Abstract
In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical (actualist) representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the (metaphysical) presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
See for example, in this same respect, the detailed analysis of the concept of space in the history of physics provided by Max Jammer in his excellent book: The Concepts of Space. The History of Theories of Space in Physics (Jammer 1993).
See de Ronde et al. (2014) for discussion and definition of this notion in the context of classical physics.
According to Bohr (Wheeler and Zurek 1983, p. 7): “[...] the unambiguous interpretation of any measurement must be essentially framed in terms of classical physical theories, and we may say that in this sense the language of Newton and Maxwell will remain the language of physicists for all time.” In this respect, he aso added [Op. cit., p. 7] that, “it would be a misconception to believe that the difficulties of the atomic theory may be evaded by eventually replacing the concepts of classical physics by new conceptual forms.”
I am grateful to Bob Coecke for this linguistic insight. Cagliari, July 2014.
Given a quantum system represented by a superposition of more than one term, \(\sum c_i | \alpha _i \rangle\), when in contact with an apparatus ready to measure, \(|R_0 \rangle\), QM predicts that system and apparatus will become “entangled” in such a way that the final ‘system + apparatus’ will be described by \(\sum c_i | \alpha _i \rangle |R_i \rangle\). Thus, as a consequence of the quantum evolution, the pointers have also become—like the original quantum system—a superposition of pointers \(\sum c_i |R_i \rangle\). This is why the measurement problem can be stated as a problem only in the case the original quantum state is described by a superposition of more than one term.
[Op. cit., p. 156].
The Born rule provides the probability of finding a certain observable via the numbers that accompany the kets within quantum superpositions.
There is in our neo-Spinozist account an implicit ontological pluralism of multiple representations which can be related to one reality through a univocity principle. This is understood in analogous manner to how Spinoza considers in his immanent metaphysics the multiple attributes as being expressions of the same one single substance, namely, nature (see de Ronde 2014, 2016). Our non-reductionistic answer to the problem of inter-theory relation escapes in this way the requirement present in almost all interpretations of QM which implicitly or explicitly attempt to explain the formalism in substantialist atomistic terms. We believe there might be an interesting connection between our neo-Spinozist approach and the ‘multiplex realism’ recently proposed by Aerts and Sassoli de Bianchi (2015). Due to the limited space of this paper we leave this particular analysis and comparison for a future work.
It is true that QBism does provide a subjectivist interpretation of probability following the Bayesian viewpoint, however, this is done so at the price of denying the very need of an interpretation for QM. See for a detailed analysis: de Ronde (2016), de Ronde (2016). Also the hidden measurement approach by Aerts provides an epistemic interpretation of quantum probability but in this case, instead of considering the quantum system alone, the approach focuses on the measurement interaction between system and apparatus (Aerts and Sassoli di Bianchi 2015, 2017).
For a more detailed discussion of the notion of immanent cause we refer to (Melamed 2013, Chapter 2).
References
Aerts, D. (2009a). Quantum particles as conceptual entities: A possible explanatory framework for quantum theory. Foundations of Science, 14, 361–411.
Aerts, D. (2009b). Quantum structure in cognition. Journal of Mathematical Psychology, 53, 314–348.
Aerts, D. (2009c). Interpreting quantum particles as conceptual entities. International Journal of Theoretical Physics, 49, 2950–2970.
Aerts, D. (2010). A Potentiality and conceptuality interpretation of quantum mechancis. Philosophica, 83, 15–52.
Aerts, D., & Aerts, S. (1994). Applications of quantum statistics in psychological studies of decision processes. Foundations of Science, 1, 85–97.
Aerts, D., & D’Hooghe, B. (2009). Classical logical versus quantum conceptual thought: Examples in economics, decision theory and concept theory. In Proceedings of QI 2009-third international symposium on quantum interaction, Lecture Notes in Computer Science (pp. 128–142). Berlin: Springer.
Aerts, D., & D’Hooghe, B. (2010). A Potentiality and conceptuality interpretation of quantum mechancis. Philosophica, 83, 15–52.
Aerts, D., & Sassoli di Bianchi, M. (2015). Many-measurements or many-worlds? A dialogue. Foundations of Science, 20, 399–427.
Aerts, D., & Sassoli di Bianchi, M. (2017). Do spins have directions? Soft Computing, 21, 1483–1504.
Albert, D. Z., & Loewer, B. (1988). Interpreting the many worlds interpretation. Synthese, 77, 195–213.
Arenhart, J. R., & Krause, D. (2015). Potentiality and contradiction in quantum mechanics. In A. Koslow & A. Buchsbaum (Eds.), The road to universal logic (Vol. II, pp. 201–211). Berlin: Springer.
Arenhart, J. R., & Krause, D. (2016). Contradiction, Quantum mechanics, and the square of opposition. Logique et Analyse, 59, 273–281.
Bacciagaluppi, G. (1996). Topics in the modal interpretation of quantum mechanics. Ph.D. dissertation, University of Cambridge, Cambridge.
Blatter, G. (2000). Schrodinger’s cat is now fat. Nature, 406, 25–26.
Bokulich, A. (2004). Open or llosed? Dirac, Heisenberg, and the relation between classical and quantum mechanics. Studies in History and Philosophy of Modern Physics, 35, 377–396.
Bub, J. (1997). Interpreting the quantum world. Cambridge: Cambridge University Press.
Curd, M., & Cover, J. A. (1998). Philosophy of science. The central issues. In Norton and Company (Eds.). Cambridge: Cambridge University Press.
da Costa, N., & de Ronde, C. (2016). Revisiting the applicability of metaphysical identity in quantum mechanics. Preprint. arXiv:1609.05361
da Costa, N., & de Ronde, C. (2013). The paraconsistent logic of quantum superpositions. Foundations of Physics, 43, 845–858.
D’Ariano, M. G., & Perinotti, P. (2016). Quantum theory is an information theory. The operational framework and the axioms. Foundations of Physics, 46, 269–281.
Dawin, R., & Thébault, K. (2015). Many worlds: Incoherent or decoherent? Synthese, 192, 1559–1580.
de Ronde, C. (2014). The problem of representation and experience in quantum mechanics. In D. Aerts, S. Aerts, & C. de Ronde (Eds.), Probing the meaning of quantum mechanics: Physical, philosophical and logical perspectives (pp. 91–111). Singapore: World Scientific.
de Ronde, C. (2015). Modality, potentiality and contradiction in quantum mechanics. In J.-Y. Beziau, M. Chakraborty, & S. Dutta (Eds.), New directions in paraconsistent logic (pp. 249–265). Berlin: Springer.
de Ronde, C. (2016a). Probabilistic knowledge as objective knowledge in quantum mechanics: Potential powers instead of actual properties. In D. Aerts, C. de Ronde, H. Freytes, & R. Giuntini (Eds.), Probing the meaning and structure of quantum mechanics: Superpositions, semantics, dynamics and identity (pp. 141–178). Singapore: World Scientific.
de Ronde, C. (2016b). Representational realism, closed theories and the quantum to classical limit. In R. E. Kastner, J. Jeknic-Dugic, & G. Jaroszkiewicz (Eds.), Quantum structural studies (pp. 105–136). Singapore: World Scientific.
de Ronde, C. (2017a). Causality and the modeling of the measurement process in quantum theory. Disputatio (forthcoming).
de Ronde, C. (2017b). Hilbert space quantum mechanics is contextual. (Reply to R. B. Griffiths). Cadernos de Filosofia (forthcoming). arXiv:1502.05396
de Ronde, C., Freytes, H., & Domenech, G. (2014). Interpreting the modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics. Studies in History and Philosophy of Modern Physics, 45, 11–18.
Deutsch, D. (1999). Quantum theory of probability and decisions. Proceedings of the Royal Society of London, A455, 3129–3137.
DeWitt, B., & Graham, N. (1973). The many-worlds interpretation of quantum mechanics. Princeton: Princeton University Press.
Dieks, D. (1988). The formalism of quantum theory: An objective description of reality. Annalen der Physik, 7, 174–190.
Dieks, D. (2007). Probability in the modal interpretation of quantum mechanics. Studies in History and Philosophy of Modern Physics, 38, 292–310.
Dieks, D. (2010). Quantum mechanics, chance and modality. Philosophica, 83, 117–137.
Dirac, P. A. M. (1974). The principles of quantum mechanics (4th ed.). London: Oxford University Press.
Dorato, M. (2006). Properties and dispositions: Some metaphysical remarks on quantum ontology. Proceedings of the AIP, 844, 139–157.
Dorato, M. (2015). Events and the ontology of quantum mechanics. Topoi, 34, 369–378.
Einstein, A. (1916). Ernst Mach. Physikalische Zeitschrift, 17, 101–104.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description be considered complete? Physical Review, 47, 777–780.
Everett, H. (1973). The theory of the universal wave function (Ph.D. Thesis, 1956). In Dewitt, B., & Graham, N. (Eds.), The many-worlds interpretation of quantum mechanics (pp. 3–140). Princeton: Princeton University Press.
Fuchs, C., Mermin, N., & Schack, R. (2014). An introduction to QBism with an application to the locality of quantum mechanics. American Journal of Physics, 82, 749.
Fuchs, C., & Peres, A. (2000). Quantum theory needs no interpretation. Physics Today, 53, 70.
Gao, S. (2015). What does it feel like to be in a quantum superposition? (preprint). http://philsci-archive.pitt.edu/11811/
Griffiths, R. B. (2002). Consistent quantum theory. Cambridge: Cambridge University Press.
Griffiths, R. B. (2013). Hilbert space quantum mechanics is non contextual. Studies in History and Philosophy of Modern Physics, 44, 174–181.
Hartle, J. (2015). Living in a quantum superposition (preprint). arXiv:1511.01550
Heisenberg, W. (1958). Physics and philosophy, world perspectives. London: George Allen and Unwin Ltd.
Heisenberg, W. (1971). Physics and beyond. New York: Harper & Row.
Heisenberg, W. (1973). Development of concepts in the history of quantum theory. In J. Mehra (Ed.), The physicist’s conception of nature (pp. 264–275). Dordrecht: Reidel.
Howard, D. (1993). Was Einstein really a realist? Perspectives on Science, 1, 204–251.
Howard, D. (2010). Einstein’s philosophy of science. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Summer 2010 Edition). http://plato.stanford.edu/archives/sum2010/entries/einstein-philscience/.
Jammer, M. (1993). Concepts of space. The history of theories of space in physics. New York: Dover.
Jansson, L. (2016). Everettian quantum mechanics and physical probability: Against the principle of ‘State Supervenience’. Studies in history and philosophy of modern physics, 53, 45–53.
Kastner, R. (2012). The transactional interpretation of quantum mechanics: The reality of possibility. Cambridge: Cambridge University Press.
Kastner, R. (2014). Einselection’ of pointer observables: The new H-theorem? Studies in History and Philosophy of Modern Physics, 48, 56–58.
Kastner, R. (2015). Understanding our unseen reality: Solving quantum riddles. London: Imperial College Press.
Kochen, S., & Specker, E. (1967). On the problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87. (Reprinted in Hooker, 1975, 293–328).
Kovachy, T., Asenbaum, P., Overstreet, C., Donnelly, C. A., Dickerson, S. M., Sugarbaker, A., et al. (2015). Quantum superposition at the half-metre scale. Nature, 528, 530–533.
Laplace, P.S. (1951). A philosophical essay on probabilities. Translated into English from the original French 6th ed. In F. W. Truscott, & F. L. Emory. New York: Dover Publications.
Melamed, Y. (2013). Spinoza’s metaphysics and thought. Oxford: Oxford University Press.
Mermin, D. (2015). Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it (preprint). arXiv:1409.2454
Nimmrichter, S., & Hornberger, K. (2013). Macroscopicity of mechanical quantum superposition states. Physical Review Letters, 110, 160403.
Omnès, R. (1994). Interpretation of quantum mechanics. Princeton: Princeton University Press.
Piron, C. (1983). Le realisme en physique quantique: une approche selon Aristote. In The concept of physical reality. Proceedings of a conference organized by the Interdisciplinary Research Group, University of Athens.
Rédei, M. (2012). Some historical and philosophical aspects of quantum probability theory and its interpretation. In D. Dieks, et al. (Eds.), Probabilities, laws, and structures (pp. 497–506). Berlin: Springer.
Saunders, S., Barrett, J., Kent, A., & Wallace, D. (Eds.). (2012). Many worlds? Everett, quantum theory, & reality. Oxford: Oxford University Press.
Schrödinger, E. (1935). The present situation in quantum mechanics. Naturwiss, 23, 807–812. Translated to English In J. A. Wheeler, W. H. Zurek (Eds.) Quantum Theory and Measurement, 1983, Princeton University Press, Princeton.
Sudbery, T. (2016). Time, chance and quantum theroy. In D. Aerts, C. de Ronde, H. Freytes, & R. Giuntini (Eds.), Probing the meaning and structure of quantum mechanics: Superpositions, semantics, dynamics and identity (pp. 324–339). Singapore: World Scientific.
Van Fraassen, B. C. (1980). The scientific image. Oxford: Clarendon.
Verelst, K., & Coecke, B. (1999). Early Greek thought and perspectives for the interpretation of quantum mechanics: Preliminaries to an ontological approach. In D. Aerts (Ed.), The Blue Book of Einstein meets Magritte (pp. 163–196). Dordrecht: Kluwer Academic Publishers.
Wallace, D. (2007). Quantum probability from subjective likelihood: Improving on Deutsch’s proof of the probability rule. Studies in the history and philosophy of modern physics, 38, 311–332.
Wallace, D. (2012). The emergent multiverse: Quantum theory according to the everett interpretation. Oxford: Oxford University Press.
Wheeler, J. A., & Zurek, W. H. (Eds.). (1983). Theory and measurement. Princeton: Princeton University Press.
Acknowledgements
I wish to thank two anonymous reviewers for their careful reading of my manuscript and their many insightful comments and suggestions. This work was partially supported by the following grants: FWO project G.0405.08 and FWO-research community W0.030.06. CONICET RES. 4541-12 and the Project PIO-CONICET-UNAJ (15520150100008CO) “Quantum Superpositions in Quantum Information Processing”.
Author information
Authors and Affiliations
Corresponding author
Additional information
Fellow Researcher of the Consejo Nacional de Investigaciones Científicas y Técnicas and Adjoint Professor of the National University Arturo Jaurteche, Buenos Aires, Argentina.
Rights and permissions
About this article
Cite this article
de Ronde, C. Quantum Superpositions and the Representation of Physical Reality Beyond Measurement Outcomes and Mathematical Structures. Found Sci 23, 621–648 (2018). https://doi.org/10.1007/s10699-017-9541-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10699-017-9541-z