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Information 2015, 6(4), 773-789; doi:10.3390/info6040773

A Non-Probabilistic Model of Relativised Predictability in Physics

1
Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
2
Centre Cavaillès, République des Savoirs, USR 3608, CNRS, Collège de France and École Normale Supérieure, 29 rue d'Ulm, 75005 Paris, France
3
Institut Néel, CNRS and Université Grenoble Alpes, 38042 Grenoble Cedex 9, France
4
Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria
*
Author to whom correspondence should be addressed.
Academic Editors: Mark Burgin and Wolfgang Hofkirchner
Received: 30 September 2015 / Accepted: 12 November 2015 / Published: 19 November 2015
(This article belongs to the Special Issue Selected Papers from the ISIS Summit Vienna 2015)
View Full-Text   |   Download PDF [211 KB, uploaded 19 November 2015]

Abstract

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. View Full-Text
Keywords: prediction; unpredictability; randomness; complementarity prediction; unpredictability; randomness; complementarity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Abbott, A.A.; Calude, C.S.; Svozil, K. A Non-Probabilistic Model of Relativised Predictability in Physics. Information 2015, 6, 773-789.

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