{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T02:25:35Z","timestamp":1791167135715,"version":"4.1.0"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,11,19]],"date-time":"2015-11-19T00:00:00Z","timestamp":1447891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FP7-PEOPLE-2010-IRSES","award":["RANPHYS"],"award-info":[{"award-number":["RANPHYS"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>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 \u201crelativised\u201d 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\u2013Specker-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.<\/jats:p>","DOI":"10.3390\/info6040773","type":"journal-article","created":{"date-parts":[[2015,11,24]],"date-time":"2015-11-24T01:57:02Z","timestamp":1448330222000},"page":"773-789","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Non-Probabilistic Model of Relativised Predictability in Physics"],"prefix":"10.3390","volume":"6","author":[{"given":"Alastair","family":"Abbott","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"},{"name":"Centre Cavaill\u00e8s, R\u00e9publique des Savoirs, USR 3608, CNRS, Coll\u00e8ge de France and \u00c9cole Normale Sup\u00e9rieure, 29 rue d'Ulm, 75005 Paris, France"},{"name":"Institut N\u00e9el, CNRS and Universit\u00e9 Grenoble Alpes, 38042 Grenoble Cedex 9, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8711-6799","authenticated-orcid":false,"given":"Cristian","family":"Calude","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-2802","authenticated-orcid":false,"given":"Karl","family":"Svozil","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"},{"name":"Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10\/136, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1038\/438743a","article-title":"The message of the quantum","volume":"438","author":"Zeilinger","year":"2005","journal-title":"Nature"},{"key":"ref_2","unstructured":"Zander, J., and Mosterman, P.J. (2013). Computation for Humanity: Information Technology to Advance Society, CRC Press."},{"key":"ref_3","first-page":"595","article-title":"Optical quantum random number generator","volume":"47","author":"Stefanov","year":"2000","journal-title":"J. Mod. Opt."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1512\/iumj.1968.17.17004","article-title":"The problem of hidden variables in quantum mechanics","volume":"17","author":"Kochen","year":"1967","journal-title":"J. Math. Mech. (Now Indiana Univ. Math. J.)"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1103\/RevModPhys.38.447","article-title":"On the problem of hidden variables in quantum mechanics","volume":"38","author":"Bell","year":"1966","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1038\/nphys1734","article-title":"The uncertainty principle in the presence of quantum memory","volume":"6","author":"Berta","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"031109","DOI":"10.1063\/1.2961000","article-title":"A high speed, postprocessing free, quantum random number generator","volume":"93","author":"Dynes","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/978-3-319-23534-9_4","article-title":"On the unpredictability of individual quantum measurement outcomes","volume":"Volume 9300","author":"Beklemishev","year":"2015","journal-title":"Fields of Logic and Computation II\u2014Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1093\/bjps\/I.2.117","article-title":"Indeterminism in quantum physics and in classical physics I","volume":"1","author":"Popper","year":"1950","journal-title":"Br. J. Philos. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1016\/j.physd.2008.03.040","article-title":"Physical limits of inference","volume":"237","author":"Wolpert","year":"2008","journal-title":"Phys. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1093\/bjps\/axi138","article-title":"Randomness is unpredictability","volume":"56","author":"Eagle","year":"2005","journal-title":"Br. J. Philos. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1093\/bjps\/axn053","article-title":"What are the new implications of chaos for unpredictability?","volume":"60","author":"Werndl","year":"2009","journal-title":"Br. J. Philos. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1103\/PhysRev.47.777","article-title":"Can quantum-mechanical description of physical reality be considered complete?","volume":"47","author":"Einstein","year":"1935","journal-title":"Phys. Rev."},{"key":"ref_14","unstructured":"Zalta, E.N. (2008). The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab, Stanford University. [Fall 2008 ed.]."},{"key":"ref_15","unstructured":"Cooper, S., and Sorbi, A. (2008). Computability in Context: Computation and Logic in the Real World, Imperial College Press\/World Scientific. Chapter 7."