The Modal-Hamiltonian Interpretation and the Relational Nature of Time
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Abstract
The Modal-Hamiltonian Interpretation was introduced to solve certain interpretation problems related to its ontology and quantum measurement. Its actualization rule establishes that every closed system has its energy well defined. Taking into account the uncertainty relation between energy and time, a well-defined energy there is a challenge regarding the temporal situation of these systems. In this work we analyze the problem of time in closed systems and we propose a reconstruction of a relational time compatible with the holistic perspective.
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Pasqualini, M., & Fortin, S. (2022). The Modal-Hamiltonian Interpretation and the Relational Nature of Time. Crítica. Revista Hispanoamericana De Filosofía, 54(161), 3–42. https://doi.org/10.22201/iifs.18704905e.2022.1320
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References
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Ardenghi, J.S., M. Castagnino y O. Lombardi, 2009, “Quantum Mechanics: Modal Interpretation and Galilean Transformations”, Foundations of Physics, vol. 39, pp. 1023–1045.
Baierlein, R.F., D.H. Sharp y J.A. Wheeler, 1962, “Three-Dimensional Geometry as Carrier of Information about Time”, Phys. Rev., vol. 126, no. 5, p. 1864.
Ballentine, L., 1998, Quantum Mechanics: A Modern Development, World Scientific, Singapore.
Barbour, J., 1999, The End of Time: The Next Revolution in Physics, Oxford University Press, Oxford.
Barbour, J., 1982, “Relational Concepts of Space and Time”, The British Journal for the Philosophy of Science, vol. 33, no. 3, pp. 251–274.
Barbour, J.B. y B. Bertotti, 1982, “Mach’s Principle and the Structure of Dynamical Theories”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 382, no. 1783, pp. 295–306.
Busch, P., 2008, “The Time–Energy Uncertainty Relation”, en J. Muga, R.S. Mayato, Í. Egusquiza (eds.), Time in Quantum Mechanics. Lecture Notes in Physics, vol. 734, Springer, Berlin, Heidelberg.
Busch, P., 1990a, “On the Energy-Time Uncertainty Relation. Part I: Dynamical Time and Time Indeterminacy”, Foundations of Physics, vol. 20, pp. 1–32.
Busch, P., 1990b, “On the Energy-Time Uncertainty Relation. Part II: Pragmatic Time Versus Energy Indeterminacy”, Foundations of Physics, vol. 20, pp. 33–43.
Castagnino, M. y O. Lombardi, 2008, “The Role of the Hamiltonian in the Interpretation of Quantum Mechanics”, Journal of Physics. Conferences Series, vol. 128, 012014.
Da Costa, N. y O. Lombardi, 2014, “Quantum Mechanics: Ontology without Individuals”, Foundations of Physics, vol. 44, pp. 1246–1257.
Da Costa, N., O. Lombardi y M. Lastiri, 2013, “A Modal Ontology of Properties for Quantum Mechanics”, Synthese, vol. 190, pp. 3671–3693.
Earman, J., 2015, “Some Puzzles and Unresolved Issues about Quantum Entanglement”, Erkenntnis, vol. 80, pp. 303–337. (https://doi.org/10.1007/s10670-014-9627-8)
Fortin, S. y C. López, 2016, “Problemas ontológicos de la mecánica cuántica”, en C.E. Vanney, I. Silva y J.F. Franck (eds.), Diccionario Interdisciplinar Austral. (http://dia.austral.edu.ar/Problemas_ontológicos_de_la_mecánica_cuántica)
Haag, R., 1993, “Local Quantum Physics and Models”, Commun. Math. Phys., vol. 155, pp. 199–204.
Horn, L.R., 2018, “Contradiction”, en E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. (https://plato.stanford.edu/archives/win2018/entries/contradiction/)
Kuchaˇr, K., 2011, “Time and Interpretations of Quantum Gravity”, International Journal of Modern Physics, vol. 20, supp 01, pp. 3–86.
Lombardi, O., 2000, El problema del determinismo en física (tesis doctoral).
Lombardi, O. y D. Dieks, 2021, “Modal Interpretations of Quantum Mechanics”, en E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
(https://plato.stanford.edu/entries/qm-modal/)
Lombardi, O. y S. Fortin, 2015, “The Role of Symmetry in the Interpretation of Quantum Mechanics”, Electronic Journal of Theoretical Physics, vol. 12, pp. 255–272.
