Via the amazing John Baez’s Week 222 of “This Week’s Finds in Mathematical Physics” I find this paper “Fractal Spacetime Structure in Asymptotically Safe Gravity” by O. Lauscher, M. Reuter:
Abstract:Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton’s constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.
Hmm..Yet another paper pointing towards a spacetime which is two dimensional at microscopic scales and four dimensional at large scales. Of course I’m told that if they add matter to these theories all hell will break lose. It will be interesting to see what hell looks like.
Dave,
if you are interested in the Reuter et al. approach you should also read Jacques Distler’s comments.
And then you should read my comment to Jacques’ comments
http://wb.homedns.org/tsm/tsm09.html#20051001
(The text contains links to Jacques’ comments.)
I can’t speak to the specific technical proposal of Reuter et al. Jacques Distler doesn’t like it, but I do not share his expertise. The general idea of creating 4 dimensions from 2 dimensions is very exciting. You could call the local 1+1-dimensional entities strings…