A Stronger Theorem Against Macro-realism

John-Mark A. Allen1, Owen J. E. Maroney2, and Stefano Gogioso1

1Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
2Faculty of Philosophy, University of Oxford, Radcliffe Humanities, Woodstock Road, Oxford, OX2 6GG, United Kingdom

Macro-realism is the position that certain macroscopic observables must always possess definite values: e.g. the table is in some definite position, even if we do not know what that is precisely. The traditional understanding is that by assuming macro-realism one can derive the Leggett-Garg inequalities, which constrain the possible statistics from certain experiments. Since quantum experiments can violate the Leggett-Garg inequalities, this is taken to rule out the possibility of macro-realism in a quantum universe. However, recent analyses have exposed loopholes in the Leggett-Garg argument, which allow many types of macro-realism to be compatible with quantum theory and hence violation of the Leggett-Garg inequalities. This paper takes a different approach to ruling out macro-realism and the result is a no-go theorem for macro-realism in quantum theory that is stronger than the Leggett-Garg argument. This approach uses the framework of ontological models: an elegant way to reason about foundational issues in quantum theory which has successfully produced many other recent results, such as the PBR theorem.


► BibTeX data

► References

[1] A. J. Leggett and A. Garg, Quantum Mechanics versus Macroscopic Realism: Is the Flux There when Nobody Looks? Physical Review Letters 54(9), 857-860 (1985). http:/​/​dx.doi.org/​10.1103/​PhysRevLett.54.857.

[2] L. E. Ballentine, Realism and Quantum Flux Tunneling. Physical Review Letters 59(14), 1493 (1987). http:/​/​dx.doi.org/​10.1103/​PhysRevLett.59.1493.

[3] A. J. Leggett and A. Garg, Comment on ``Realism and Quantum Flux Tunneling''. Physical Review Letters 59(14), 1621 (1987). http:/​/​dx.doi.org/​10.1103/​PhysRevLett.59.1621.

[4] A. J. Leggett, Experimental Approaches to the Quantum Measurement Paradox. Foundations of Physics 18(9), 939-952 (1988). http:/​/​dx.doi.org/​10.1007/​BF01855943.

[5] A. J. Leggett, Probing Quantum Mechanics Towards the Everyday World: Where do we Stand? Physica Scripta 2002(T102), 69 (2002). http:/​/​dx.doi.org/​10.1238/​Physica.Topical.102a00069.

[6] A. J. Leggett, Testing the Limits of Quantum Mechanics: Motivation, State of Play, Prospects. Journal of Physics: Condensed Matter 14(15), R415 (2002). http:/​/​dx.doi.org/​10.1088/​0953-8984/​14/​15/​201.

[7] J. Kofler and Ċaslav Brukner, Condition for Macroscopic Realism Beyond the Leggett-Garg Inequalities. Physical Review A 87(5), 052115 (2013). arXiv:1207.3666 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevA.87.052115.

[8] O. J. E. Maroney and C. G. Timpson, Quantum- vs. Macro- Realism: What does the Leggett-Garg Inequality Actually Test? British Journal for the Philosophy of Science In Production (2017). arXiv:1412.6139 [quant-ph].

[9] C. Emary, N. Lambert, and F. Nori, Leggett-Garg Inequalities. Reports on Progress in Physics 77(1), 016001 (2014). arXiv:1304.5133 [quant-ph] , http:/​/​dx.doi.org/​10.1088/​0034-4885/​77/​1/​016001.

[10] G. C. Knee, K. Kakuyanagi, M.-C. Yeh, Y. Matsuzaki, H. Toida, H. Yamaguchi, S. Saito, A. J. Leggett, and W. J. Munro, A Strict Experimental Test of Macroscopic Realism in a Superconducting Flux Qubit. Nature Communications 7, 13253 (2016). arXiv:1601.03728 [quant-ph] , http:/​/​dx.doi.org/​10.1038/​ncomms13253.

[11] E. Huffman and A. Mizel, Violation of Noninvasive Macrorealism by a Superconducting Qubit: Implementation of a Leggett-Garg Test that Addresses the Clumsiness Loophole. Physical Review A 95(3), 032131 (2017). arXiv:1609.05957 [quant-ph] , https:/​/​doi.org/​10.1103/​PhysRevA.95.032131.

[12] Z.-Q. Zhou, S. F. Huelga, C.-F. Li, and G.-C. Guo, Experimental Detection of Quantum Coherent Evolution through the Violation of Leggett-Garg-Type Inequalities. Physical Review Letters 115(11), 113002 (2015). arXiv:1209.2176 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevLett.115.113002.

[13] L. Clemente and J. Kofler, Necessary and Sufficient Conditions for Macroscopic Realism from Quantum Mechanics. Physical Review A 91(6), 062103 (2015). arXiv:1501.07517 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevA.91.062103.

[14] L. Clemente and J. Kofler, No Fine Theorem for Macrorealism: Limitations of the Leggett-Garg Inequality. Physical Review Letters 116(15), 150401 (2016). arXiv:1509.00348 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevLett.116.150401.

