The tetrads are spin 1 fields in flat spacetime and they are square roots of the Einstein spin 2 tensor field.

The qubit Penrose spinors are the square roots of the tetrads - intuitively speaking, hence 4th roots of the Einstein metric field.

A non-zero energy momentum tensor using the tetrads & spin connections as the basic gravity fields rather than the Levi-Civita connection may be possible. The two formulations would be compatible.

Note, that in the analogy with Yang-Mills fields

connection = gauge potential

curvature = field

From this POV, the gravity field energy tensor should be made from the 4th rank curvature tensor Ruvwl analog to Yang-Mills Fuv^a

But that is not obviously compatible with Einstein's field equation

Guv + kTuv = 0

where

Tuv^;v = 0

; relative to Levi-Civita connection

Waldyr et-al use new connections willy nilly - the theory is defined in terms of the connection e.g. Ashtekar - so Waldyr has an alternative gravity theory that needs an operational measurement theory or it is only a formal game without physics. Einstein's GR has a very clear successful measurement theory.

On May 6, 2010, at 8:06 PM, Paul Zielinski wrote:

http://arxiv.org/PS_cache/arxiv/pdf/0909/0909.4472v4.pdf

Note that Waldyr has Poltorak's non-metricity model toward the end of the paper, but no mention of Poltorak in the text, and no citation in the bibliography.

I think the relationship between Waldyr's and Kleinert's models for gravity would be an interesting topic for discussion, especially if you could get Kleinert and Rodrigues directly involved.