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john baez
May19-04, 08:28 PM
P: 169
Quote Quote by selfAdjoint
Mike2 on the other thread raised the question of whether the quantum gravity model assumed by AJL had been rigorously developed.
As far as I can tell, it's completely rigorous. And I'm a mathematician by training, so I'm more fussy about these things than most.

I know of rigorous (1,1)-dimensional theories and maybe some (1,2)-dimensional ones, but I don't know of any fully (1,3) relativistic quantized ones.
It's easier to make discrete models rigorous than models that assume spacetime is a continuum. That's the main reason I like discrete models.

In particular, all the 3+1-dimensional spin foam models of quantum gravity I've worked on - various versions of the Barrett-Crane model - are mathematically rigorous and background-free.

The problem is, we haven't gotten good evidence that these spin foam models "work" - namely, that they reduce to general relativity in the limit of distance scales that are large compared to the Planck length.

See my Marseille talk for a taste of the problems:

Since we don't have any experimental evidence concerning quantum gravity, mathematical rigor is one way to make sure we're not playing tennis with the net down. I will be very happy when we get any rigorously well-defined background-free quantum theory of gravity that works in the sense defined above.

More precisely: I will be very happy if we get numerical evidence that it works, and ecstatic if we can mathematically prove that it works. But since such a model is likely to be nonperturbative, a mathematical proof of this sort might be very difficult. Nobody has even proved confinement in lattice QCD, even though numerical calculations have convinced everyone it's true.