Wednesday, June 21, 2006

Not Even Wrong book inspired comment on LQG

Copy of comment in case it is deleted:;

nigel said...
Some genuine questions I have about the loops of LQG, inspired by Woit's "Not Even Wrong", pages 189-190.

A loop is a rotational transformation in the vacuum. Is the loop physically the exchange of energy-delivering field radiation from one mass to another, and back to the first mass again?

Like the exchange radiation in Yang-Mills (Standard Model) theories, but with the added restriction of the conservation (looping between masses) of the exchange radiation?

Things accelerated by a gravity field are losing gravitational potential energy and gaining kinetic energy, so the exchange radiation carries energy.

If the LQG spinfoam vacuum does describes a Yang-Mills energy exchange scheme, you can get solid checkable predictions by taking account of the effect of the expansion of the universe on these conserved gravity field mediators.

If silly, please delete.
6/21/2006 11:35:07 AM

(I don't think it is silly, but have to show some humility or it looks awful.)

'In loop quantum gravity, the basic idea is to use the standard methods of quantum theory, but to change the choice of fundamental variables that one is working with. It is well known among mathematicians that an alternative to thinking about geometry in terms of curvature fields at each point in a space is to instead think about the holonomy [whole rule] around loops in space. The idea is that in a curved space, for any path that starts out somewhere and comes back to the same point (a loop), one can imagine moving along the path while carrying a set of vectors, and always keeping the new vectors parallel to older ones as one moves along. When one gets back to where one started and compares the vectors one has been carrying with the ones at the starting point, they will in general be related by a rotational transformation. This rotational transformation is called the holonomy of the loop. It can be calculated for any loop, so the holonomy of a curved space is an assignment of rotations to all loops in the space.'

- P. Woit, Not Even Wrong, Cape, London, 2006, p189.

He goes on, on the same page, to discuss the problem that loop quantum gravity doesn't seem to say anything useful about the Standard Model (Yang-Mills type quantum field theory).