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Sean Carroll writes:

"As can be seen from (1.2), in the definition of torsion (unlike that of the curvature)
a single vector field such as X or Y serves both as a direction in spacetime along which
a covariant derivative is taken and as the object being differentiated. This is clearly only
possible when the vector field is a section of the tangent bundle rather than an “internal”
vector bundle; thus, the existence of torsion distinguishes the connection on the tangent
bundle from the connections familiar from conventional gauge theories."

Therefore you cannot, for example, describe Maxwell's electromagnetism as a torsion field.
As I recall Gennady tries to get fields like EM as torsion effects?


Apr 11
Discussion on massive gravitons and propagating torsion in arbitrary dimensions
C. A. Hernaski, A. A. Vargas-Paredes†, J. A. Helay¨el-Neto‡
Centro Brasileiro de Pesquisas F´?sicas,
Rua Dr. Xavier Sigaud 150, Urca,
Rio de Janeiro, Brazil, CEP 22290-180

"In this paper, we reassess a particular R2-type gravity action in D dimensions, recently studied by Nakasone and Oda, now taking torsion effects into account. Considering that the vielbein and the spin connection carry independent propagating degrees of freedom, we conclude that ghosts and tachyons are absent only if torsion is nonpropagating, and we also conclude that there is no room for massive gravitons. To include these excitations, we understand how to enlarge Nakasone-Oda’s model by means of explicit torsion terms in the action and we discuss the unitarity of the enlarged
model for arbitrary dimensions."

I think the opposite should be considered, i.e. real on shell ghosts violating spin-statistics and real tachyons with propagating torsion waves.

"the graviton acquires mass via a spontaneous breakdown of general coordinate reparametrization symmetry ... massive gravitons is drawing a great deal of attention, in view of the possibility of their production at LHC and the feasibility of detection of quantum gravity effects at the TeV scale ... as it is usual in all Higgs-type mechanisms, a nonvanishing vacuum expectation value for an extra scalar field is needed in the description. There is also an alternative way to generate mass in three dimensions, as proposed by Jackiw, Deser and Templeton [7]. There, a topological parity-violating term is added to the Einstein-Hilbert gravity Lagrangian in order to describe a massive graviton. The final theory is also unitary ...
we asked if it is possible to build up a unitarity and parity-preserving model that generates mass for the graviton without the need of an extra field. Bergshoeff, Hohm and Townsend obtain such a model for D = 3 [8] by considering a nonlinear theory that is equivalent to the Pauli-Fierz model at the linear level. ...  Three-dimensional gravity has no local degrees of freedom. The Riemann tensor has the same number of components as the Ricci tensor, which means that all solutions in these theories are trivial, with the exception of those that consider topological effects. However, the situation might change if we consider massive spin-2 propagating modes in three dimensions. ...

We work with the vielbein (aka tetrad) and the spin connection as independent fields. Our viewpoint is that this is a more fundamental approach to gravitation, since it is based on the fundamental ideas of the Yang-Mills approach"

Exactly, this is from localizing the 10-parameter global Poincare group of 1905 SR.

"explicit terms in the torsion field are needed in order to describe a propagating massive graviton."

(Note I use (4) in my emergent gravity model from the 8 post-inflation Goldstone vacuum phases via what I call the "M-Matrix" of Cartan 1-forms)

"our model is invariant under linearized general coordinates and local Lorentz transformations. ... for a massive propagating particle not to be a tachyon or a ghost, we must require that ..."

This may be an erroneous assumption in my opinion. I am not loath to consider the possibility that unitarity may not be preserved under all conditions and that there are not on-mass-shell real ghost and tachyonic particles. Note that ghosts have "wrong" spin-statistics and tachyons are thought to induce vacuum instabilities.

Apr 11

NASA Flyby Anomaly Solved? Raju's response

Posted by: JackSarfatti |
Tagged in: Untagged 

On Apr 10, 2011, at 8:26 PM, c_k_raju@vsnl.net wrote:

What happens if you add Wheeler-Feynman advanced effects? - another line of inquiry.

An interesting line of enquiry. The key difficulty is how to solve the resulting equations. I have been trying to solve such equations in the case of electrodynamics ("Simulating a tilt in the arrow of time", 1995 unpublished conference paper), and I did suggest a technique some years ago, but did not follow it up, though I intend to do so shortly. Hence, the retardation is explicit in the title.


On Apr 10, 2011, at 8:20 PM, c_k_raju@vsnl.net wrote:

Dear Jack,

Thanks for your questions.

Are you sure that Einstein's GR in the post-Newtonian approximation
does not already contain the new terms you use?

No, I am not sure since I did not do the calculations myself, but the published claim is that the GR frame drag cannot account for the flyby anomaly.

There would be further difficulties. If oblateness is important, one cannot use the Kerr solution. One could patch an external Kerr-like solution to an oblate object using my method ("Junction Conditions in General Relativity", J. Phys. A: 15 (1982) 1785-97, or its generalisation arXiv:0804.1991), but it seems  complicated.  

There is no clear-cut statistical way of going from a system of particles to a density in GRT, as there is in classical thermodynamics. Though the galaxy  seems a collection of discrete stars a typical relativist would model it using a "fluid". However, the  observed mass distribution can be related to the theoretically assumed one only "intuitively". Moreover, as far as I know, no one has actually managed to account for galactic rotation curves in this way.

Accordingly, I have not yet taken a position on whether or not GRT can account for the effects that are a clear consequence of RGT.

Clearly, RGT is so much *easier* for many-body problems.

Since Lorentz covariance is absolutely essential to [present-day] physics, it seems to me more important to first settle *experimentally* the question of (a) RGT vs Newtonian gravitation, before tackling the question of (b) RGT vs GRT.


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