Monday, 16 February 2009

Torsion and axial forces.

Regular readers, we know that I been discussing an axial force, on these pages. Its a force that depends upon the direction of spin of the particles carrying it, reverse one of the spins, and you reverse the force. Traditionally such a force is thought to be destroyed by quantum effects. Something called the quantum chiral anomaly makes axial charges non-conserved. And if the charge is non-conserved it cannot source a force. In my paper I just arranged enough extra copies of particles to cancel out the chiral anomaly, allowing an axial force with particular charges on quarks and neutrinos. It works, but perhaps nature is more subtle. A recent paper at ArXiv, by P. Mahato, show that once general relativity been extended to contain Torsion, conserved Axial currents exist.

So what is Torsion?, and should we believe in it?. Torsion is spin-spin coupling in one of the simplest extensions to General Relativity, called Einstein-Cartan Theory.
And it turns out that once we try to couple Fermions (half integral spin particles) to generally relativity, we quickly find we need Torsion. Here is an example construction, that might explain inflation. In fact both string theory and loop quantum gravity seem actually to be theories of Einstein-Cartan gravity, its just difficult to have fermions in a quantum gravity theory without Torsion.

Torsion is a very small effect, its generally a four-fermion interaction scaled by the gravitional constant G. So is too weak to be measured in normal circumstances in the universe. However, if the above paper by Mahato is true, then existance of torsion, leaves open the existance of axial forces which may much stronger.