Most visual form of quantum GR?

[marcus]

Gen Rel is highly visual---as well as being formulated abstractly.

I don't want to seem to be claiming that a successful quantization will need to be visual as well. If it has a clear rigorous abstract formulation and it works, makes testable predictions etc., that should be enough.

But all the same it's worth asking what approaches are especially visual for you.

what I mean is remember the GR idea that matter shapes space and the shape, in return, guides the flow of matter-----it is a dynamic geometry idea (dynamic just means "changing": the shape of space evolving in response to matter and to its own past history)----so in a quantized theory one might be able to visualize the evolution of a fuzzy, or flickering, shape

or a shape that explores all possible shapes in a jittery way, as a particle explores all possible ways (in a Feynman path integral) of getting from point A to point B.

that is, maybe a quantum Gen Rel can allow us to visualize an uncertain geometry that is, itself, jittering its way from shape A to shape B.

and uncertain matter slurping around in it too all the while, I guess, but let's not bother with that right now

so I'm asking please do not assume that a theory that is more visual is necessarily better than one that is more abstract and nonvisual----but would you say, for example, that Dynamical Triangulations is a bit more vivid than, say SpinFoams, or possibly than Loop?

 

[marcus]

I will give some links to CDT papers (causal dynamical triangulations) that I've been reading this past weekend. there are some more explanatory ones going back to 2000 and 2001 that I should have started with----the 2004 papers assume them.

What is especially visual for me in CDT is the Monte Carlo moves.

You take a spacetime history (done in simplexes to make it discrete but essentially a 4D manifold---a possible evolution of the universe)

and you go all thru it making Monte Carlo moves (with a certain probability) and after a pass, then the whole spacetime geometric development is different

you have this finite list of moves (in 3D it is around 5 moves, in 4D it is more, like 10, I forget how many) and they are ERGODIC in the sense that they explore all the possibilities

a pass thru making moves from this finite list is like SHUFFLING the geometry. like shuffling a deck of cards which if it is a good shuffle will eventually get all possible orderings of the deck.
well here we are not talking about the orderings of anything but about the history of the SHAPE
with the big bang at the beginning and (in this case) a crunch at the end, and lots of different expansion and contraction behavior in between.

so these montecarlo moves shuffle the shape and help you get a random shape or a random spacetime history.
then they measure things about it and run it thousands of times on the computer and average things up.

I had better get a few links, in case anyone wants to look. But I think
many people at PF already have seen some of the CDT computergraphic output.

 

[marcus]

I don't have time to edit this right now. this is just copy-paste from the Arxiv list of Ambjorn papers about CDT.
I deleted a couple of short ones about CDT from around 2002.
I haven't looked at all of these.
It is in reverse chronol. order. You have to go down the list a ways to find the articles with more introductory expository treatment.
I will highlight a few of those.

there is no clean exposition yet the early papers, although they have stuff essential for understanding the recent, 2004, ones, also have
stuff where they are exploring alternatives that didnt work!

Somebody would have to go thru and pull out sections of the earlier papers and cobble together a kind of introductory reader consisting of fragments

1. http://arxiv.org/hep-th/0411152
Title: Semiclassical Universe from First Principles
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: 15 pages, 4 figures*

5. http://arxiv.org/hep-th/0404156
Title: Emergence of a 4D World from Causal Quantum Gravity
Authors: J. Ambjorn (1 and 3), J. Jurkiewicz (2), R. Loll (3) ((1) Niels Bohr Institute, Copenhagen, (2) Jagellonian University, Krakow, (3) Spinoza Institute, Utrecht)
Comments: 11 pages, 3 figures; some short clarifying comments added; final version to appear in Phys. Rev. Lett
Journal-ref: Phys.Rev.Lett. 93 (2004) 131301

10. http://arxiv.org/hep-th/0307263
Title: Renormalization of 3d quantum gravity from matrix models
Authors: J. Ambjorn (NBI, Copenhagen), J. Jurkiewicz (U. Krakow), R. Loll (Spinoza Inst. and U. Utrecht)
Comments: 14 pages, 3 figures
Journal-ref: Phys.Lett. B581 (2004) 255-262

http://arxiv.org/hep-th/0201104
Title: A Lorentzian cure for Euclidean troubles
Authors: J. Ambjorn, A. Dasgupta, J. Jurkiewicz, R. Loll

