On the relationship between Hamiltonian chaos and classical gravity
Abstract
It is known that Hamiltonian equations of motion for lowdimensional chaotic systems are typically formulated using fractional derivatives. The evolution of such systems is governed by the fractional diffusion equation. We confirm, in this context, that the dynamics of a Brownian particle driven by pathdependent random fluctuations evolves towards Hamiltonian chaos and fractional diffusion. The corresponding motion of the particle has a timedependent and nowhere vanishing acceleration. Invoking the equivalence principle of General Relativity leads to the conclusion that fractional diffusion is locally equivalent to a transient gravitational field. It is shown that gravity becomes renormalizable as Newton's constant acquires a positive mass dimension.
 Publication:

APS Four Corners Section Meeting Abstracts
 Pub Date:
 October 2003
 Bibcode:
 2003APS..4CFS10022G