Abstract
Some authors, inspired by the theoretical requirements for the formulation of a quantum theory of gravity, proposed a relational reconstruction of the quantum parameter-time—the time of the unitary evolution, which would make quantum mechanics compatible with relativity. The aim of the present work is to follow the lead of those relational programs by proposing a relational reconstruction of the event-time—which orders the detection of the definite values of the system’s observables. Such a reconstruction will be based on the modal-Hamiltonian interpretation of quantum mechanics, which provides a clear criterion to select which observables acquire a definite value and to specify in what situation they do so.
Similar content being viewed by others
References
Page, D., Wootters, W.: Evolution without evolution. Physical Review D 27, 2885–2892 (1983)
Rovelli, C.: Quantum mechanics without time: A model. Phys. Rev. D 42, 2638–2646 (1990)
Rovelli, C.: “Is there incompatibility between the ways time is treated in general relativity and in standard quantum mechanics?” In: Ashtekar, A., Stachel, J. (eds.) Conceptual Problems of Quantum Gravity, pp. 126–136. Birkhauser, New York (1991)
Rovelli, C.: Forget time. Essay written for the FQXi contest on the Nature of Time (2008).
Wootters, W.: “Time” replaced by quantum correlations. Int. J. Theor. Phys. 23, 701–711 (1984)
Ardenghi, J.S., Castagnino, M., Lombardi, O.: Quantum mechanics: modal interpretation and Galilean transformations. Found. Phys. 39, 1023–1045 (2009)
Ardenghi, J.S., Castagnino, M., Lombardi, O.: Modal-Hamiltonian interpretation of quantum mechanics and Casimir operators: the road to quantum field theory. Int. J. Theor. Phys. 50, 774–791 (2009)
Castagnino, M., Lombardi, O.: The role of the Hamiltonian in the interpretation of quantum mechanics. J. Phys. 28, 012014 (2008)
Lombardi, O., Castagnino, M.: A modal-Hamiltonian interpretation of quantum mechanics. Stud. Hist. Philos. Mod. Phys. 39, 380–443 (2008)
Lombardi, O., Castagnino, M., Ardenghi, J.S.: The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics. Stud. Hist. Philos. Mod. Phys. 41, 93–103 (2010)
Barnes, J. (ed.): The Complete Works of Aristotle, Volumes I and II. Princeton University Press, Princeton (1984)
Alexander, H.G. (ed.): The Leibniz-Clarke Correspondence. Manchester University Press, Manchester (1956)
Mach, E.: The Science of Mechanics: A critical and Historical Account of its Development, trans. by T. J. McCormack. Open Court, La Salle (1883) [1960]
Hoefer, C.: Einstein’s formulations of Mach’s Principle. In: Barbour, J., Pfister, H. (eds.) Mach’s Principle. From Newton’s Bucket to Quantum Gravity, pp. 67–87. Birkhäuser, Boston (1995)
Barbour, J., Bertotti, B.: Gravity and inertia in a Machian framework. Nuovo Cimento 38B, 1–27 (1977)
Barbour, J., Bertotti, B.: Mach’s Principle and the structure of dynamical theories. Proc. R. Soc. (Lond.) 382, 295–306 (1982)
Barbour, J.: Relational concepts of space and time. Br. J. Philos. Sci. 33, 251–274 (1982)
Pooley, O., Brown, H.: Relationalism rehabilitated? I: Classical mechanics. Br. J. Philos. Sci. 53, 183–204 (2002)