Lombardi, O., J.S. Ardenghi, S. Fortin y M. Castagnino, 2011, “Compatibility between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics”, Philosophy of Science, vol. 78, pp. 1024–1036.
Lombardi, O., M. Castagnino, y J.S. Ardenghi, 2010, “The Modal-Hamiltonian Interpretation and the Galilean Covariance of Quantum Mechanics”, Studies in History and Philosophy of Modern Physics, vol. 41, pp. 93–103.
Lombardi, O., S. Fortin, J. Ardenghi y M. Castagnino, 2010, Introduction to the Modal-Hamiltonian Interpretation of Quantum Mechanics, Nova Science Publishers Inc., Nueva York.
Lombardi, O. y M. Castagnino, 2008, “A Modal-Hamiltonian Interpretation of Quantum Mechanics”, Studies in History and Philosophy of Modern Physics, vol. 39, pp. 380–443.
Maudlin, T., 2019, Philosophy of Physics, Princeton University Press, Princeton.
Menzel, C., 2020, “In Defense of the Possibilism-Actualism Distinction”, Philos Stud, vol. 177, pp. 1971–1997. (https://doi.org/10.1007/s11098-019-01294-0)
Okon, E. y D. Sudarsky, 2016, “Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere”, Foundations of Physics, vol. 46, pp. 852–879.
Pooley, O. y H. Brown, 2002, “Relationalism Rehabilitated? I: Classical Mechanics”, The British Journal for the Philosophy of Science, vol. 53, no. 2, pp. 183–204.
van Fraassen, B.C., 1972, “A Formal Approach to the Philosophy of Science”, en R. Colodny (ed.), Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, University of Pittsburgh Press, Pittsburgh, pp. 303–366.
Vanni, L. y R. Laura, 2005, “Mediciones cuánticas sin colapso de la función de onda”, Anales AFA, vol. 17, no. 1, pp. 25–27.
(https://anales.fisica.org.ar/journal/index.php/analesafa/article/view/144)
Vermaas, P., 1999, A Philosopher’s Understanding of Quantum Mechanics, Cambridge University Press, Cambridge.
von Neumann, J., 1932, Mathematische Grundlagen der Quantenmechanik, Springer, Berlín.
Ardenghi, J.S. y O. Lombardi, 2012, “Interpretación modal-hamiltoniana: una versión invariante ante las transformaciones de Galileo”, en Cibelle Celestino Silva y Luis Salvatico (eds.), Filosofia e história da ciência no Cone Sul: seleção de trabalhos do 7o Encontro da AFHIC, Entrementes Editorial, Porto Alegre, pp. 222–230.
Ardenghi, J.S., M. Castagnino y O. Lombardi, 2009, “Quantum Mechanics: Modal Interpretation and Galilean Transformations”, Foundations of Physics, vol. 39, pp. 1023–1045.
Baierlein, R.F., D.H. Sharp y J.A. Wheeler, 1962, “Three-Dimensional Geometry as Carrier of Information about Time”, Phys. Rev., vol. 126, no. 5, p. 1864.
Ballentine, L., 1998, Quantum Mechanics: A Modern Development, World Scientific, Singapore.
Barbour, J., 1999, The End of Time: The Next Revolution in Physics, Oxford University Press, Oxford.
Barbour, J., 1982, “Relational Concepts of Space and Time”, The British Journal for the Philosophy of Science, vol. 33, no. 3, pp. 251–274.
Barbour, J.B. y B. Bertotti, 1982, “Mach’s Principle and the Structure of Dynamical Theories”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 382, no. 1783, pp. 295–306.
Busch, P., 2008, “The Time–Energy Uncertainty Relation”, en J. Muga, R.S. Mayato, Í. Egusquiza (eds.), Time in Quantum Mechanics. Lecture Notes in Physics, vol. 734, Springer, Berlin, Heidelberg.
Busch, P., 1990a, “On the Energy-Time Uncertainty Relation. Part I: Dynamical Time and Time Indeterminacy”, Foundations of Physics, vol. 20, pp. 1–32.
Busch, P., 1990b, “On the Energy-Time Uncertainty Relation. Part II: Pragmatic Time Versus Energy Indeterminacy”, Foundations of Physics, vol. 20, pp. 33–43.
