RE: [asa] Causal Dynamical Triangulations

From: Alexanian, Moorad <alexanian@uncw.edu>
Date: Thu Jul 03 2008 - 14:04:15 EDT

A quantum theory of gravity would have not only to derive the structure of spacetime but also its existence or emergence. Now usually we have a background or a matrix in which we embedded what we are dealing with. What is the space in which the theory uses to describe what exists and concludes with the existence of spacetime?

 
Moorad

________________________________

From: asa-owner@lists.calvin.edu on behalf of George Murphy
Sent: Thu 7/3/2008 1:43 PM
To: Randy Isaac; asa@calvin.edu
Subject: Re: [asa] Causal Dynamical Triangulations

2 comments here, really more on the Sci Am article than on Randy's comments.
 
First, I think it's unfortunate that many discussions of quantum gravity today make it sound as if work on it only began in the 70s. Actually the first work on quantization of gravitation was in (I think) 1932 by Rosenfeld, and in the 50s & 60s there was a great deal of effort by Bergman, Dirac, DeWitt, Feynman, Misner & others directed toward both canonical and covariant quantization of Einstein's theory. While these ran into severe problems (e.g., finding that quantum gravity in a conventional sense is not renormalizable), a good deal still was learned. The most elementary result is the fact that there is in a real sense a lower limit to space-time measurements due to the combined effects of gravitational redshift and the uncertainty principle. I.e., the Planck length isn't just a dimensional artifact. (Smolin's Three Roads to Quantum Gravity makes this mistake, as does the current Sci Am article.
 
Then on a positive note, the approach taken in this article, with space being built up of triangles, has intriguing similarity with Plato's description of the creation of the world in the Timaeus 2400 years ago. Heisenberg's described in his Physics and Beyond the impact that that aspect of Plato's thought had on him in his gymnasium days and it's clear that the ideas of mathematical symmetry in that passage had a powerful influence on his work throughout his career. (I've sometimes described Heisenberg's autobiography as a description of a struggle between Mach and Plato - with Plato finally winning.)
 
Shalom
George
http://web.raex.com/~gmurphy/

        ----- Original Message -----
        From: Randy Isaac <mailto:randyisaac@comcast.net>
        To: asa@calvin.edu
        Sent: Thursday, July 03, 2008 10:57 AM
        Subject: [asa] Causal Dynamical Triangulations

        We'll be traveling in Europe for the next two weeks so I'll be temporarily signing off in a day or two. But before I leave, I wanted to draw your attention to a fascinating article in the July 2008 issue of Scientific American, which some of you may already have read. On page 42, there is an article by Ambjorn, Jurkiewicz and Loll called "The Self-Organizing Quantum Universe."
         
        This article deals with a topic we have periodically addressed on this list, namely the attempts to reconcile quantum theory and the general theory of relativity in a theory of quantum gravity. The most popular approach, favored by most theoretical physicists is string theory which leads to as many as 11 or more dimensions and all sorts of exotic features. It still hasn't had a verifiable prediction and continues to be speculative research. The main alternative is loop quantum gravity which starts by quantizing space in discrete atoms of volume. A third approach called Euclidean quantum gravity was promoted by Stephen Hawking in "A Brief History of Time." It received a lot of attention in the 80's and 90's but ultimately it turned out to be a dead-end street in that it could not accurately describe our own universe. The fourth approach, first suggested by these authors in 1998 and now touted for the public in this article, is a variation of the Euclidean approach with a key!
  additional assumption.
         
        The additional assumption has to do with time and causality and this is why I thought it might be of interest to this group. Hawking's approach did not build in a notion of causality but treated space and time equally. "Because Euclidean universes have no distinct notion of time, they have no structure to put events into a specific order; people living in these universes would not have the words "cause" or "effect" in their vocabulary." In other words, the expectation was that causality would emerge as a property without building it in as an assumption. But it didn't happen.
         
        These authors put causality in from the beginning. "Causality is the principle that events occur in a specific temporal sequence of cause and effect, rather than as a haphazard jumble. In the authors' approach to quantum gravity, the distinction between cause and effect is fundamental to nature, rather than a derived property." The way they do this is that each elemental triangle used as a building block to construct space is connected with an arrow of time pointing from past to future. Adjacent triangles must be synchronized to preserve causality in time. Hence the name of this approach "causal dynamical triangulations."
         
        The authors duly note that this approach has also not produced a verifiable prediction and that much more work is necessary to see if this direction is fruitful. However, I found it intriguing that introducing causality and time as a fundamental parameter had such a dramatic impact on the theoretical constructs of Euclidean quantum gravity, leading toward a reasonable description of space in our universe. If you're interested, I encourage you to read the whole article and its references. What it all means, I have no idea. But it certainly is interesting.
         
        Randy
         
         

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Received on Thu Jul 3 14:04:04 2008

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