The sacred geometry of reality

Thoughts on stochastic quantum physics and the fractal geometry of spacetime.

In Chapter 11 of “Irrational mechanics” I outlined Edward Nelson’s stochastic formulation of quantum mechanics based on “a kind of Brownian motion that agitates all particles of matter.”

I also outlined the related idea, proposed by several scientists and in particular by Laurent Nottale, that spacetime itself is not smooth but fractal, with bumps at all scales, and quantum behavior follows. General relativity lives in a smooth spacetime, but quantum mechanics lives in a rough, fractal, fractured spacetime. A particle bumps into an irregularity in the fractal structure of spacetime and changes course, then it bumps into another irregularity, and in between the two there’s an infinite number of bumps and the particle changes course an infinite number of times.

Surface detail of the Mandelbulb, a solid fractal analogous to the Mandelbrot set. Image from Wikimedia Commons.