  A new law of physics is proposed, defined on the cosmological scale but with
significant implications for the microscale. Motivated by nonlinear dynamical
systems theory and black-hole thermodynamics, the Invariant Set Postulate
proposes that cosmological states of physical reality belong to a
non-computable fractal state-space geometry I, invariant under the action of
some subordinate deterministic causal dynamics. An exploratory analysis is made
of a possible causal realistic framework for quantum physics, based on key
properties of I. For example, sparseness is used to relate generic
counterfactual states to points not lying on I, thus providing a geometric
basis for the essential contextuality of quantum physics and the role of the
abstract Hilbert Space in quantum theory. Also, self-similarity, described in a
symbolic setting, provides a possible "realistic" perspective on the essential
role of complex numbers and quaternions in quantum theory. A new interpretation
is given to the standard "mysteries" of quantum theory: superposition,
measurement, nonlocality, emergence of classicality and so on. It is proposed
that heterogeneities in the fractal geometry of I are manifestations of the
phenomenon of gravity. Since quantum theory is inherently blind to the
existence of such state-space geometries, the analysis here suggests that
attempts to formulate unified theories of physics within a conventional
quantum-theoretic framework are misguided, and that a successful quantum theory
of gravity should unify the causal non-Euclidean geometry of space time with
the atemporal fractal geometry of state space.
