Requardt’s papers
Back in 2005, when I started to read more and more papers on quantum gravity, I have found one paper that really interested (and still interests) me a lot, and was the subject of one of my first posts back at my older blog.
- The Continuum Limit of Discrete Geometries, by Manfred Requardt [http://arxiv.org/abs/math-ph/0507017]
It is a well written paper, with lots of interesting mathematics (Gromov’s geometric group theory, random graphs, etc). As far as I know, it has not been much discussed in other blogs.
Recently, Requardt posted another interesting one, which I am presently reading:
- About the Minimal Resolution of Space-Time Grains in Experimental Quantum Gravity, by Manfred Requardt [http://arxiv.org/abs/0807.3619]
Abstract:
We critically analyse and compare various recent thought experiments, performed by Amelino-Camelia, Ng et al., Baez et al., Adler et al., and ourselves, concerning the (thought)experimental accessibility of the Planck scale by space-time measurements. We show that a closer inspection of the working of the measuring devices, by taking their microscopic quantum many-body nature in due account, leads to deeper insights concerning the extreme limits of the precision of space-time measurements. Among other things, we show how certain constraints like e.g. the Schwarzschild constraint can be circumvented and that quantum fluctuations being present in the measuring devices can be reduced by designing more intelligent measuring instruments. Consequences for various phenomenological quantum gravity models are discussed.
I like his writting style and the various points that he covers in his papers with sensible criticism.
August 15, 2008 at 1:44 pm
Hi Christine,
Thanks for pointing out these papers. I haven’t thought much about these issues since Urs and I wrote our paper back in 2004. I just started skimming the first paper and hope to give it more attention, but I was immediately struck by one minor point. It seems that when he defines a graph, it is a “spatial” graph. Urs and I worked with “space-time” graphs, i.e. to move along any edge in any (possibly random) graph requires one tick of a clock. This automatically introduces a causal structure and has many other nice features.
Space-time graphs would possibly impact things like Definition 1.3 regarding connected graphs, which would then become statements about space-like and time-like separated points. Observation 1.4 might be modified to a statement about the number of paths connecting points rather than the length of paths connecting points, etc.
I somehow missed this paper, so thanks again for pointing it out. I’d be interested borrowing some of the ideas presented there and applying them to space-time graphs. The basic ideas seem like they would translate over fairly easily.
Best regards
August 24, 2008 at 5:15 pm
Hi phorgyphynance,
Thanks for your input. Indeed, it appears that he has focused on spatial graphs at this point. I’m not certain how “time” or “dynamics” is considered there, if at all. I still did not get to the end of the paper, though. I’ll take a look.
Would you please provide a link to your paper? Thanks!
Best,
Christine