Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-18T23:39:21.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Another No-go Theorem for Hidden Variable Models of Inaccurate Spin 1 Measurements

Published online by Cambridge University Press:  01 January 2022

Thomas Breuer
Get access Rights & Permissions [Opens in a new window]

Abstract

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier theorem (Breuer 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy.

Type
Quantum Field Theory, Bell's Theorem, and Hidden Variables
Information
Philosophy of Science , Volume 70 , Issue 5: Proceedings of the 2002 Biennial Meeting of The Philosophy of Science Association. Part I: Contributed Papers , December 2003 , pp. 1368 - 1379
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Appleby, David M. (2001), “Nullification of the Nullification”, quant-ph/0109034.Google Scholar
Breuer, Thomas (2002), “A Kochen-Specker Theorem for Finite Precision Spin-1 Measurements”, A Kochen-Specker Theorem for Finite Precision Spin-1 Measurements 88: 240402, quant-ph/0206035.Google Scholar
Busch, Paul, Grabowski, Marian, and Lahti, Pekka (1995), Operational Quantum Physics, LNP m31, Heidelberg: Springer.CrossRefGoogle Scholar
Cabello, Adan (2002), “Finite-precision Measurement Does not Nullify the Kochen-Specker Theorem”, Finite-precision Measurement Does not Nullify the Kochen-Specker Theorem A 65: 052101, quant-ph/0104024.Google Scholar
Cabello, Adan, and García-Alcaine, Guillermo (1998), “Proposed Experimental Tests of the Bell-Kochen-Specker Theorem”, Proposed Experimental Tests of the Bell-Kochen-Specker Theorem 80:1797–1799, quant-ph/9709047.Google Scholar
Clifton, Rob, and Kent, Adrian (2000), “Simulating Quantum Mechanics by Non-Contextual Hidden Variables”, Simulating Quantum Mechanics by Non-Contextual Hidden Variables A 456:2101–2114, quant-ph/9908031.Google Scholar
Havlicek, Hans, Krenn, Günter, Summhammer, Johann, and Svozil, Karl (2001), “Coloring the Rational Quantum Sphere and the Kochen-Specker Theorem”, Coloring the Rational Quantum Sphere and the Kochen-Specker Theorem A 34(14): 3071–3077, quant-ph/9911040.Google Scholar
Held, Carsten (2000), “The Kochen-Specker Theorem”, Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/kochen-specker/index.html.Google Scholar
Holevo, Alexander S. (1982), Probabilistic and Statistical Aspects of Quantum Theory. Amsterdam: North Holland.Google Scholar
Kent, Adrian (1999), “Non-contextual Hidden Variables and Physical Measurements”, Non-contextual Hidden Variables and Physical Measurements 83:3755–3758, quant-ph/9906006.Google Scholar
Kochen, Simon, and Specker, Ernst (1967), “The Problem of Hidden Variables in Quantum Mechanics”, The Problem of Hidden Variables in Quantum Mechanics 17:59–87.Google Scholar
Mermin, N. David (1999), “A Kochen-Specker Theorem for Imprecisely Specified Measurements”, quant-ph/9912081.Google Scholar
Meyer, David A. (1999), “Finite Precision Measurement Nullifies the Kochen-Specker Theorem”, Finite Precision Measurement Nullifies the Kochen-Specker Theorem 83:3751–3754, quant-ph/9905080.Google Scholar
Peres, Asher (1995), Quantum Theory: Concepts and Methods. Dordrecht: Kluwer.Google Scholar
Pitowsky, Itamar (1985), “Quantum Mechanics and Value Definiteness”, Quantum Mechanics and Value Definiteness 52:154–156.Google Scholar
Pitowsky, Itamar (1998), “Infinite and Finite Gleason's Theorems and the Logic of Indeterminacy”, Infinite and Finite Gleason's Theorems and the Logic of Indeterminacy 39:218–228.Google Scholar
Simon, Christoph, Zukowski, Marek, Weinfurter, Harald, and Zeilinger, Anton (2000), “A Feasible Kochen-Specker Experiment with Single Particles”, A Feasible Kochen-Specker Experiment with Single Particles 85:1783–1786, quant-ph/0009074.Google ScholarPubMed
Simon, Christoph, Bruckner, Časlav, and Zeilinger, Anton (2001), “Hidden-variable Theorems for Real Experiments”, Hidden-variable Theorems for Real Experiments 86:4427–4430, quant-ph/0006043.Google ScholarPubMed
Zimba, Jason, and Penrose, Roger (1993), “On Bell Non-locality without Probabilities: More Curious Geometry”, On Bell Non-locality without Probabilities: More Curious Geometry 24:697–720.Google Scholar