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.ic.2008.06.006","article-title":"Semiclassical analysis and sensitivity to initial conditions","volume":"207","author":"Paul","year":"2009","journal-title":"Inf. Comput."},{"key":"ref_17","unstructured":"Devaney, R.L. (1989). An Introduction to Chaotic Dynamical Systems, Addison-Wesley. [2nd ed.]."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1038\/nature09008","article-title":"Random numbers certified by Bell\u2019s theorem","volume":"464","author":"Pironio","year":"2010","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","article-title":"Quantum cryptography","volume":"74","author":"Gisin","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1023\/A:1018820410908","article-title":"A Foundational principle for quantum mechanics","volume":"29","author":"Zeilinger","year":"1999","journal-title":"Found. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"062109","DOI":"10.1103\/PhysRevA.86.062109","article-title":"Strong Kochen\u2013Specker theorem and incomputability of quantum randomness","volume":"86","author":"Abbott","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102201","DOI":"10.1063\/1.4931658","article-title":"A variant of the Kochen\u2013Specker theorem localising value indefiniteness","volume":"56","author":"Abbott","year":"2015","journal-title":"J. Math. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1063\/1.532334","article-title":"Infinite and finite Gleason\u2019s theorems and the logic of indeterminacy","volume":"39","author":"Pitowsky","year":"1998","journal-title":"J. Math. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"022102","DOI":"10.1103\/PhysRevA.85.022102","article-title":"Nonlocality with less complementarity","volume":"85","author":"Fritz","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1007\/BF01889696","article-title":"Generalized urn models","volume":"20","author":"Wright","year":"1990","journal-title":"Found. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10773-005-7052-0","article-title":"Logical equivalence between generalized urn models and finite automata","volume":"44","author":"Svozil","year":"2005","journal-title":"Int. J. Theor. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Fl\u00fcgge, S. (1958). Handbuch der Physik. Band V, Teil 1. Prinzipien der Quantentheorie I, Springer. (in German).","DOI":"10.1007\/978-3-642-80539-4"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/BF01397280","article-title":"\u00dcber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik","volume":"43","author":"Heisenberg","year":"1927","journal-title":"Zeitschrift f\u00fcr Physik"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"042111","DOI":"10.1063\/1.4871444","article-title":"Measurement uncertainty relations","volume":"55","author":"Busch","year":"2014","journal-title":"J. Math. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1038\/498419a","article-title":"Proof mooted for quantum uncertainty","volume":"498","author":"Cowen","year":"2013","journal-title":"Nat. News"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"100404","DOI":"10.1103\/PhysRevLett.109.100404","article-title":"Violation of Heisenberg\u2019s measurement-disturbance relationship by weak measurements","volume":"109","author":"Rozema","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1103\/PhysRev.34.163","article-title":"The uncertainty principle","volume":"34","author":"Robertson","year":"1929","journal-title":"Phys. Rev."},{"key":"ref_33","unstructured":"Popper, K.R. (1992). Quantum Theory and the Schism in Physics, Routledge."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"28","DOI":"10.2307\/2270580","article-title":"Limiting recursion","volume":"30","author":"Gold","year":"1965","journal-title":"J. Symb. Log."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1103\/PhysRev.85.166","article-title":"A suggested interpretation of the quantum theory in terms of \u201chidden\u201d variables. I","volume":"85","author":"Bohm","year":"1952","journal-title":"Phys. Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1103\/PhysRev.85.180","article-title":"A suggested interpretation of the quantum theory in terms of \u201chidden\u201d variables. II","volume":"85","author":"Bohm","year":"1952","journal-title":"Phys. Rev."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/6\/4\/773\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:52:24Z","timestamp":1760215944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/6\/4\/773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,19]]},"references-count":36,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["info6040773"],"URL":"https:\/\/doi.org\/10.3390\/info6040773","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,19]]}}}