  A realistic measurement-free theory for the quantum physics of multiple
qubits is proposed. This theory is based on a symbolic representation of a
fractal state-space geometry which is invariant under the action of
deterministic and locally causal dynamics. This symbolic representation is
constructed from self-similar families of quaternionic operators. Using
number-theoretic properties of the cosine function, the statistical properties
of the symbolic representation of the invariant set are shown to be consistent
with the contextual requirements of the Kochen-Specker theorem, are not
constrained by Bell inequalities, and mirror the statistics of entangled
qubits. These number-theoretic properties in turn reflect the sparseness of the
invariant set in state space, and relate to the metaphysical notion of
counterfactual incompleteness. Using the concept of probability, the complex
Hilbert Space can be considered the completion of this symbolic representation
into the state space continuum. As a result, it is proposed that the complex
Hilbert Space should merely be considered a computational convenience in the
light of the algorithmic intractability of the invariant set geometry, and
consequently the superposed state should not be considered a fundamental aspect
of physical theory. The physical basis for the proposed theory is relativistic
gravity; for example the symbols used to describe the invariant set themselves
label gravitationally distinct cosmological space-times. This implies that the
very notion of a `quantum theory of gravity' may be profoundly misguided -
erroneously putting the quantum cart before the gravitational horse. Here some
elements of an alternative `gravitational theory of the quantum' are proposed,
based on a deterministic and locally causal theory of gravity which extends
general relativity by being geometric in both space-time and state space.
