has ELASTIC terms LINEAR in Bu^a and PLASTIC terms NONLINEAR in Bu^a.
The VANISHING "gauge force" curvature is NOT the same as the geometrodynamic tidal stretch-squeeze GCT tensor curvature! You garbled that Paul by simply looking at the spelling of the same word with two different meanings in complementary contexts!
[Z] You are saying that they don't replace curvature with contortion? That they still need Riemann curvature to describe the tidal aspects of the gravitational field? I say this is FALSE. You are simply projecting your own prejudices into their paper. They say they use contortion to describe the gravitational field in its entirety, as an *alternative* to the usual geometric model.
[S] No Paul, you obviously have not understood their equation (49) on p.7
R* = R + Q = 0
R* is the teleparallel gauge force "curvature
R is Einstein's 1916 GR tidal stretch-squeeze (LC) geodesic deviation GCT tensor curvature
Q = teleparallel covariant curl of the teleparallel CONTORTION K.
R(Einstein Geometrodynamics) = - Q(Teleparallel Gauge Force) =/= 0
This is not Einstein-Cartan-Shipov type theory agreed. However, it is not contradictory to the latter which would be an extension. You can have an Einstein-Cartan-Shipov extension of this Brazilian-Weitzenbock theory.
[Z] No math that you were able to understand. :-)
[S] No math you were ever able to write down. I cannot understand what you cannot manifest in formal language.
[Z] What I gave you was formal:
(LC) = A_ - Q
Then you complained that it was too formal.
It's either too formal, or not formal enough.
What kind of a game is this?
[S] Paul you need to define A_ and Q. You have not done that. Also it's not good enough to say Alex does it.
You need to do it in TWO ways mathematical and physical. Otherwise it is too vague and useless.
[Z] In the Brazilian paper, the intrinsic geometry of the spacetime manifold is implicitly defined by the teleparallel connection, and it is therefore no longer the curved Riemannian manifold of standard GR. As I read the paper, there is no need for Riemann curvature in this teleparallel approach.
[S] That's not what eq. 49 p. 7 says.
[Z] If you don't see this then you haven't yet understood their thesis IMO.
I am just trying to find a way to do the same thing within the framework of standard GR.
[S] Exactly, which shows you do not understand at all what the Brazilians have done!
[Z] More likely that you haven't, since they actually spell it out:
"The definition of an energy-momentum density for the gravitational field is one of the oldest and most controversial problems of gravitation."
[S] So? That spells out nothing.
"As a true field, it would be natural to expect that gravity should have its own local energy-momentum density." (Brazilians)
[Z] Exactly.
[S] IN WHAT CONTEXT? In what representation! Relative to what connection? Measured how?
Loud silence by Zielinski on this key point.
"However, it is usually asserted that such a density cannot be locally defined because of the equivalence principle."
[Z] Note the phraseology: "...it is usually *asserted* that such a density cannot be locally defined...".
[S] So? What of it? What unwarranted inference do you make of that?
"As a consequence, any attempt to identify an energy-momentum density for the gravitational field leads to complexes that are not true tensors."
[Z] Uh huh.
[S] Hardly news Paul.
[Z] Right. But wait, there's more....
"The first of such attempt was made by Einstein who proposed an expression for the energy-momentum density of the gravitational field which was nothing but the canonical expression obtained from Noether’s theorem. Indeed, this quantity is a pseudotensor, an object that depends on the coordinate system. Several other attempts have been made, leading to different expressions for the energy-momentum pseudotensor for the gravitational field."
[Z] As I have been saying.
[S] As found in every text book. So far nothing has been solved.
[Z] This is all direct from Arcos and Pereira.
[S] So what? It's common knowledge defining The Question. It is not The Answer you yearn for Paul.
"Despite the existence of some controversial points related to the formulation of the equivalence principle, it seems true that, in the context of general relativity, no tensorial expression for the gravitational energy-momentum density can exist."
[Z] Note the phraseology: "...it *seems* true that...". Not "is true", but "seems true".
[S] And it IS true!
[Z] As they write, it is "usually asserted". I agree that this is simply an "assertion". There is no proof. And the Brazilians know that. That's why they write, "it *seems* true that...". Get it?
