MTd2 spotted this interesting paper by Florian Conrady (Perimeter postdoc).(adsbygoogle = window.adsbygoogle || []).push({});

To go with this paper the author has provided two animations to watch: MTd2 said: ↑http://arxiv.org/abs/1009.3195

Space as a low-temperature regime of graphs

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Florian Conrady (Perimeter Inst. Theor. Phys.)

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... Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear...

http://www.florianconrady.com/simulations.html

Thesecondone of these two simulations ("Model with 2D interactions") shows the crystalization of a 2D space out of chaos as it cools. There is a helpful description of the simulation there that one can read. Because the actual simulation needed to run for a long time before 2D space actually emerged, what is shown is only the initial 2 minutes of action. Then what has resulted by that time is rotated for inspection, so one can examine. Then there is a pause in the animation while time is speeded up, and the final end result is reached. This final result of the cooling/crystalization is then displayed and rotated for examination.

As I understand it, the process is purely combinatorial and only looks like it is occurring in 3D space because of the presentation software being used. The software is useful since it is easier to visualize the process of links joining when we can see it spatially as "approaching coming together", but there is no surrounding space and so no motion involved in the actual calculation. The only "space" here is what eventually emerges when the links finally get themselves properly connected in a recognizable 2D network.

The "atoms" of the process are single isolated links. At high temperature they appear as a kind of "gas". Like a cloud of random disconnected match-sticks, or toothpicks. Their eventual connections with each other are governed by a Hamiltonian which Conrady has devised.

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# Conrady's animation visualizes chaos cooling and 2D space crystalizing out

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