  The origin of the uncertainty inherent in quantum measurements has been
discussed since quantum theory's inception, but to date the source of the
indeterminacy of measurements performed at an angle with respect to a quantum
state's preparation is unknown. Here I propose that quantum uncertainty is a
manifestation of the indeterminism inherent in mathematical logic. By
explicitly constructing pairs of classical Turing machines that write into each
others' program space, I show that the joint state of such a pair is
determined, while the state of the individual machine is not, precisely as in
quantum measurement. In particular, the eigenstate of the individual machines
are undefined, but they appear to be superpositions of classical states, albeit
with vanishing eigenvalue. Because these "classically entangled" Turing
machines essentially implement undecidable "halting problems", this
construction suggests that the inevitable randomness that results when
interrogating such machines about their state is precisely the randomness
inherent in the bits of Chaitin's halting probability.

Quantum Physics;Formal Languages and Automata Theory