[S] I claim it is true. For example see Penrose "The Road to Reality" 19.8 "Gravitational Field Energy" there is no LOCAL pure gravity stress-energy density GCT tensor vacuum field apart from the trivial one
tuv(vacuum) = (c^4/8piG)(Guv + /\zpfguv)
Note, when the exotic dark energy vanishes, i.e. /\zpf = 0, then Guv -> Ruv = R = 0 and so
tuv(non-exotic vacuum) = 0
However, in the presence of either dark energy (negative pressure) or dark matter (positive pressure), both have w = -1 but positive pressure clumps look like w = 0 to distant observers (us),
tuv(exotic vacua) = (c^4/8piG)/\zpfguv =/= 0
Not in context of the geometrodynamic representation, but possibly in context of a Bohr complementary Newtonian gauge force representation! A VERY DIFFERENT STORY FROM YOURS PAUL!
[Z] That is merely your personal hallucination. That is not in their paper. What is in their paper is the statement that the teleparallel treatment is an "alternative" to the standard formal description of the
gravitational field in terms of spacetime curvature. You are trying to impose your own eccentric interpretation on their paper -- but your interpretation contradicts their actual remarks.
[S] I am imposing my interpretation on their eccentric paper that is true. I do not see the contradiction because you do not understand what "alternative" means.
[Z] I note that the Brazilians only say that there "seems" to be no such solution within the standard 1916 curved-manifold framework -- which they offer as a sales point for their flavor of teleparallelism (which effectively returns gravitational physics to a flat spacetime manifold and "forces").
[S] You completely misunderstand the paper! They never say that the 1916 GR tidal "curvature" is zero.
"As already discussed, in general relativity torsion is assumed to vanish from the very beginning, whereas in teleparallel gravity curvature is assumed to vanish." - p 2
[S] IT'S NOT SAME "CURVATURE"!
Gauge force curvature = Geometrodynamic Einstein Curvature - Torsion type term = 0
[Z] But note that the intrinsic geometry of the manifold is now *defined* by the torsion connection. There is no longer any underlying curvature, and we are no longer dealing with the Riemannian manifold of standard GR. This is the subtlety that has evidently escaped you.
[S] False. Again eq. 49 p. 7 you have over-extrapolated.
"In the present work, we will separate the notions of space and connections. From a formal point of view, curvature and torsion are in fact properties of a connection."
[S] Yes.
"Strictly speaking, there is no such a thing as curvature or torsion of spacetime, but only curvature or torsion of connections. This becomes evident if we remember that many different connections are allowed to exist in the same spacetime. Of course, when restricted to the specific case of general relativity, universality of gravitation allows the Levi–Civita connection to be interpreted as part of the spacetime definition as all particles and fields feel this connection the same."
[S] Yes
"However, when considering several connections with different curvature and torsion, *it seems far wiser and convenient to take spacetime simply as a manifold*, and connections (with their curvatures and torsions) as additional structures."
- Arcos & Pereira, p 4
[S] Yes. Standard orthodox same as in Penrose's "The Road to Reality" so what?
"We may then say that the gravitational interaction can be described in terms of curvature, as is usually done in general relativity, or *alternatively* in terms of torsion, in which case we have the so called teleparallel gravity." - p 2
[S] YES EXACTLY! That simply means
GAUGE FORCE TORSION TYPE TERM equivalent to GEOMETRODYNAMIC TIDAL STRETCH-SQUEEZE
in two qualitatively different pictures.
[Z] It means that the torsion formalism *completely replaces* the geometric model as an alternative exhaustive description of the gravitational field -- contrary to what you wrote.
[S] It means nothing of the sort. That's you over-interpreting again. Just look at eq. (49) p. 7
"...whereas in general relativity gravitation is described in terms of the curvature tensor, in teleparallel gravity it is described in terms of torsion." - p 20
[S] Yes, if
A ~ B - C
and if
A ~ 0
Therefore,
B ~ C
I use ~ not = in sense of a EQUIVALENCE RELATION that is the MAPPING between the TWO Bohr COMPLEMENTARITY pictures of teleparallelism with torsion* and zero curvature* ~ Einstein geometrodynamics without torsion but with curvature.
Note "curvature*" =/= "curvature"
AND
"torsion*" =/= "torsion"
Paul you are confused by SURFACE LABELS! You have found FOOL'S GOLD and the END OF THE RAINBOW.
Again loud silence from Paul in this devastatingly accurate remark - checkmate, "As I end the refrain, thrust home." Cyrano De Bergerac (Rostand)
"...whereas in general relativity gravitation is described in terms of the curvature tensor, in teleparallel gravity it is described in terms of torsion." - p 20
[Z] Plain as day. Where is the "curvature" here?
