An Operationalist Perspective on Setting Dependence

A well known logical loophole for Bell’s theorem is that it relies on setting independence: the assumption that the state of a system is independent of the settings of a measurement apparatus probing the system. In this paper the implications of rejecting this assumption are studied from an operationalist perspective. To this end a generalization of the ontic models framework is proposed that allows setting dependence. It is shown that within this framework Bell’s theorem reduces to the conclusion that no-signaling requires randomness at the epistemic level even if the underlying ontology is taken to be deterministic. The ideas underlying the framework are further used to defend setting dependence against the charges of being incompatible with free will and scientific methodology. The paper ends however with the sketch of a new problem for setting dependence: a necessary gap between the ontic and the epistemic level that may prevent the formulation of a successful setting dependent theory.

[1]  Steven Weinstein.  Nonlocality Without Nonlocality , 2008, 0812.0349.

[2]  M. P. Seevinck,et al.  Monogamy of correlations versus monogamy of entanglement , 2009, Quantum Inf. Process..

[3]  N. Gisin,et al.  General properties of nonsignaling theories , 2005, quant-ph/0508016.

[4]  M. Redhead,et al.  Nonlocality and the Kochen-Specker paradox , 1983 .

[5]  What Does the Free Will Theorem Actually Prove , 2009, 0905.4641.

[6]  Huw Price,et al.  Disentangling the Quantum World , 2015, Entropy.

[7]  Frederick M. Kronz.  Hidden Locality, Conspiracy and Superluminal Signals , 1990, Philosophy of Science.

[8]  E. Specker,et al.  The Logic of Propositions Which are not Simultaneously Decidable , 1975 .

[9]  Matthew F Pusey,et al.  On the reality of the quantum state , 2011, Nature Physics.

[10]  Christopher G. Timpson,et al.  Quantum Bayesianism: A study , 2008, 0804.2047.

[11]  Katherine Robertson.  Can the two-time interpretation of quantum mechanics solve the measurement problem? , 2017 .

[12]  Simon Kochen,et al.  The Strong Free Will Theorem , 2008, 0807.3286.

[13]  Y. Aharonov,et al.  Measurement and collapse within the two-state vector formalism , 2014, 1406.6382.

[14]  M. S. Leifer,et al.  Is the Quantum State Real? An Extended Review of -ontology Theorems , 2014, 1409.1570.

[15]  C. J. Wood,et al.  The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning , 2012, 1208.4119.

[16]  K. Landsman.  On the notion of free will in the Free Will Theorem , 2017 .

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

[18]  J. Berkovitz.  On predictions in retro-causal interpretations of quantum mechanics , 2008 .

[19]  Christopher A. Fuchs,et al.  Notwithstanding Bohr, the Reasons for QBism , 2017, 1705.03483.

[20]  C. Wuthrich.  Can the world be shown to be indeterministic after all , 2010 .

[21]  Michael Esfeld,et al.  Bell’s Theorem and the Issue of Determinism and Indeterminism , 2015 .

[22]  D. Lewis.  Are we free to break the laws , 2008 .

[23]  R. Spekkens.  Contextuality for preparations, transformations, and unsharp measurements , 2004, quant-ph/0406166.

[24]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

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

[26]  Matthew F Pusey,et al.  Is a time symmetric interpretation of quantum theory possible without retrocausality? , 2016, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[27]  R. Spekkens,et al.  Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity , 2010 .

[28]  K. Landsman.  Foundations of Quantum Theory: From Classical Concepts to Operator Algebras , 2017 .

[29]  Gerard 't Hooft,et al.  The Cellular Automaton Interpretation of Quantum Mechanics , 2014, 1405.1548.

[30]  A. Fine.  Hidden Variables, Joint Probability, and the Bell Inequalities , 1982 .

[31]  Anton Zeilinger,et al.  Dance of the Photons: From Einstein to Quantum Teleportation , 2010 .

[32]  Peter J. Lewis.  Conspiracy Theories of Quantum Mechanics , 2006, The British Journal for the Philosophy of Science.

[33]  R. Spekkens.  Evidence for the epistemic view of quantum states: A toy theory , 2004, quant-ph/0401052.

[34]  Arthur Fine,et al.  Joint distributions, quantum correlations, and commuting observables , 1982 .

[35]  Y. Aharonov,et al.  Two-time interpretation of quantum mechanics , 2005, quant-ph/0507269.

[36]  M. Seevinck.  Monogamy of Correlations vs . Monogamy of Entanglement , 2009 .

[37]  E. Cator,et al.  Constraints on Determinism: Bell Versus Conway–Kochen , 2014, Foundations of Physics.

[38]  H. Price,et al.  A Live Alternative to Quantum Spooks , 2015, 1510.06712.

[39]  Simon Kochen,et al.  The Free Will Theorem , 2006 .