Evolving dimensions - the start of something big?

Well, this is interesting. Bee at her Backreaction blog has post explaining (not exactly in layman terms, but you can get the general drift) a big, pretty new, idea in physics that may actually go somewhere:

The idea that space-time might not be higher-dimensional on short distances but instead be lower-dimensional has been around for some while, inspired by results from causal dynamical triangulation. In a paper last year, Anchordoqui et al proposed to examine the possibility of lower dimensionality at small distances for its phenomenology in their paper

Vanishing Dimensions and Planar Events at the LHC
Luis Anchordoqui, De Chang Dai, Malcolm Fairbairn, Greg Landsberg, Dejan Stojkovic
arXiv:1003.5914v2 [hep-ph]

Greg Landsberg gave a talk about this work on our last year's workshop on Experimental Search for Quantum Gravity (recording of the talk here). The basic idea is that the dimensionality of space changes with distance in such a way that it is 3-dimensional on scales we have tested it, lower dimensional on distances shorter than we have probed yet (about 1/1000 of a femtometer) and possibly higher-dimensional on distances larger than we can observe. The picture suggested is that of a (one-dimensional) string being knitted, and the knitted sheet (2-dimensional) being crumpled to a ball (3-dimensional). The authors dubbed this "evolving dimensionality." The merit of having a smaller number of space-like dimensions at small distances or high energies is that it improves the renormalizability of quantum field theories and esp. that of quantum gravity. (In contrast to additional dimensions which actually make the problem worse.)

Sounds interesting. As Bee goes on to note, the idea has a big problem ("lacks a mathematical model for the new fundamental structure and the dynamics of quantum fields in it") but even so makes some (I think) testable predictions.

Now I'll annoy science types by admitting something: my reason for liking the sound of it is that it seems to get us back to a possible "higher dimension". I always thought it a pity that physics lost the 4th big dimension as a place in which locate God and places like heaven and hell. You can always get around that by living in a type of cyber-heaven in the mind of God, like Tipler uses for his Omega Point, but a hyper-dimensional realm has its own nice feel about it too.