New Forms of Quantum Value Indefiniteness Suggest That Incompatible Views on Contexts Are Epistemic

Extensions of the Kochen–Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single context is epistemic. A remark by Gleason about the ad hoc construction of probability measures in Hilbert spaces as a result of the Pythagorean property of vector components is interpreted platonically. Unless there is a total match between preparation and measurement contexts, information about the former from the latter is not ontic, but epistemic. This is corroborated by configurations of observables and contexts with a truth-implies-value indefiniteness property.

[1]  W. Myrvold.  Statistical mechanics and thermodynamics: A Maxwellian view , 2011 .

[2]  Karl Svozil.  Quantum information via state partitions and the context translation principle , 2003 .

[3]  Karl Svozil,et al.  Quantum scholasticism: On quantum contexts, counterfactuals, and the absurdities of quantum omniscience , 2007, Inf. Sci..

[4]  Ron Wright.  Generalized urn models , 1990 .

[5]  Karl Svozil,et al.  Generalized event structures and probabilities , 2015, 1509.03480.

[6]  Murat Ünver,et al.  CZECH TECHNICAL UNIVERSITY IN PRAGUE , 2018 .

[7]  Hong-Yi Su,et al.  Hardy's paradox for high-dimensional systems , 2013, 1308.4468.

[8]  Jean Petitot,et al.  CONSTITUTING OBJECTIVITY The Western Ontario Series in Philosophy of Science , 2009 .

[9]  F. Gonseth,et al.  DIE LOGIK NICHT GLEICHZEITIG ENTSCHEIDBARER AUSSAGEN , 1990 .

[10]  Allen Stairs.  Quantum Logic, Realism, and Value Definiteness , 1983, Philosophy of Science.

[11]  M. Hulliung.  The Republic That Was , 2017 .

[12]  Antony Valentini,et al.  De Broglie-Bohm Pilot-Wave Theory , 2010 .

[13]  Itamar Pitowsky,et al.  Deterministic model of spin and statistics , 1983 .

[14]  Jeffrey K. Uhlmann,et al.  Quantum Computer Science , 2008, Synthesis Lectures on Quantum Computing.

[15]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .

[16]  E. Schrödinger.  Die gegenwärtige Situation in der Quantenmechanik , 2005, Naturwissenschaften.

[17]  Cristian S. Calude,et al.  Value-indefinite observables are almost everywhere , 2013, 1309.7188.

[18]  I. Pitowsky.  The range of quantum probability , 1986 .

[19]  K. Svozil.  Contexts in Quantum, Classical and Partition Logic , 2006, quant-ph/0609209.

[20]  K. Svozil,et al.  Automaton logic , 1996 .

[21]  E. Specker.  DIE LOGIK NICHT GLEICHZEITIG ENTSC HEIDBARER AUSSAGEN , 1960 .

[22]  Karl Svozil,et al.  Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden-variable theories , 2018, Physical Review A.

[23]  Edward F. Moore,et al.  Gedanken-Experiments on Sequential Machines , 1956 .

[24]  M. Scha,et al.  Automaton Partition Logic Versus Quantum Logic , 1994 .

[25]  J A Spiers.  A Survey of Hidden Variables Theories , 1974 .

[26]  A. Zeilinger.  A Foundational Principle for Quantum Mechanics , 1999, Synthese Library.

[27]  Don Howard,et al.  Who Invented the “Copenhagen Interpretation”? A Study in Mythology , 2004, Philosophy of Science.

[28]  Ehud Hrushovski,et al.  Generalizations of Kochen and Specker's theorem and the effectiveness of Gleason's theorem , 2003 .

[29]  Itamar Pitowsky,et al.  Substitution and Truth in Quantum Logic , 1982, Philosophy of Science.

[30]  Karl Svozil,et al.  Non-contextual chocolate balls versus value indefinite quantum cryptography , 2014, Theor. Comput. Sci..

[31]  Rob Clifton,et al.  Getting contextual and nonlocal elements‐of‐reality the easy way , 1993 .

[32]  M. Redhead,et al.  Incompleteness, Nonlocality, and Realism: A Prolegomenon to thePhilosophy of Quantum Mechanics , 1989 .

[33]  G. Bruns.  ORTHOMODULAR LATTICES (London Mathematical Society Monographs, 18) , 1984 .

[34]  Adan Cabello,et al.  No hidden variables proof for two spin 1/2 particles preselected and postselected in unentangled states , 1997, quant-ph/9706016.

[35]  J. Bell.  On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[36]  Cristian S. Calude,et al.  A variant of the Kochen-Specker theorem localising value indefiniteness , 2015, 1503.01985.

[37]  J. Neumann.  Mathematische grundlagen der Quantenmechanik , 1935 .

[39]  Adán Cabello,et al.  A simple proof of the Kochen-Specker theorem , 1994 .

[40]  Georges Chevalier.  Commutators and decompositions of orthomodular lattices , 1989 .

