Abstract:
We develop a general, non-probabilistic model of prediction which is suitable for assessing the
(un)predictability of individual physical events. We use this model to provide, for the first time, a rigorous
proof of the unpredictability of a class of individual quantum measurement outcomes, a well-known
quantum attribute postulated or claimed for a long time.
We prove that quantum indeterminism—formally modelled as value indefiniteness—-is incompatible
with the supposition of predictability: value indefinite observables are unpredictable. The proof makes
essential use of a strengthened form of the Kochen-Specker theorem proven previously to identify value
indefinite observables. As a result, quantum unpredictability, like the Kochen-Specker theorem, relies on
three assumptions: compatibility with quantum mechanical predictions, non-contextuality, and the value
definiteness of observables corresponding to the preparation basis of a quantum state.
Finally, quantum unpredictability is used to prove that quantum randomness is "maximally incomputable"
and to discuss a real model of hypercomputation whose computational power has yet to be determined. The
paper ends with a further open problem.