Barbour, J.B.: The End of Time: The Next Revolution in Our Understanding of the Universe. Weidenfeld & Nicholson, London (1999)
Butterfield, J.: The end of time? Br. J. Philos. Sci. 53, 289–330 (2001)
Pooley, O.: Relationalism rehabilitated? II: Relativity. PhilSci Arch., p. http://philsci-archive.pitt.edu/221/ (2001)
Albert, D.Z.: Wave function realism. In: Ney, A., Albert, D.Z. (eds.) The Wave Function: Essays on the Metaphysics of Quantum Mechanics. Oxford University Press, Oxford (2013)
Busch, P.: The time-energy uncertainty relation. In: Muga, J., Mayato, R.S., Egusquiza, I. (eds.) Time in Quantum Mechanics. Lecture Notes in Physics, vol. 734, pp. 73–105. Springer, Berlin-Heidelberg (2008)
Bohr, N.: Das Quantenpostulat und die neuere Entwicklung der Atomistik. Naturwissenschaften 16, 245–257 (1928)
Busch, P.: On the energy-time uncertainty relation. Part I: Dynamical time and time indeterminacy. Found. Phys. 20, 1–32 (1990)
Busch, P.: On the energy-time uncertainty relation. Part II: Pragmatic time versus energy Indeterminacy. Found. Phys. 20, 33–43 (1990)
Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172–198 (1927)
Pauli: Die allgemeinen Prinzipien der Wellenmechanik. In: Geiger, H., Scheel, K. (eds.) Handbuch der Physik, vol. 24, 2nd edn., pp. 83–272. Springer-Verlag, Berlin (1933)
Mandelstam, L., Tamm, I.: The uncertainty relation between energy and time in non-relativistic quantum mechanics. J. Phys. (USSR) 9, 249–254 (1945)
Ballentine, L.: Quantum Mechanics. A Modern Development. World Scientific, Singapore (1989)
Messiah, A.: Quantum Mechanics, vol. 1. North-Holland, Amsterdam (1961)
Isham, C.J.: Canonical quantum gravity and the problem of time. In: Ibort, L.A., Rodríguez, M.A. (eds.) Integrable Systems, Quantum Groups, and Quantum Field Theories, NATO ASI Series (Series C: Mathematical and Physical Sciences), vol. 409, pp. 157–287. Springer, Dordrecht (1993)
Kuchař, K.: The problem of time in canonical quantization. In: Ashtekar, A., Stachel, J. (eds.) Conceptual Problems of Quantum Gravity, pp. 141–171. Birkhäuser, Boston (1991)
Marletto, C., Vedral, V.: Evolution without evolution and without ambiguities. Phys. Rev. D 95, 043510 (2017)
DeWitt, B.S.: Quantum theory of gravity. Phys. Rev. D 160, 1113–1148 (1967)
Everett, H.: Relative state formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957)
Rovelli, C.: Partial observables. Phys. Rev. D 65, 124013 (2002)
Van Fraassen, B.C.: A formal approach to the philosophy of science. In: Colodny, R. (ed.) Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, pp. 303–366. University of Pittsburgh Press, Pittsburgh (1972)
Van Fraassen, B.C.: Semantic analysis of quantum logic. In: Hooker, C.A. (ed.) Contemporary Research in the Foundations and Philosophy of Quantum Theory, pp. 80–113. Reidel, Dordrecht (1973)
Van Fraassen, B.C.: The Einstein-Podolsky-Rosen paradox. Synthese 29, 291–309 (1974)
Dieks, D., Vermaas, P.E.: The Modal Interpretation of Quantum Mechanics. Kluwer Academis Publishers, Dordrecht (1998)
Lombardi, O., Dieks, D.: Modal interpretations of quantum mechanics. In: Zalta, E.N. (ed) Stanford Encyclopedia of Philosophy (Winter 2021 Edition). Stanford University, Stanford. https://plato.stanford.edu/entries/qm-modal/ (2021).