[S] Eq. 49 p.7
Note, this is not same idea as Shipov's theory.
[Z] Duly noted.
"...the classical equivalence between teleparallel gravity and general relativity implies that curvature and torsion might be simply *alternative ways* of describing *the gravitational field*, and consequently related to the *same degrees of freedom of gravity*." - p 32.
"A further consequence that emerges from the conceptual differences between general relativity and teleparallel gravity is that, whereas in the former curvature is used to geometrize the gravitational interaction—spinless particles follow geodesics — in the latter torsion describes the gravitational interaction by acting as a force—trajectories are not given by geodesics, but by force equations.
[S] SO WHAT?
You can write
But you CANNOT write
According to the teleparallel approach, therefore, the role played by torsion is quite well defined: it appears as an *alternative* to curvature in the description of the gravitational field...". - p 32
But you DID NOT UNDERSTAND the paper's real meaning!
[Z] Either I'm hallucinating or you are.
[S] Agreed.
[Z] I think it's you.
[S] Which proves it's you! ;-)
"...the role played by torsion is quite well defined: it appears as an *alternative* to curvature in the description of the gravitational field..."
[Z] Jack, what part of "alternative" didn't you understand?
[S] I understand the math that they actually DO.
[Z] That wasn't the question. What do you think they mean here by "alternative"? Wave-particle duality?
[S] Yes, you can look at it EITHER WAY! Gestalt Shift!
http://www.neurosemantics.com/Stuttering/foreground-background.htm
http://online.sfsu.edu/~psych200/unit6/68.htm
You really understand NOTHING of what they do because you are stuck on the surface of the words like "curvature" and "torsion" without understanding their very different meanings in the two alternative pictures!
[Z] Really?
[S] Really.
You read the words not not the equations.
[Z] I read the words and looked at the equations.
[S] WITHOUT UNDERSTANDING ANY OF IT.
[Z] Or perhaps I do understand the author's purposes and intentions, while you are hallucinating?
[S] Am I Jack Sarfatti thinking he is Robin Williams, or am I Robin Williams thinking he is Jack Sarfatti?
Let's leave Buddhism out of this.
The curvature that vanishes is a DIFFERENT curvature from Einstein's 1916 which is battle-tested based on geodesic deviation - all relative to the LC connection - not a bigger one!
[Z] You are trying to have your cake *and* eat it.
The authors are quite clear in this point:
"...theoretical speculations have since the early days of general relativity discussed the necessity of including torsion, in addition to curvature, in the description of the gravitational interaction."
[S] Again the words "torsion" and "curvature" are being used too sloppily EVEN BY THE BRAZILIANS.
[Z] Because their actual use of these terms in the paper doesn't support your eccentric "complementarity" gloss on their treatment?
{s} Look Paul given any connection C with a covariant derivative D
TORSION means
[Du,Dv]SCALAR = TORSIONuv^w(Scalar),w
,w is ordinary partial derivative
CURVATURE means
[Du,Dv]Aw = (CURVATURE)uvw^lAl
Where TORSION and CURVATURE are BOTH tensors relative to the given group e.g. GCT if we are doing 1916 GR.
[Z] They say that in GR, the gravitational field is described by a curvature tensor -- which obvious means the Riemann tensor R^u_vwl. They say that *this* curvature is absent in their treatment.
[S] Hogwash Paul. Again you have not understood their eq. 49 p. 7.
[Z] The point is that the intrinsic geometry of the manifold is now defined entirely by the teleparallel connection. Are you saying that this teleparallel connection must have non-vanishing Riemann curvature in their treatment?
[S] Yes, that's eq. 49 p. 7
Now in the Brazilian paper the gauge force connection C* is NOT same as the 1916 GR (LC) connection.
[Z] Right.
[S] Indeed Bu is the Gauge Force Connection
C* = Bu
Du* = ,u - Bu
Just like in EM!
[Z] Exactly.
[S] In contrast, in the geometrodynamic representation
C = (LC)
Du = ,u - (LC)
Therefore Paul you have been comparing apples with oranges. Your head is in the clouds, but your feet are not on the ground. You are a LUFTMENSCH right out of Thomas Mann's "Felix Krull" - or maybe I am? ;-)
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