[41]  K. Kreutz-Delgado,et al.  - Finite-Dimensional Vector Spaces , 2018, Physical Components of Tensors.

[42]  L. Hardy,et al.  Nonlocality for two particles without inequalities for almost all entangled states. , 1993, Physical review letters.

[43]  Niels Bohr,et al.  Atomic Theory and the Description of Nature , 1934 .

[44]  B. Tsirelson.  Some results and problems on quan-tum Bell-type inequalities , 1993 .

[45]  D. Meyer.  Finite Precision Measurement Nullifies the Kochen-Specker Theorem , 1999, quant-ph/9905080.

[46]  I. Pitowsky.  Infinite and finite Gleason’s theorems and the logic of indeterminacy , 1998 .

[47]  Itamar Pitowsky.  Quantum Mechanics as a Theory of Probability , 2006 .

[48]  M. Bourennane,et al.  Simple hardy-like proof of quantum contextuality. , 2013, Physical review letters.

[49]  B. Franklin,et al.  Cambridge Texts in the History of Political Thought , 1992 .

[50]  L. Hardy,et al.  Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. , 1992, Physical review letters.

[51]  Karl Svozil,et al.  On generalized probabilities: correlation polytopes for automaton logic and generalized urn models, extensions of quantum mechanics and parameter cheats , 2000 .

[52]  Adán Cabello Quintero.  Pruebas algebraicas de imposibilidad de variables ocultas en mecánica cuántica , 1996 .

[53]  Anatolij Dvurecenskij,et al.  Partition Logics, Orthoalgebras and Automata , 2018, 1806.04271.

[54]  Karl Svozil,et al.  Physical (A)Causality: Determinism, Randomness and Uncaused Events , 2018 .

[55]  F. De Martini,et al.  LADDER PROOF OF NONLOCALITY WITHOUT INEQUALITIES : THEORETICAL AND EXPERIMENTAL RESULTS , 1997 .

[56]  Jeffrey Bub,et al.  Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics , 1990 .

[57]  K. Svozil.  Logical Equivalence Between Generalized Urn Models and Finite Automata , 2002, quant-ph/0209136.

[58]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[59]  Ron Wright.  THE STATE OF THE PENTAGON A NONCLASSICAL EXAMPLE , 1978 .

[60]  K. Svozil.  Staging quantum cryptography with chocolate balls , 2005, physics/0510050.

[61]  Mirko Navara,et al.  The Pasting Constructions for Orthomodular Posets , 1991 .

[62]  Helle Bechmann Johansen.  Comment on ‘‘Getting contextual and nonlocal elements‐of‐reality the easy way,’’ by R. Clifton [Am. J. Phys. 61, 443–447 (1993)] , 1994 .

[63]  Josef Tkadlec.  Greechie Diagrams of Small Quantum Logics with Small State Spaces , 1998 .

[64]  Jan-Åke Larsson,et al.  Pentagrams and Paradoxes , 2009, 0909.4713.

[65]  M. Froissart.  Constructive generalization of Bell’s inequalities , 1981 .

[66]  A E Bostwick,et al.  THE THEORY OF PROBABILITIES. , 1896, Science.

[67]  E. G. Beltrametti,et al.  On the range of non-classical probability , 1995 .

[68]  Jeffrey Bub,et al.  Contextuality and Nonlocality in ‘No Signaling’ Theories , 2009, 0903.1462.

[69]  A. Cabello,et al.  Bell-Kochen-Specker theorem: A proof with 18 vectors , 1996, quant-ph/9706009.

[70]  Simon Kochen,et al.  Logical Structures Arising in Quantum Theory , 1990 .

[71]  N. Bohr.  The Quantum Postulate and the Recent Development of Atomic Theory , 1928, Nature.

[72]  Adán Cabello,et al.  A hidden-variables versus quantum mechanics experiment , 1995 .

[73]  Cristian S. Calude,et al.  Strong Kochen-Specker theorem and incomputability of quantum randomness , 2012, Physical Review A.

[74]  Pieter E. Vermaas.  Comment on ‘‘Getting contextual and nonlocal elements‐of‐reality the easy way,’’ by Rob Clifton [Am. J. Phys. 61, 443–447 (1993)] , 1994 .

[75]  M. A. Can,et al.  Simple test for hidden variables in spin-1 systems. , 2007, Physical review letters.

[76]  I. Pitowsky,et al.  Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability , 2002, quant-ph/0208121.

[77]  Jeffrey Bub,et al.  Contextuality in Quantum Mechanics: Testing the Klyachko Inequality , 2010 .

[78]  Josef Tkadlec,et al.  Greechie diagrams, nonexistence of measures in quantum logics, and Kochen–Specker‐type constructions , 1996 .

[79]  Richard J. Greechie,et al.  Orthomodular Lattices Admitting No States , 1971 .

[80]  I. Pitowsky,et al.  George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle , 1994, The British Journal for the Philosophy of Science.