Lombardi, O.: The Modal-Hamiltonian Interpretation: measurement, invariance and ontology. In: Lombardi, O., Fortin, S., López, C., Holik, F. (eds.) Quantum Worlds Perspectives on the Ontology of Quantum Mechanics, pp. 32–50. Cambridge University Press, Cambridge (2018)
Ardenghi, J.S., Lombardi, O., Narvaja, M.: Modal interpretations and consecutive measurements. In: Karakostas, V., Dieks, D. (eds.) EPSA 2011: Perspectives and Foundational Problems in Philosophy of Science, pp. 207–217. Springer, Berlin (2013)
Fortin, S., Lombardi, O., Martínez González, J.C.: A new application of the modal-Hamiltonian interpretation of quantum mechanics: the problem of optical isomerism. Stud. Hist. Philos. Mod. Phys. 62, 123–135 (2018)
Lombardi, O., Fortin, S.: The role of symmetry in the interpretation of quantum mechanics. Electron. J. Theor. Phys. 12, 255–272 (2015)
Da Costa, N., Lombardi, O.: Quantum mechanics: ontology without individuals. Found. Phys. 44, 1246–1257 (2014)
Da Costa, N., Lombardi, O., Lastiri, M.: A modal ontology of properties for quantum mechanics. Synthese 190, 3671–3693 (2013)
Fortin, S., Lombardi, O.: Entanglement and indistinguishability in a quantum ontology of properties. Stud. Hist. Philos. Sci. (Forthcoming, 2021)
Lombardi, O., Dieks, D.: Particles in a quantum ontology of properties. In: Bigaj, T., Wüthrich, C. (eds.) Metaphysics in Contemporary Physics, pp. 123–143. Brill-Rodopi, Leiden (2016)
Omnés, R.: The Interpretation of Quantum Mechanics. Princeton University Press, Princeton (1994)
Omnés, R.: Understanding Quantum Mechanics. Princeton University Press, Princeton (1999)
Albert, D., Loewer, B.: Wanted dead or alive: two attempts to solve Schrödinger’s paradox. In: Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, vol. 1, pp. 277–285. Philosophy of Science Association, East Lansing (1990)
Albert, D., Loewer, B.: Non-ideal measurements. Found. Phys. Lett. 6, 297–305 (1993)
Elby, A.: Why ‘modal’ interpretations don’t solve the measurement problem. Found. Phys. Lett. 6, 5–19 (1993)
Lombardi, O., Fortin, S., López, C.: Measurement, interpretation and information. Entropy 17, 7310–7330 (2015)
Cohen-Tannoudji, C., Diu, B., Lalöe, F.: Quantum Mechanics. Wiley, New York (1977)
Laura, R., Vanni, L.: Conditional probabilities and collapse in quantum measurements. Int. J. Theor. Phys. 47, 2382–2392 (2008)
Faye, J.: Copenhagen interpretation of quantum mechanics. In: Zalta, E.N (ed.) Stanford Encyclopedia of Philosophy (Winter 2019 Edition). Stanford University, Stanford. https://plato.stanford.edu/entries/qm-copenhagen/ (2019)
Ghirardi, G.C., Rimini, A., Weber, T.: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470–491 (1986)
De Witt, B.: Quantum mechanics and reality. Phys. Today 23, 30–35 (1970)
Vermaas, P.E.: Unique transition probabilities in the modal interpretation. Stud. Hist. Philos. Mod. Phys. 27, 133–159 (1996)
Earman, J.: An attempt to add a little direction to «the problem of the direction of time». Philos. Sci. 41, 15–47 (1974)
Castagnino, M., Lara, L., Lombardi, O.: The cosmological origin of time-asymmetry. Class. Quantum Gravity 20, 369–391 (2003)
Castagnino, M., Lombardi, O.: The generic nature of the global and non-entropic arrow of time and the double role of the energy-momentum tensor. J. Phys. A 37, 4445–4463 (2004)
Castagnino, M., Lombardi, O.: The global non-entropic arrow of time: from global geometrical asymmetry to local energy flow. Synthese 169, 1–25 (2009)
Castagnino, M., Lombardi, O., Lara, L.: The global arrow of time as a geometrical property of the universe. Found. Phys. 33, 877–912 (2003)
Gryb, S., Thébault, K.: Time remains. Br. J. Philos. Sci. 67, 663–705 (2016)
Hawking, S., Ellis, G.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)
Rovelli, C.: The disappearance of space and time. In: Dieks, D. (ed.) The Ontology of Spacetime, pp. 25–35. Elsevier, Amsterdam (2006)
Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637–1678 (1996)
Laudisa, F., Rovelli, C.: Relational quantum mechanics. In: Zalta, E.N (ed) Stanford Encyclopedia of Philosophy (Spring 2021 Edition). Stanford University, Stanford. https://plato.stanford.edu/entries/qm-relational/ (2021)
Acknowledgements
This work was supported by grant ID-61785 of the John Templeton Foundation and by grant PICT-04519 of the Agencia Nacional de Promoción Científica y Tecnológica of Argentina.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fortin, S., Lombardi, O. & Pasqualini, M. Relational Event-Time in Quantum Mechanics. Found Phys 52, 10 (2022). https://doi.org/10.1007/s10701-021-00528-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-021-00528-8