kev said:
Marcus,
I wouldn't mind seeing those links you mentioned,..
Sure, for Ambjorn and Loll the two recent papers are
want to join me in studying up on CDT in early 2008 then the articles to print off so you have hardcopy to scribble are:
http://arxiv.org/abs/0711.0273 (21 pages)
The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
"Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical approximation scheme, and produces robust results, which go beyond showing mere internal consistency of the formalism? The answer is a resounding yes: it is the attempt to construct a nonperturbative theory of quantum gravity, valid on all scales, with the technique of so-called Causal Dynamical Triangulations. Despite its conceptual simplicity, the results obtained up to now are far from trivial. Most remarkable at this stage is perhaps the fully dynamical emergence of a classical background (and solution to the Einstein equations) from a nonperturbative sum over geometries, without putting in any preferred geometric background at the outset. In addition, there is concrete evidence for the presence of a fractal spacetime foam on Planckian distance scales. The availability of a computational framework provides built-in reality checks of the approach, whose importance can hardly be overestimated."
http://arxiv.org/abs/0712.2485 (10 pages)
Planckian Birth of the Quantum de Sitter Universe
"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."
marcus said:
Ambjorn and Loll's computer models are all of that type. they run sims of quantum universes that come into existence, grow, shrink, and disappear according to some simple rules. They use S3 spatial sections. ...
Ashtekar group's computer models, many of them, are also of that type. that's where they replace the cosmological singularity with a bounce----a prior universe which is spatially a "bumpy" threesphere collapses to Planck density and re-expands. They use S3 spatial sections. ...
these are experimental quantum cosmology modeling----I'm not saying the real universe spatial topology is S3 because we don't know---I'm saying what some leading model-builders do.
I'll get a link to some Ashtekar et al work.
http://arxiv.org/abs/gr-qc/0612104
Loop quantum cosmology of k=1 FRW models
Abhay Ashtekar et al
(Submitted on 18 Dec 2006)
In this paper they do not put in the effect of a postive cosmological constant, so the universes eventually collapse. that wouldn't have to happen----you could have a contracting phase, a bounce, and then an expanding phase that went on expanding indefinitely. k=1 means the case with space looking like S
3
FRW means Friedmann Robertson Walker----the prevailing model in cosmology which has various flavors depending on what parameters you put in.
With technical papers there is usually an understandable non-technical introduction section and conclusions section. Not to worry about understanding the whole paper. Just get what you can out of it. And this is just to get a sample of people doing computer models
But I favour 4 macro spatial + Loads o other macros not relevant to us but take no notice of me on that 1 !