Hamiltonian Chaos & the Fractal Topology of Spacetime (Part 1)

Abstract

Fractals and multifractals are self-similar structures endowed with continuous dimensions. This tutorial traces the origins of fractal spacetime to the universal features of Hamiltonian chaos, conjectured to develop far above the Fermi scale (v = 246 GeV). A representative signature of Hamiltonian chaos is the fragmentation of phase-space into islands of stability embedded within ergodic layers. Fractal topology of Hamiltonian chaos may account for the multiply connected structure of the large-scale Universe, hinted by recent cosmological data. These observations raise the possibility that gravitational physics and Quantum Field Theory emerge from the chaotic regime of the early Universe.

This is Part 1 of a two-part review article.