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A new law of physics is proposed, defined on the cosmological scale but withsignificant implications for the microscale. Motivated by nonlinear dynamicalsystems theory and black-hole thermodynamics, the Invariant Set Postulateproposes that cosmological states of physical reality belong to anon-computable fractal state-space geometry I, invariant under the action ofsome subordinate deterministic causal dynamics. An exploratory analysis is madeof a possible causal realistic framework for quantum physics, based on keyproperties of I. For example, sparseness is used to relate genericcounterfactual states to points not lying on I, thus providing a geometricbasis for the essential contextuality of quantum physics and the role of theabstract Hilbert Space in quantum theory. Also, self-similarity, described in asymbolic setting, provides a possible "realistic" perspective on the essentialrole of complex numbers and quaternions in quantum theory. A new interpretationis given to the standard "mysteries" of quantum theory: superposition,measurement, nonlocality, emergence of classicality and so on. It is proposedthat heterogeneities in the fractal geometry of I are manifestations of thephenomenon of gravity. Since quantum theory is inherently blind to theexistence of such state-space geometries, the analysis here suggests thatattempts to formulate unified theories of physics within a conventionalquantum-theoretic framework are misguided, and that a successful quantum theoryof gravity should unify the causal non-Euclidean geometry of space time withthe atemporal fractal geometry of state space.

The Invariant Set Postulate: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity