On Formalisms and Interpretations

Veronika Baumann1,2 and Stefan Wolf1

1Faculty of Informatics, Università della Svizzera italiana, Via G. Buffi 13, CH-6900 Lugano, Switzerland
2Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism $\textit{versus}$ interpretation. In this note, we make a clear distinction between them and show that there are actually two $\textit{inequivalent}$ quantum formalisms, namely the relative-state formalism and the standard formalism with the Born and measurement-update rules. We further propose a different probability rule for the relative-state formalism and discuss how Wigner's-friend-type experiments could show the inequivalence with the standard formalism. The feasibility in principle of such experiments, however, remains an open question.

► BibTeX data

► References

[1] Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, and Paul Skrzypczyk. Quantum cheshire cats. New Journal of Physics, 15 (11): 113015, 2013. 10.1088/​1367-2630/​15/​11/​113015.

[2] Veronika Baumann, Arne Hansen, and Stefan Wolf. The measurement problem is the measurement problem is the measurement problem. arXiv:1611.01111, 2016. URL https:/​/​arxiv.org/​abs/​1611.01111.

[3] John S Bell. On the Einstein Podolsky Rosen paradox. Physics, 1 (3): 195-200, 1964. 10.1103/​PhysicsPhysiqueFizika.1.195.

[4] John Stewart Bell. Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge university press, 2004. 10.1017/​CBO9780511815676.

[5] Max Born. The statistical interpretation of quantum mechanics. Nobel Lecture, 11: 1942-1962, 1954. 10.1126/​science.122.3172.675.

[6] Caslav Brukner. On the quantum measurement problem. arXiv:1507.05255, 2015. URL https:/​/​arxiv.org/​abs/​1507.05255.

[7] Giulio Chiribella, G Mauro D'Ariano, and Paolo Perinotti. Quantum circuit architecture. Physical Review Letters, 101 (6): 060401, 2008. 10.1103/​PhysRevLett.101.060401.

[8] Giulio Chiribella, Giacomo Mauro D'Ariano, and Paolo Perinotti. Probabilistic theories with purification. Physical Review A, 81 (6): 062348, 2010. 10.1103/​PhysRevA.81.062348.

[9] David Deutsch. Quantum theory as a universal physical theory. International Journal of Theoretical Physics, 24 (1): 1-41, 1985.

[10] David Deutsch. Quantum theory of probability and decisions. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 455, pages 3129-3137. The Royal Society, 1999. 10.1098/​rspa.1999.0443.

[11] Detlef Dürr, Sheldon Goldstein, and Nino Zanghi. Bohmian mechanics as the foundation of quantum mechanics. In Bohmian mechanics and quantum theory: an appraisal, pages 21-44. Springer, 1996. 10.1007/​978-94-015-8715-0_2.

[12] Hugh Everett III. "Relative State" formulation of quantum mechanics. Reviews of Modern Physics, 29 (3): 454, 1957. 10.1103/​RevModPhys.29.454.

[13] Daniela Frauchiger and Renato Renner. Quantum theory cannot consistently describe the use of itself. Nature communications, 9 (1): 3711, 2018. 10.1038/​s41467-018-05739-8.

[14] Christopher A Fuchs. Qbism, the perimeter of quantum bayesianism. arXiv:1003.5209, 2010. URL https:/​/​arxiv.org/​abs/​1003.5209.

[15] Gian Carlo Ghirardi, Alberto Rimini, and Tullio Weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34 (2): 470, 1986. 10.1103/​PhysRevD.34.470.

[16] Lucien Hardy. Quantum theory from five reasonable axioms. arXiv:quant-ph/​0101012, 2001. arXiv:quant-ph/​0101012.

[17] Grete Hermann. Die naturphilosophischen Grundlagen der Quantenmechanik. Naturwissenschaften, 23 (42): 718-721, 1935. 10.1007/​BF01491142.

[18] Grete Hermann and Dirk Lumma. The foundations of quantum mechanics in the philosophy of nature. The Harvard Review of Philosophy, 7 (1): 35-44, 1999. 10.5840/​harvardreview1999715.

[19] Simon Kochen and Ernst P Specker. The problem of hidden variables in quantum mechanics. In The logico-algebraic approach to quantum mechanics, pages 293-328. Springer, 1975. 10.1007/​978-94-010-1795-4_17.

[20] Johannes Kofler and Časlav Brukner. Classical world arising out of quantum physics under the restriction of coarse-grained measurements. Physical Review Letters, 99 (18): 180403, 2007. 10.1103/​PhysRevLett.99.180403.

[21] Lluís Masanes and Markus P Müller. A derivation of quantum theory from physical requirements. New Journal of Physics, 13 (6): 063001, 2011. 10.1088/​1367-2630/​13/​6/​063001.

[22] Ognyan Oreshkov, Fabio Costa, and Časlav Brukner. Quantum correlations with no causal order. Nature communications, 3: 1092, 2012. 10.1038/​ncomms2076.

[23] Karl Popper. Logik der Forschung. Springer, 1935. 10.1524/​9783050050188.

[24] Carlo Rovelli. Relational quantum mechanics. International Journal of Theoretical Physics, 35 (8): 1637-1678, 1996. 10.1007/​BF02302261.

[25] Simon Saunders. Derivation of the Born rule from operational assumptions. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 460, pages 1771-1788. The Royal Society, 2004. 10.1098/​rspa.2003.1230.

[26] Sally Shrapnel, Fabio Costa, and Gerard Milburn. Updating the born rule. New Journal of Physics, 20 (5): 053010, 2018. 10.1088/​1367-2630/​aabe12.

[27] Anthony Sudbery. Quantum mechanics and the particles of nature. Cambridge University Press, 1986.

[28] Anthony Sudbery. Single-world theory of the extended Wigner's friend experiment. Foundations of Physics, 47 (5): 658-669, 2017. 10.1007/​s10701-017-0082-7.

[29] John Archibald Wheeler, Wojciech Hubert Zurek, and Leslie E Ballentine. Quantum theory and measurement. American Journal of Physics, 52 (10): 955-955, 1984. 10.1119/​1.13804.

[30] Eugene P Wigner. The problem of measurement. American Journal of Physics, 31 (1): 6-15, 1963. 10.1119/​1.1969254.

[31] Wojciech Hubert Zurek. Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75 (3): 715, 2003. 10.1103/​RevModPhys.75.715.

Cited by

[1] Nuriya Nurgalieva and Lídia del Rio, "Inadequacy of Modal Logic in Quantum Settings", arXiv:1804.01106.

[2] Igor Salom, "To the rescue of Copenhagen interpretation", arXiv:1809.01746.

The above citations are from SAO/NASA ADS (last updated 2019-06-18 23:13:19). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2019-06-18 23:13:18).

1 thought on “On Formalisms and Interpretations

  1. Pingback: Weekly Papers on Quantum Foundations (42)