On the Origin of Quantum Uncertainty

The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theorys inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum states 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 Chaitins halting probability.