15. http://arxiv.org/gr-qc/0201028
Title: Simplicial Euclidean and Lorentzian Quantum Gravity
Authors: J. Ambjorn
Comments: 23 pages, 4 eps figures, Plenary talk GR16

16. http://arxiv.org/hep-lat/0201013
Title: 3d Lorentzian, Dynamically Triangulated Quantum Gravity
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: Lattice2001(surface)
Journal-ref: Nucl.Phys.Proc.Suppl. 106 (2002) 980-982

19. http://arxiv.org/hep-th/0105267
Title: Dynamically Triangulating Lorentzian Quantum Gravity
Authors: J. Ambjorn (NBI, Copenhagen), J. Jurkiewicz (U. Krakow), R. Loll (AEI, Golm)
Comments: 41 pages, 14 figures
Journal-ref: Nucl.Phys. B610 (2001) 347-382

24. http://arxiv.org/hep-th/0011276
Title: Non-perturbative 3d Lorentzian Quantum Gravity
Authors: J. Ambjorn (NBI, Copenhagen), J. Jurkiewicz (U. Krakow), R. Loll (AEI, Golm)
Comments: 35 pages, 17 figures, final version, to appear in Phys. Rev. D (some clarifying comments and some references added)
Journal-ref: Phys.Rev. D64 (2001) 044011

http://arxiv.org/hep-lat/0011055
Title: Computer Simulations of 3d Lorentzian Quantum Gravity
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: 4 pages, contribution to Lattice 2000 (Gravity and Matrix Models), typos corrected
Journal-ref: Nucl.Phys.Proc.Suppl. 94 (2001) 689-692

31. http://arxiv.org/hep-th/0002050
Title: A non-perturbative Lorentzian path integral for gravity
Authors: J. Ambjorn (Niels Bohr Institute), J. Jurkiewicz (Jagellonian Univ.), R. Loll (Albert-Einstein-Institut)
Comments: 11 pages, LaTeX, improved discussion of reflection positivity, conclusions unchanged, references updated
Journal-ref: Phys.Rev.Lett. 85 (2000) 924-927

33. http://arxiv.org/hep-th/0001124
Title: Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: 69 pages, 16 figures, references added

34. http://arxiv.org/hep-th/9912267
Title: On the relation between Euclidean and Lorentzian 2D quantum gravity
Authors: J. Ambjorn, J. Correia, C. Kristjansen (NBI), R. Loll (AEI)
Comments: 12 pages, 2 figures
Journal-ref: Phys.Lett. B475 (2000) 24-32

36. http://arxiv.org/hep-th/9910232
Title: Making the gravitational path integral more Lorentzian, or: Life beyond Liouville gravity
Authors: R. Loll (Albert-Einstein-Institut, MPI), J. Ambjorn (Niels Bohr Institute), K.N. Anagnostopoulos (Univ. of Crete)
Comments: 4 pages, 2 figures (postscript), uses espcrc2.sty
Journal-ref: Nucl.Phys.Proc.Suppl. 88 (2000) 241-244

I need to edit this some more, have to go now.
There is a point of studying #24 where they explain how they do it in 3D, that is 2+1D instead of the full 3+1D,
because there are fewer montecarlo moves and they are easier to visualize and the whole thing is simpler but analogous to the way it is in 4D.

 

[Demystifier]

For me, the most visual form of quantum GR is the Bohmian interpretation of Wheeler-DeWitt equation. Why WDW? Because it works with metric, which is a quite visual thing. Why Bohmian? Because it kinematically looks just like classical gravity: there is a unique and objective deterministically evolving space-time geometry. In particular, there is no problem of time there: the state does not depend on time, but metric does.

 

[william donnelly]

I would say the most visual is the category theoretic approach advocated by John Baez, particularly in his quantum quandaries - http://math.ucr.edu/home/baez/quantum/. In the quantum gravity seminars of past years he makes many non-intuitive features of quantum mechanics clear by providing "picture proofs". It doesn't get more visual than that.

It is also closely related to the "general boundary" approach of Robert Oeckl, which is also TQFT-inspired - http://arxiv.org/abs/hep-th/0306025 A "general boundary" formulation for quantum mechanics and quantum gravity. I like this one because it retains all the nice background-independent structure of TQFTs but has an obvious connection to ordinary QFT on a fixed background.