[15] G. Bacciagaluppi, Leggett-Garg Inequalities, Pilot Waves and Contextuality. International Journal of Quantum Foundations 1, 1-17 (2015). arXiv:1409.4104 [quant-ph].

[16] M. M. Wilde and A. Mizel, Addressing the Clumsiness Loophole in a Leggett-Garg Test of Macrorealism. Foundations of Physics 42(2), 256-265 (2012). arXiv:1001.1777 [quant-ph] , http:/​/​dx.doi.org/​10.1007/​s10701-011-9598-4.

[17] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press, Cambridge (1987). http:/​/​dx.doi.org/​10.1017/​CBO9780511815676.

[18] M. F. Pusey, J. Barrett, and T. Rudolph, On the Reality of the Quantum State. Nature Physics 8(6), 475-478 (2012). arXiv:1111.3328 [quant-ph] , http:/​/​dx.doi.org/​10.1038/​nphys2309.

[19] L. Hardy, Quantum Ontological Excess Baggage. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35(2), 267-276 (2004). http:/​/​dx.doi.org/​10.1016/​j.shpsb.2003.12.001.

[20] M. S. Leifer, Is the Quantum State Real? An Extended Review of $\psi$-ontology Theorems. Quanta 3(1), 67-155 (2014). arXiv:1409.1570 [quant-ph] , http:/​/​dx.doi.org/​10.12743/​quanta.v3i1.22.

[21] D. Bohm and B. J. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge (1995).

[22] D. Dürr and S. Teufel, Bohmian Mechanics: The Physics and Mathematics of Quantum Theory. Springer, Berlin (2009). http:/​/​dx.doi.org/​10.1007/​b99978.

[23] D. Bohm, A Suggested Interpretation of the Quantum Theory in Terms of ``Hidden'' Variables. I. Physical Review 85(2), 166-179 (1952). http:/​/​dx.doi.org/​10.1103/​PhysRev.85.166.

[24] D. Bohm, A Suggested Interpretation of the Quantum Theory in Terms of ``Hidden'' Variables. II. Physical Review 85(2), 180-193 (1952). http:/​/​dx.doi.org/​10.1103/​PhysRev.85.166.

[25] L. de Broglie, The New Dynamics of Quanta. In Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference, eds. G. Bacciagaluppi and A. Valentini, pp. 373-406, Cambridge University Press, Cambridge (2009), ISBN 9780521814218. arXiv:quant-ph/​0609184 [quant-ph].

[26] J.-M. A. Allen, Quantum Superpositions cannot be Epistemic. Quantum Studies: Mathematics and Foundations 3(2), 161-177 (2016). arXiv:1501.05969 [quant-ph] , http:/​/​dx.doi.org/​10.1007/​s40509-015-0066-2.

[27] N. Harrigan and T. Rudolph, Ontological Models and the Interpretation of Contextuality (2007). arXiv:0709.4266 [quant-ph].

[28] N. Harrigan and R. W. Spekkens, Einstein, Incompleteness, and the Epistemic View of Quantum States. Foundatations of Physics 40(2), 125 (2010). arXiv:0706.2661 [quant-ph] , http:/​/​dx.doi.org/​10.1007/​s10701-009-9347-0.

[29] E. G. Beltrametti and S. Bugajski, A Classical Extension of Quantum Mechanics. Journal of Physics A 28(12), 3329 (1995). http:/​/​dx.doi.org/​10.1088/​0305-4470/​28/​12/​007.

[30] L. Ballentine, Ontological Models in Quantum Mechanics: What do they Tell Us? (2014). arXiv:1402.5689 [quant-ph].

[31] M. S. Leifer and O. J. E. Maroney, Maximally Epistemic Interpretations of the Quantum State and Contextuality. Physical Review Letters 110(12), 120401 (2013). arXiv:1208.5132 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevLett.110.120401.

[32] O. J. E. Maroney, How Statistical are Quantum States? (2012). arXiv:1207.6906 [quant-ph].

[33] C. M. Caves, C. A. Fuchs, and R. Schack, Conditions for Compatibility of Quantum-State Assignments. Physical Review A 66(6), 062111 (2002). arXiv:quant-ph/​0206110 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevA.66.062111.

[34] J. Barrett, E. G. Cavalcanti, R. Lal, and O. J. E. Maroney, No $\psi$-Epistemic Model Can Fully Explain the Indistinguishability of Quantum States. Physical Review Letters 112(25), 250403 (2014). arXiv:1310.8302 [quant-ph] , http:/​/​dx.doi.org/​10.1103/​PhysRevLett.112.250403.

[35] S. Kochen and E. P. Specker, The Problem of Hidden Variables in Quantum Mechanics. Journal of Mathematics and Mechanics 17, 59-87 (1967).

[36] J.-M. A. Allen, Reality, Causality, and Quantum Theory (2017). Forthcoming doctoral thesis to be made available on the arXiv.

[37] R. Hermens and O. J. E. Maroney, Constraints on Macroscopic Realism Without Assuming Non-invasive Measurability (2017). arXiv:1706.01641 [quant-ph].