Requardt---The Continuum Limit of Discrete Geometries
Christine Dantas has flagged an interesting paper in her blog, one that I didn't know about.
Here is her entry
http://christinedantas.blogspot.com/2005/11/continuum-limit-of-discrete-geometries.html
Here is the paper. It's by someone at Göttingen
http://arxiv.org/abs/math-ph/0507017
The Continuum Limit of Discrete Geometries
Manfred Requardt
29 pages
"In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be constructed from a more primordial and basically discrete underlying substratum, which may behave in a quite erratic and irregular way. We develop such a framework within the category of general metric spaces by combining recent work of our own and ingeneous ideas of Gromov et al, developed in pure mathematics. A central role is played by two core concepts. For one, the notion of intrinsic scaling dimension of a (discrete) space or, in mathematical terms, the growth degree of a metric space at infinity, on the other hand, the concept of a metrical distance between general metric spaces and an appropriate scaling limit (called by us a geometric renormalisation group) performed in this metric space of spaces. In doing this we prove a variety of physically interesting results about the nature of this limit process, properties of the limit space as e.g. what preconditions qualify it as a smooth classical space-time and, in particular, its dimension."
Requardt's work connects to Loll CDT because he is studying metric (non-manifold) structures which are rough enough to have no fixed dimensionality------they can have, say, microscopic 2D but higher at larger scale increasing to, say, macroscopic 4D.
Manfred Requardt has a scary haircut.
But however he writes well----he is a physicist but he can also organize his thoughts into theorems with efficient proofs, like a mathematician---which can be a good way to communicate clearly. At least this is my first impression.
I don't know if I think he is on a good track, it is too early for me to have any guesses, but I see that what he is doing could shed some light on the picture of spacetime growing up from work of both Loll and Reuter
I think Christine is neat because she is an ASTROPHYSICIST who knows about observational tests of QUANTUM GRAVITY (she even lists ten or so papers about this) which is a upcoming field that many people do not even know is starting! But she ALSO knows about something entirely different from the QG phenomenology and testing, namely the still-very-tentative new model of spacetime at a fundamental level, that is shaping up
these are two very different research developments and she is perceptive about both
