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I heard recently in a talk by Alain Connes that a certain Woodword (or Woodward or Woodard, not sure with reccording quality) showed an important result that a quantum theory of gravity cannot be built directly from Planck-scale elementary degrees of freedom (like causal sets do, I presume), and required instead a more global approach (like non-commutative geometry or loop quantum gravity), even though those global approaches may eventually lead to planck-scale quantised behaviours (as LQG does).

I was a bit surprised, own to the abundant literature on "bottom-up" quantum gravity, and suspected that there should be specific assumptions behind such a result - but I could not find the reference for this work, to check that point.

So does anyone know this result? And if so, do you have the refence for it?

Thanks beforehand

Mathias
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1 Answers1

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There are a lot of papers written by R.P Woodard. But even classical GR does not have local gauge-invariant observables (see Torre's review arXiv:gr-qc/9306030), so I am not sure we should be surprised that quantization would somehow change this.

Woodard has argued in a number of places that the "number of spatial points" must be conserved in these discrete approaches. (Section 2.6 of 0907.4238, for example.) This would predict a much smaller radius of the universe (about $10^{16}$ meters) than what we observe (about $10^{26}$ meters).

I am not entirely convinced that the number of spatial points must be a conserved quantity, but I haven't carefully examined Woodard's argument.

Alex Nelson
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