**Subject:** Fwd: Just What is 4-d torsion

**Date:** Wed, 1 Apr 2009 03:35:29 EDT

Myron,

The problem I have been struggling with lately is “just what is 4-d torsion?” I have I think an intuitive understanding of 2-d and maybe 3-d torsion, but my intuition draws a blank trying to think about 4-d torsion. Have you written an article about that or is there an article you can point me to?

Thanks, Dave Feustel

It is better not to try to use intuition in relativity, the mathematics must be used. Popular books in words are of very little use. The torsion tensor is the difference of two gamma connections, and by hypothesis is proportional to angular energy momentum density. The theory of angular momentum has been highly developed in many ways – see for example the articles and book on the Omnia Opera section of _www.aias.us_ (http://www.aias.us) . A good book on angular momentum in quantum mechanics is P. W. Atkins, “Molecular Quantum Mechanics” (Oxford University Press, many editions). To see how ot get angular momentum form angular momentum density see L. H. Ryder, “Quantum Field Theory” (Cambridge University Press, second edition, 1996), chapter three. In quantum mechanics the theory of angular momentum has been very highly developed, for example the orbitals of hydrogen. Dirac theory has also been very highly developed. So before starting to read GCUFT one needs courses like this. I taught Atkins at graduate level at UNCC. when Dirac was asked if the general public could understand relativistic quantum mechanics he said “no”. Inded few chemists ever go into the Dirac equation, they use L + 2S. To understand even L + 2S one needs an undergraduate degree in chemistry. So GCUFT is an advanced level monograph. The best way to understadn it is to code it up and produce computer generated animations.

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