Castagnino, M. y O. Lombardi, 2008, “The Role of the Hamiltonian in the Interpretation of Quantum Mechanics”, Journal of Physics. Conferences Series, vol. 128, 012014.
Da Costa, N. y O. Lombardi, 2014, “Quantum Mechanics: Ontology without Individuals”, Foundations of Physics, vol. 44, pp. 1246–1257.
Da Costa, N., O. Lombardi y M. Lastiri, 2013, “A Modal Ontology of Properties for Quantum Mechanics”, Synthese, vol. 190, pp. 3671–3693.
Earman, J., 2015, “Some Puzzles and Unresolved Issues about Quantum Entanglement”, Erkenntnis, vol. 80, pp. 303–337. (https://doi.org/10.1007/s10670-014-9627-8)
Fortin, S. y C. López, 2016, “Problemas ontológicos de la mecánica cuántica”, en C.E. Vanney, I. Silva y J.F. Franck (eds.), Diccionario Interdisciplinar Austral. (http://dia.austral.edu.ar/Problemas_ontológicos_de_la_mecánica_cuántica)
Haag, R., 1993, “Local Quantum Physics and Models”, Commun. Math. Phys., vol. 155, pp. 199–204.
Horn, L.R., 2018, “Contradiction”, en E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. (https://plato.stanford.edu/archives/win2018/entries/contradiction/)
Kuchaˇr, K., 2011, “Time and Interpretations of Quantum Gravity”, International Journal of Modern Physics, vol. 20, supp 01, pp. 3–86.
Lombardi, O., 2000, El problema del determinismo en física (tesis doctoral).
Lombardi, O. y D. Dieks, 2021, “Modal Interpretations of Quantum Mechanics”, en E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
(https://plato.stanford.edu/entries/qm-modal/)
Lombardi, O. y S. Fortin, 2015, “The Role of Symmetry in the Interpretation of Quantum Mechanics”, Electronic Journal of Theoretical Physics, vol. 12, pp. 255–272.
Lombardi, O., J.S. Ardenghi, S. Fortin y M. Castagnino, 2011, “Compatibility between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics”, Philosophy of Science, vol. 78, pp. 1024–1036.
Lombardi, O., M. Castagnino, y J.S. Ardenghi, 2010, “The Modal-Hamiltonian Interpretation and the Galilean Covariance of Quantum Mechanics”, Studies in History and Philosophy of Modern Physics, vol. 41, pp. 93–103.
Lombardi, O., S. Fortin, J. Ardenghi y M. Castagnino, 2010, Introduction to the Modal-Hamiltonian Interpretation of Quantum Mechanics, Nova Science Publishers Inc., Nueva York.
Lombardi, O. y M. Castagnino, 2008, “A Modal-Hamiltonian Interpretation of Quantum Mechanics”, Studies in History and Philosophy of Modern Physics, vol. 39, pp. 380–443.
Maudlin, T., 2019, Philosophy of Physics, Princeton University Press, Princeton.
Menzel, C., 2020, “In Defense of the Possibilism-Actualism Distinction”, Philos Stud, vol. 177, pp. 1971–1997. (https://doi.org/10.1007/s11098-019-01294-0)
Okon, E. y D. Sudarsky, 2016, “Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere”, Foundations of Physics, vol. 46, pp. 852–879.
Pooley, O. y H. Brown, 2002, “Relationalism Rehabilitated? I: Classical Mechanics”, The British Journal for the Philosophy of Science, vol. 53, no. 2, pp. 183–204.
van Fraassen, B.C., 1972, “A Formal Approach to the Philosophy of Science”, en R. Colodny (ed.), Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, University of Pittsburgh Press, Pittsburgh, pp. 303–366.
Vanni, L. y R. Laura, 2005, “Mediciones cuánticas sin colapso de la función de onda”, Anales AFA, vol. 17, no. 1, pp. 25–27.
(https://anales.fisica.org.ar/journal/index.php/analesafa/article/view/144)
Vermaas, P., 1999, A Philosopher’s Understanding of Quantum Mechanics, Cambridge University Press, Cambridge.
von Neumann, J., 1932, Mathematische Grundlagen der Quantenmechanik, Springer, Berlín.
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