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marcus
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Sep5-03, 03:41 PM
Astronomy
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Originally posted by selfAdjoint
Baez's discussion of Bojowald's recent work is in This weeks Finds #167. (Down near the bottom). Baez lists Bojowald's papers in #165.
thanks much for the reference to Baez "This Week's Finds" #167 discussion of Bojowald work----that was 2001 so I imagine the papers he's referring to are earlier. The one's I gave links for are mostly 2002 and 2003 so there wont be much overlap.

I shall quote snatches of Baez (this is from the Usenet newsgroup he hosts called "sci.physics.research")

"...Bojowald's progress comes from looking at "minisuperspace models", where we assume the universe is highly symmetrical - as people often do in cosmology. This allows him to tackle the problem of time by treating the volume of the universe as a notion of time. It's like having one aspect of the system you're studying be the clock that you use to see how other things change. This idea per se is not new; what's new is carrying it out in the framework of loop quantum gravity. In loop quantum gravity volume is discrete... so Bojowald's "clock" ticks in discrete steps. By adapting Thiemann's formula for the Hamiltonian constaint to this highly symmetrical context, he can write it as an evolution equation saying how other observables change as a function of the volume of the universe. Since volume is discrete, this equation is a difference equation rather than a differential equation.

He can solve this equation on the computer... and he finds that even when the universe is very small, on the order of the Planck length, it closely mimics the classically expected behavior. However, there is no singularity at t = 0, or more precisely, at zero volume..."

As always, Baez knows how to put things clearly.
since 2001, when he wrote that, things have only gotten better.