Saturday, April 04, 2009

Chaos Incarnate

Could chaos be the root of reality? If Dario Benedetti is right, the unification of Quantum and Relativity may be at hand using Chaos as the weapon of choice.

“It is an old idea in that at short scales spacetime might appear foamy, fuzzy, fractal or similar,” Benedetti told “In my work, I suggest that quantum groups are a valid candidate for the description of such a quantum spacetime. Furthermore, computing the spectral dimension, I provide for the first time a link between quantum groups/noncommutative geometries and apparently unrelated approaches to quantum gravity, such as Causal Dynamical Triangulations and Exact Renormalization Group. And establishing links between different topics is often one of the best ways we have to understand such topics.”

In looking at fractals, the action always occurs at the edge, not the center as the edge separates two or more regions with differing properties. Because fractals are self similar and use feedback to drive the 2 1/2 space in stochastic fashion, (when fractals inhabit 2 space, in 3 space, the dimension goes to 3 1/2) the ability to see how chaos unifies quantum and relativity in reasonable fashion is difficult at best. Also, Mandlebrot's fractal (the top image) appears, to me, to be too stiff to handle the kind of transformations envisioned by Benedetti's concept of a fractal universe constantly changing dimension at different scales to encompass the totality of reality in which all things reside. Because nature abhors gradients, the fractals Benedetti may be thinking about, must, IMHO, be fluid enough to deal with nature's unsurpassed ability to eliminate gradients using her two laws of thermodynamics.

Another question to ask is what powers the fractals? Nature is an open system but there must be a "engine" to drive this amazing process. Ah, as Einstein said, "Question everything".

To address the visualization part of the equation, here is Apophysis, a truly innovative program that generates 3D fractals with the kind of transparency and grace akin to nature's as depicted by the image seen below courtesy of RM and Apophysis.

Now if only I could do math, maybe then I could finally understand what the Einstein's of the world are talking about. :)
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