Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-30T17:06:13.076Z Has data issue: false hasContentIssue false
  • English
  • Français

Relativistic Invariance and Modal Interpretations

Published online by Cambridge University Press:  01 January 2022

John Earman  and
Laura Ruetsche
Get access Rights & Permissions [Opens in a new window]

Abstract

A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton (2000), comes out trivial when applied to a number of systems of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do.

Type
Research Article
Information
Philosophy of Science , Volume 72 , Issue 4 , October 2005 , pp. 557 - 583
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

We are grateful to Michael Dickson, Gerard Emch, Hans Halvorson, and Wayne Myrvold for helpful comments on earlier drafts of this paper. Needless to say, this does not imply that they agree with the opinions expressed herein.

References

Arageorgis, Aristidis, Earman, John, and Ruetsche, Laura (2002), “Fulling Non-uniqueness, Rindler Quanta, and the Unruh Effect: A Primer on Some Aspects of Quantum Field Theory”, Fulling Non-uniqueness, Rindler Quanta, and the Unruh Effect: A Primer on Some Aspects of Quantum Field Theory 70:164–202.Google Scholar
Arntzenius, Frank (1998), “Curiouser and Curiouser: A Personal Evaluation of Modal Interpretations”, in Dieks, Dennis and Vermaas, Pieter (eds.), The Modal Interpretation of Quantum Mechanics. Dordrecht: Kluwer, 337–377.CrossRefGoogle Scholar
Bacciagaluppi, Guido, Donald, Matthew, and Vermaas, Pieter (1995), “Continuity and Discontinuity of Definite Properties in the Modal Interpretation”, Continuity and Discontinuity of Definite Properties in the Modal Interpretation 68:679–704.Google Scholar
Berkovitz, Jossi, and Hemmo, Meir (2005a), “Modal Interpretations of Quantum Mechanics and Relativity: A Reconsideration”, Modal Interpretations of Quantum Mechanics and Relativity: A Reconsideration 25:373–397.Google Scholar
Berkovitz, Jossi, and Hemmo, Meir (2005b), “How to Reconcile Modal Interpretations of Quantum Mechanics with Relativity”, Philosophy of Science, forthcoming.CrossRefGoogle Scholar
Bisognano, Joseph J., and Wichmann, Eyvind H. (1975), “On the Duality for a Hermitian Scalar Field”, On the Duality for a Hermitian Scalar Field 16:985–1007.Google Scholar
Bratteli, Ola, and Robinson, Derek W. (1997), Operator Algebras and Quantum Statistical Mechanics II. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Bub, Jeffrey (1997), Interpreting the Quantum World. Cambridge: Cambridge University Press.Google Scholar
Bub, Jeffrey, and Clifton, Robert (1996), “A Uniqueness Theorem for ‘No Collapse’ Interpretations of Quantum Mechanics”, A Uniqueness Theorem for ‘No Collapse’ Interpretations of Quantum Mechanics 27:181–219.Google Scholar
Clifton, Robert (2000), “The Modal Interpretation of Algebraic Quantum Field Theory”, The Modal Interpretation of Algebraic Quantum Field Theory 271:167–177.Google Scholar
Combes, François (1967), “Sur les Ėtats Factoriels d’une C*-Algebra”, Sur les Ėtats Factoriels d’une C*-Algebra 265:736–739.Google Scholar
Connes, Allain, and Rovelli, Carlo (1993), “Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in Generally Covariant Quantum Theories”, Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in Generally Covariant Quantum Theories 11:2899–2917.Google Scholar
Dickson, Michael (1995), “Faux-Boolean Algebras and Classical Models”, Faux-Boolean Algebras and Classical Models 8:401–415.Google Scholar
Dickson, Michael, and Clifton, Robert (1998), “Lorentz-Invariance in Modal Interpretations”, in Dieks, Dennis and Vermaas, Pieter (eds.), The Modal Interpretation of Quantum Mechanics. Dordrecht: Kluwer, 9–47.CrossRefGoogle Scholar
Dieks, Dennis, and Vermaas, Pieter (eds.) (1998) The Modal Interpretation of Quantum Mechanics. Dordrecht: Kluwer.CrossRefGoogle Scholar
Doplicher, Sergio, and Longo, Roberto (1984), “Standard and Split Inclusions of von Neumann Algebras”, Standard and Split Inclusions of von Neumann Algebras 74:493–536.Google Scholar
Driessler, Walt (1975), “Comments on Lightlike Translations and Applications in Relativistic Quantum Field Theory”, Comments on Lightlike Translations and Applications in Relativistic Quantum Field Theory 44:133–141.Google Scholar
Emch, Gerard (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York; Wiley-Interscience.Google Scholar
