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marcus

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## Main Question or Discussion Point

Loll will deliver three one-hour talks at Oporto in mid July Here's the abstract

Renate Loll, Quantum Gravity from Causal Dynamical Triangulations

Abstract:

I discuss motivation, implementation and results of the nonperturbative approach to quantum gravity based on Causal Dynamical Triangulations, including the recent reconstruction of de Sitter space from quantum fluctuations.

A published version of some of what she will be talking about is here:

http://arxiv.org/abs/0712.2485

J. Ambjorn, A. Gorlich, J. Jurkiewicz, R. Loll

published in Physical Review Letters, 7 March 2008

10 pages, 3 figures

(Submitted on 17 Dec 2007)

"We show that the quantum universe emerging from a nonperturbative, Lorentzian

==========================

The sum-over-geometries is analogous to a Feynman path integral. The universe takes a path through a regularized collection of possible spatial geometries. Each path is a possible spacetime. In effect integrating to get the "average" path gives de Sitter spacetime. That is an oversimplification but the key idea is that it picks out de Sitter as a special distinguished background geometry---that was not put in by hand at the beginning.

what one puts in at the beginning are local dynamics of microscopic geometry. there is no guarantee that any recognizable global spacetime will result, or even that you will get something four dimensional. But something recognizable does indeed come out of the path integral. So there is a suggestion of uniqueness here.

============================

Chamseddine will also be giving three one-hour talks at Oporto: on research hinting at the uniqueness of the standard particle model. I am not announcing this. (I already announced the Oporto Meeting lineup.) I am initiating a discussion, or at least proposing one. Hopefully people will find these two matters of interest. Here is the Oporto minicourse abstract:

Ali Chamseddine, Classification of discrete noncommutative geometries and the uniqueness of the standard model

Abstract:

Assuming that space-time is a product of a continuous four-dimensional manifold times a discrete space F, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors. Remarkably we find that the noncommutative geometry of the standard model results almost uniquely, with all the necessary details. In particular we prove that the number of fermions per generation is 16, the square of an even integer. The spectral action of this geometry is constructed, and the model is analyzed.

=====================

This corresponds to a published paper also:

http://arxiv.org/abs/0706.3688

Ali H. Chamseddine, Alain Connes

13 pages

(Submitted on 25 Jun 2007)

"The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation:

Both these lines of research, highlighted by the Oporto Meeting, are clearly driving towards establishing a kind of uniqueness. In terms of such and such a theory (CDT, NCG) the world can only be one way, the way we see it. That is the general idea or thrust---naturally there are qualifications and stuff to be worked out, but that's where both are heading.

I want to do some explication and I'm going to start with a few quotes from Loll's paper.

Renate Loll, Quantum Gravity from Causal Dynamical Triangulations

Abstract:

I discuss motivation, implementation and results of the nonperturbative approach to quantum gravity based on Causal Dynamical Triangulations, including the recent reconstruction of de Sitter space from quantum fluctuations.

A published version of some of what she will be talking about is here:

http://arxiv.org/abs/0712.2485

**Planckian Birth of the Quantum de Sitter Universe**J. Ambjorn, A. Gorlich, J. Jurkiewicz, R. Loll

published in Physical Review Letters, 7 March 2008

10 pages, 3 figures

(Submitted on 17 Dec 2007)

"We show that the quantum universe emerging from a nonperturbative, Lorentzian

**sum-over-geometries**can be described with high accuracy by a four-dimensional**de Sitter spacetime**. By a scaling analysis involving Newton's constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly,**the measured quantum fluctuations around the de Sitter universe**in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal dynamical triangulations."==========================

The sum-over-geometries is analogous to a Feynman path integral. The universe takes a path through a regularized collection of possible spatial geometries. Each path is a possible spacetime. In effect integrating to get the "average" path gives de Sitter spacetime. That is an oversimplification but the key idea is that it picks out de Sitter as a special distinguished background geometry---that was not put in by hand at the beginning.

what one puts in at the beginning are local dynamics of microscopic geometry. there is no guarantee that any recognizable global spacetime will result, or even that you will get something four dimensional. But something recognizable does indeed come out of the path integral. So there is a suggestion of uniqueness here.

============================

Chamseddine will also be giving three one-hour talks at Oporto: on research hinting at the uniqueness of the standard particle model. I am not announcing this. (I already announced the Oporto Meeting lineup.) I am initiating a discussion, or at least proposing one. Hopefully people will find these two matters of interest. Here is the Oporto minicourse abstract:

Ali Chamseddine, Classification of discrete noncommutative geometries and the uniqueness of the standard model

Abstract:

Assuming that space-time is a product of a continuous four-dimensional manifold times a discrete space F, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors. Remarkably we find that the noncommutative geometry of the standard model results almost uniquely, with all the necessary details. In particular we prove that the number of fermions per generation is 16, the square of an even integer. The spectral action of this geometry is constructed, and the model is analyzed.

=====================

This corresponds to a published paper also:

http://arxiv.org/abs/0706.3688

**Why the Standard Model**Ali H. Chamseddine, Alain Connes

13 pages

(Submitted on 25 Jun 2007)

"The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation:

**space-time has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F.**...Under an additional hypothesis of quaternion linearity,**the geometry which reproduces the Standard Model is singled out**(and one gets k=4)with the correct quantum numbers for all fields. The spectral action applied to**the product MxF delivers the full Standard Model,with neutrino mixing, coupled to gravity, and makes predictions(the number of generations is still an input).**"Both these lines of research, highlighted by the Oporto Meeting, are clearly driving towards establishing a kind of uniqueness. In terms of such and such a theory (CDT, NCG) the world can only be one way, the way we see it. That is the general idea or thrust---naturally there are qualifications and stuff to be worked out, but that's where both are heading.

I want to do some explication and I'm going to start with a few quotes from Loll's paper.

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