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marcus

Science Advisor

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Hal Haggard's ILQGS talk should be quite interesting.

The plan is to have the slides PDF uploaded sometime Monday at

http://bohr.physics.berkeley.edu/hal/pubs/Talks/ILQGS2013/haggard021213.pdf

It's potentially helpful to let people look at the slides a day in advance of the Tuesday 12 February talk so they can get used to any unfamiliar ideas.

I suppose there could be enhanced questions from people who have had the opportunity to think about the topic ahead of time.

It's important to the UV finiteness of LQG that the volume operator has a smallest positive eigenvalue. In other words there is a "gap" in the spectrum of volume between measuring zero volume and the smallest nonzero volume measurement. The question naturally arises whether Nature is actually this way! Do we have some evidence---some indication say from classical physics---that we are prevented from measuring volume below a certain point? Like in a hydrogen atom you don't have a lower energy orbital, below a certain level.

Curiously, there is some indication from classical physics. Consider a pentahedron whose shape is "oscillating" all over the place---stretching in this direction, shrinking in that direction, skewing this way and that, but staying the same volume. A bit like a cartoon creature expressing excitement---animated movie artists sometimes draw sequences like that. It turns out, when you construct the phase space and set up a dynamical system for the shape-fluctuating pentahedron, that it is chaotic.

A small change in initial conditions can result in a drastic change of shape-trajectory. This is somewhat unintuitive, it does not happen with simpler shapes like the tetrahedron.

This is classical evidence that volume can be hard to get your hands on. Hard to nail down. It was interesting to see that Berndt Müller, a QFT physicist at Duke, recently got interested in pentahedron chaos and put out a paper. It appears to confirm and elaborate on some earlier results by Haggard.

Some references:

http://arxiv.org/abs/1211.7311

Pentahedral volume, chaos, and quantum gravity

http://arxiv.org/abs/1212.1930 (Müller et al paper)

A "Helium Atom" of Space: Dynamical Instability of the Isochoric Pentahedron

http://arxiv.org/abs/1208.2228 (Bianchi and Haggard)

Bohr-Sommerfeld Quantization of Space

The plan is to have the slides PDF uploaded sometime Monday at

http://bohr.physics.berkeley.edu/hal/pubs/Talks/ILQGS2013/haggard021213.pdf

It's potentially helpful to let people look at the slides a day in advance of the Tuesday 12 February talk so they can get used to any unfamiliar ideas.

I suppose there could be enhanced questions from people who have had the opportunity to think about the topic ahead of time.

It's important to the UV finiteness of LQG that the volume operator has a smallest positive eigenvalue. In other words there is a "gap" in the spectrum of volume between measuring zero volume and the smallest nonzero volume measurement. The question naturally arises whether Nature is actually this way! Do we have some evidence---some indication say from classical physics---that we are prevented from measuring volume below a certain point? Like in a hydrogen atom you don't have a lower energy orbital, below a certain level.

Curiously, there is some indication from classical physics. Consider a pentahedron whose shape is "oscillating" all over the place---stretching in this direction, shrinking in that direction, skewing this way and that, but staying the same volume. A bit like a cartoon creature expressing excitement---animated movie artists sometimes draw sequences like that. It turns out, when you construct the phase space and set up a dynamical system for the shape-fluctuating pentahedron, that it is chaotic.

A small change in initial conditions can result in a drastic change of shape-trajectory. This is somewhat unintuitive, it does not happen with simpler shapes like the tetrahedron.

This is classical evidence that volume can be hard to get your hands on. Hard to nail down. It was interesting to see that Berndt Müller, a QFT physicist at Duke, recently got interested in pentahedron chaos and put out a paper. It appears to confirm and elaborate on some earlier results by Haggard.

Some references:

http://arxiv.org/abs/1211.7311

Pentahedral volume, chaos, and quantum gravity

http://arxiv.org/abs/1212.1930 (Müller et al paper)

A "Helium Atom" of Space: Dynamical Instability of the Isochoric Pentahedron

http://arxiv.org/abs/1208.2228 (Bianchi and Haggard)

Bohr-Sommerfeld Quantization of Space

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