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Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

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Nature is relentless and unchangeable, and it is indifferent as to whether its hidden reasons and actions are understandable to man or not.

–Galileo Galilie.

Abstract

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?

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Notes

  1. The mathematical formalism of quantum theory has been subjected to physical and philosophical interpretation since its inception. Bacciagaluppi and Valentini (2009) discuss the interpretative positions advanced by the theory’s founders at the 1927 Solvay Conference and reproduce their original papers. Bunge (1956) reviews the largely-unchanged interpretative landscape 30 years later. Bastin (1971) provides a revealing glimpse of interpretative discussions following the introduction of Everett’s (1957) relative-state interpretation, but prior to both the reformulation of Everett’s interpretation in terms of “multiple worlds” by DeWitt (1970) and the introduction of decoherence by Zeh (1970). Landsman (2007) and Wallace (2008) provide more recent synoptic reviews, the former with an emphasis on decoherence and the latter with an emphasis on multiple worlds. The diversity of opinions on basic questions of interpretation remains large, as documented by Norsen and Nelson (2013), Schlosshauer et al. (2013) and Sommer (2013) by surveying participants at relevant conferences. Both physicists and philosophers have found the seemingly irresolvable differences between interpretative stances disturbing. Fuchs (2002) parodies interpretative “camps” as fundamentalist churches. Cabello (2015) titles a recent, fairly exhaustive overview of the diversity of interpretative assumptions a “map of madness”.

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Acknowledgments

Thanks to Don Hoffman for encouraging me to think about 1-bit information transfers, to The Federico and Elvia Faggin Foundation for financial support during the final stages of this work, and to an anonymous referee for suggestions and an additional reference.

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    Chris Fields

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Fields, C. Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory. Axiomathes 26, 279–311 (2016). https://doi.org/10.1007/s10516-016-9289-z

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