A Non-Probabilistic Model of Relativised Predictability in Physics

Information

Alastair A. Abbott¹  Cristian S. Calude¹  Karl Svozil¹  Mark Burgin² 

[1] Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand; E-Mail:;Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand; E-Mail

关键词: prediction;    unpredictability;    randomness;    complementarity;   

DOI  :  10.3390/info6040773

来源: mdpi

【 摘 要 】

Unpredictability is an important concept throughout physics and plays a central role in quantum information theory. Despite this, little effort has been devoted to studying generalised notions or models of (un)predictability in physics. In this paper, we continue the programme of 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 of 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 the degree of unpredictability certified by different quantum phenomena further, 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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.