On the Unpredictability of Individual Quantum Measurement Outcomes

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.