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marcus

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## Main Question or Discussion Point

This confirms a beautiful result of Modesto's earlier paper, that LQG seems to coincide with two other very different types of quantum geometry/gravity on the business of dimensionality declining continuously with scale. Fractal-like microstructure of space time. As scale decreases the observed dimensionality goes smoothly down from 4D to 2D.

Analogous to a fractal sponge which looks like a cube to a large wavelength probe but has a lot of holes, that can be revealed and probed with higher energy, and that make it have less dimensionality when seen under magnification. Like soapsuds is really 2D not 3D.

Analogous to a crumpled ball of wire. It looks like a 3D ball but if you examine closely you see a 1D wire.

The surprising thing is that both Loll Triangulations QG and Reuter AsymptSafe QG which are extremely different from each other, both got this result. And then, to top it off, Modesto showed that you get this kind of behavior with LQG, which is different from the other two.

Anyway, MTd2 found and posted the abstract for Modesto's new paper:

http://arxiv.org/abs/0905.1665

Leonardo Modesto

(Submitted on 11 May 2009)

"In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase when the energy of a probe scalar field decreases from high to low energy in a fictitious time T. We calculated also the spectral dimension of space-time using the scaling of the area spectrum operator calculated on spin-foam models.

BTW Modesto includes a picture of that fractal sponge that I was talking about.

You also get that in Loll's SciAm article. That is very good for a nontechnical article. I have the link in my sig. It gives a lot of intuition about ways in which spacetime microgeometry might be different, essentially for Heisenberg or quantum reasons, from the more familiar macro-scale geometry. Something that seems to happen consistently in Loll's computer simulations of universes.

It seems bizarre that this same behavior is coming up in the context of several different approaches to quantum geometry/gravity. Happened in the Horava-Lifgarbagez case too. And Benedetti recenty drew a connection with non-commutative geometry.

Analogous to a fractal sponge which looks like a cube to a large wavelength probe but has a lot of holes, that can be revealed and probed with higher energy, and that make it have less dimensionality when seen under magnification. Like soapsuds is really 2D not 3D.

Analogous to a crumpled ball of wire. It looks like a 3D ball but if you examine closely you see a 1D wire.

The surprising thing is that both Loll Triangulations QG and Reuter AsymptSafe QG which are extremely different from each other, both got this result. And then, to top it off, Modesto showed that you get this kind of behavior with LQG, which is different from the other two.

Anyway, MTd2 found and posted the abstract for Modesto's new paper:

http://arxiv.org/abs/0905.1665

**Fractal Quantum Space-Time**Leonardo Modesto

(Submitted on 11 May 2009)

"In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase when the energy of a probe scalar field decreases from high to low energy in a fictitious time T. We calculated also the spectral dimension of space-time using the scaling of the area spectrum operator calculated on spin-foam models.

**The main result is that the effective dimension is 2 at the Planck scale and 4 at low energy. This result is consistent with two other approaches to non perturbative quantum gravity: "causal dynamical triangulation" and "asymptotically safe quantum gravity".**We studied the scaling properties of all the possible curvature invariants and we have shown that the singularity problem seems to be solved in the covariant formulation of quantum gravity in terms of spin-foam models. For a particular form of the scaling (or for a particular area operator spectrum) all the curvature invariants are regular also in the Trans-Planckian regime."BTW Modesto includes a picture of that fractal sponge that I was talking about.

You also get that in Loll's SciAm article. That is very good for a nontechnical article. I have the link in my sig. It gives a lot of intuition about ways in which spacetime microgeometry might be different, essentially for Heisenberg or quantum reasons, from the more familiar macro-scale geometry. Something that seems to happen consistently in Loll's computer simulations of universes.

It seems bizarre that this same behavior is coming up in the context of several different approaches to quantum geometry/gravity. Happened in the Horava-Lifgarbagez case too. And Benedetti recenty drew a connection with non-commutative geometry.

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