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A realistic measurement-free theory for the quantum physics of multiplequbits is proposed. This theory is based on a symbolic representation of afractal state-space geometry which is invariant under the action ofdeterministic and locally causal dynamics. This symbolic representation isconstructed from self-similar families of quaternionic operators. Usingnumber-theoretic properties of the cosine function, the statistical propertiesof the symbolic representation of the invariant set are shown to be consistentwith the contextual requirements of the Kochen-Specker theorem, are notconstrained by Bell inequalities, and mirror the statistics of entangledqubits. These number-theoretic properties in turn reflect the sparseness of theinvariant set in state space, and relate to the metaphysical notion ofcounterfactual incompleteness. Using the concept of probability, the complexHilbert Space can be considered the completion of this symbolic representationinto the state space continuum. As a result, it is proposed that the complexHilbert Space should merely be considered a computational convenience in thelight of the algorithmic intractability of the invariant set geometry, andconsequently the superposed state should not be considered a fundamental aspectof physical theory. The physical basis for the proposed theory is relativisticgravity; for example the symbols used to describe the invariant set themselveslabel gravitationally distinct cosmological space-times. This implies that thevery notion of a `quantum theory of gravity' may be profoundly misguided -erroneously putting the quantum cart before the gravitational horse. Here someelements of an alternative `gravitational theory of the quantum' are proposed,based on a deterministic and locally causal theory of gravity which extendsgeneral relativity by being geometric in both space-time and state space.

Quantum Theory and The Symbolic Dynamics of Invariant Sets: Towards a Gravitational Theory of the Quantum