Questions about torsion


Subject: Fwd: Questions about torsion
Date: Tue, 27 Feb 2007 11:52:47 EST

The governing relation between geometry and energy momentum density in ECE theory is always:

R = -kT ————————— (1)

where R is the scalar curvature and is defined from the tetrad postulate in terms of the spin connection and general gamma connection. Here k is the Einsetin consatnt and T is the index reduced canonical energy momentum density. The general gamma connection is the Christoffel connection if and only if it is symmetric in its lower two indices. So Eq. (1) describes T due to torsion as well as T due to curvature. There may be gravitational torsion and electromagnetic torsion. The latter gives rise to the electromagnetic field:

F = A(0) T ————————— (2)

where in Eq. (2) T is shorthand for the Cartan torsion. The electromagnetic field equation is derived from the first Bianchi identity:

d ^ T + omega ^ T = R ^ q

re-expressed as

d ^ F = mu0 j —————————- (3)

and Hodge dual:

d ^ F tilde = mu0 J —————————– (3a)

.. The current j is

j = (A(0) / mu0) (R ^ q – omega ^ T) ———- (4)

The T in eqs. (2) and (4) is a shorthand for Cartan torsion (a vector valued two-form). In Eq. (1) T is the index reduced canonical energy momentum density. When there is interaction between gravitation and electromagnetism, j in Eq. (4) is not zero. This fact gives rise to optical effects such as polarization changes in light deflected by gravitation. These are observed and provide one of the numerous successful experimental tests of ECE theory (see News Section, thirty advantages)

Dear Dr. Evans, my name is Nicolò and I already e-mailed you about the wedge product present in the antisymmetric metric. There’s a thing that I still don’t understand about the sources of the torsion field, since to me they are still energetic and then I suppose they should be source of a gravitational field. I don’t understand what are the electromagnetic sources you refer to in the antisymmetric equation. Can you please explain it to me clearly because I’m very interested in this part of the theory. Furthermore, I would like to know how do you explain electrostatics in terms of geometry or within your field equations, since this is another thing I wasn’t able to understand. Thank you for your patience.

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