Emch, Gerard. (1984), Mathematical and Conceptual Foundations of 20th-Century Physics. New York: North-Holland.Google Scholar
Fleming, Gordon N. (1996), “Just How Radical Is Hyperplane Dependence?”, in Clifton, R. (ed.), Perspectives on Quantum Reality. Dordrecht: Kluwer, 11–28.CrossRefGoogle Scholar
Fleming, Gordon N.. (2000), “Reeh-Schleider Meets Newton-Wigner”, Reeh-Schleider Meets Newton-Wigner 69 (Proceedings): S495–S515.Google Scholar
Fleming, Gordon N.. (2003), “Observations on Hyperplanes: I. State Reduction and Unitary Evolution”, e-print at http://philsci-archive.pitt.edu/archive/00001533/.Google Scholar
Fredenhagen, Klaus (1987), “Structure of Local Algebras of Observables”, Structure of Local Algebras of Observables 62:153–165.Google Scholar
Haag, Rudolf (1996), Local Quantum Physics. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Healey, Richard (1989), The Philosophy of Quantum Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Healey, Richard, and Hellman, Geoffrey (eds.) (1998), Quantum Measurement, Decoherence, and Modal Interpretations. Minnesota Studies in the Philosophy of Science, vol. 17. Minneapolis: University of Minnesota Press.Google Scholar
Hislop, Peter D., and Longo, Roberto (1982), “Modular Structure of the Local Algebras Associated with the Free Massless Scalar Field”, Modular Structure of the Local Algebras Associated with the Free Massless Scalar Field 84:71–85.Google Scholar
Horuzhy, Sergei S. (1990), Introduction to Algebraic Quantum Field Theory. Dordrecht: Kluwer.Google Scholar
Hugenholtz, Nicolaas M. (1967), “On the Factor Type of Equilibrium States in Quantum Statistical Mechanics”, On the Factor Type of Equilibrium States in Quantum Statistical Mechanics 6:189–193.Google Scholar
Kadison, Richard V., and Ringrose, John R. (1983), Fundamentals of the Theory of Operator Algebras. Vol. 1. New York: Academic Press.Google Scholar
Kadison, Richard V., and Ringrose, John R. (1986), Fundamentals of the Theory of Operator Algebras. Vol. 2. New York: Academic Press.Google Scholar
Kastler, Daniel, and Robinson, Donald W. (1966), “Invariant States in Statistical Mechanics”, Invariant States in Statistical Mechanics 3:151–180.Google Scholar
Kitajima, Yuichiro (2004), “A Remark on the Modal Interpretation of Algebraic Quantum Field Theory”, A Remark on the Modal Interpretation of Algebraic Quantum Field Theory 331:181–186.Google Scholar
Kochen, Simon (1985), “A New Interpretation of Quantum Mechanics”, in Lahti, Pekka and Mittelstaedt, Paul (eds.), Symposium on the Foundations of Modern Physics. Teaneck, NJ: Word Scientific Publishing Co., 151–170.Google Scholar
Lévy-Leblond, Jean-Marc (1967), “Galilean Quantum Field Theories and a Ghostless Lee Model”, Galilean Quantum Field Theories and a Ghostless Lee Model 3:151–180.Google Scholar
Longo, Roberto (1982), “Algebraic and Modular Structure of von Neumann Algebras of Physics”, Algebraic and Modular Structure of von Neumann Algebras of Physics Vol. 38, part 2, 551–565.Google Scholar
Myrvold, Wayne (2002), “Modal Interpretations and Relativity”, Modal Interpretations and Relativity 32:1773–1784.Google Scholar
Myrvold, Wayne. (2005), “Chasing Chimeras”, preprint.Google Scholar
Pedersen, Gert K., and Takesaki, Masamichi (1973), “The Radon-Nikodym Theorem for von Neumann Algebras”, The Radon-Nikodym Theorem for von Neumann Algebras 130:53–87.Google Scholar
Rovelli, Carlo (1993), “Statistical Mechanics of Gravity and the Thermodynamical Origin of Time”, Statistical Mechanics of Gravity and the Thermodynamical Origin of Time 10:1549–1566.Google Scholar
Ruelle, David (1966), “States of Physical Systems”, States of Physical Systems 3:133–150.Google Scholar
St⊘rmer, Erling (1967), “Types of von Neumann Algebras Associated with Extremal Invariant States”, Types of von Neumann Algebras Associated with Extremal Invariant States 6:194–204.Google Scholar
van Fraassen, Bas C. (1991), Quantum Mechanics: An Empiricist View. Oxford: Oxford University Press.CrossRefGoogle Scholar
Vermaas, Pieter E. (1999), A Philosopher’s Understanding of Quantum Mechanics: Possibilities and Impossibilities of a Modal Interpretation. Cambridge: Cambridge University Press.Google Scholar
Wald, Robert M. (1994), Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago: University of Chicago Press.Google Scholar