A Non-Probabilistic Model of Relativised Predictability in Physics

TL;DR

This paper develops a refined, non-probabilistic model of unpredictability in physics, analyzing how quantum phenomena like complementarity and value indefiniteness relate to different degrees of relativised unpredictability.

Contribution

It introduces a more nuanced model of unpredictability that distinguishes between various quantum phenomena and their implications for predictability in physics.

Findings

Quantum complementarity guarantees a weaker form of unpredictability than Kochen-Specker value indefiniteness.

Complementarity allows for the production of computable sequences, unlike value indefiniteness.

The model enables studying different degrees of relativised unpredictability in physical systems.

Abstract

Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed inherent unpredictability of measurement outcomes. In this paper we continue the programme started in [1] developing a general, non-probabilistic model of (un)predictability in physics. We present a more refined model that is capable of studying different degrees of "relativised" unpredictability. This model is based on the ability for an agent, acting via uniform, effective means, to predict correctly and reproducibly the outcome of an experiment using finite information extracted from the environment. We use this model to study further the degree of unpredictability certified by different quantum phenomena, showing that quantum complementarity guarantees a form of relativised unpredictability that is weaker than that guaranteed by Kochen-Specker-type value indefiniteness. We exemplify further the difference between certification by complementarity and value indefiniteness by showing that, unlike value indefiniteness, complementarity is compatible with the production of computable sequences of bits.