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marcus

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Steve Carlip gave the first talk of a weeklong conference on Planck Scale physics that just ended July 4 (yesterday). The pdf of his slides is online.

We here at PF have been discussing since 2005 from time to time the odd coincidence that several very different approaches to quantizing GR give a spacetime of less than 4D at small scale. As you zoom in, and measure things like areas and volumes at smaller and smaller scale you find in these various quantized-geometry models that the geometry is behaving as if it was fractional dimensioned less than 4. Going continuously down to 3.9 and 3.8 and 3.7 ...and finally approaching 2D.

Dimensionality does not have to be a whole number, like exactly 2, or exactly 3. There are easy ways to measure the dimensionality of whatever space you are in----like by comparing radius with volume to see how the volume grows---or by conducting a random walk diffusion and seeing of fast diffusion happens. And these easy ways to measure dimension experimentally can give non-integer answers. And there are many well-known examples of spaces that you can construct that have non-whole-number dimension. Renate Loll had a SciAm article about this, with nice illustrations, and saying why this could be how it works at Planck Scale. The link is in my signature if anyone wants.

So from our point of view it's great that Steve Carlip is focusing some attention on this strange coincidence. Why should the different approaches of Renate Loll, Martin Reuter, Petr Horava, and even also Loop QG, why should these very different models all arrive at the bizarre

**spontaneous dimensional reduction at small scale**(that is the title of Carlip's talk.)

Carlip is prominent and a widely recognized expert so IMHO it nice he is thinking about this.

Here is the whole schedule of the Planck Scale conference which now has online PDF for many of the talks for the whole week

http://www.ift.uni.wroc.pl/~planckscale/index.html?page=timetable