Graph explorer

Invariant Set Theory

Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$ is treated as a deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. In this approach, the geometry of $I_U$, and not a set of differential evolution equations in space-time $\mathcal M_U$, provides the most primitive description of the laws of physics. As such, IST is non-classical. The geometry of $I_U$ is based on Cantor sets of space-time trajectories in state space, homeomorphic to the algebraic set of $p$-adic integers, for large but finite $p$. In IST, the non-commutativity of position and momentum observables arises from number theory - in particular the non-commensurateness of $ϕ$ and $\cos ϕ$. The complex Hilbert Space and the relativistic Dirac Equation respectively are shown to describe $I_U$, and evolution on $I_U$, in the singular limit of IST at $p=\infty$; particle properties such as de Broglie relationships arise from the helical geometry of trajectories on $I_U$ in