Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-04T19:37:56.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Reeh-Schlieder Defeats Newton-Wigner: On Alternative Localization Schemes in Relativistic Quantum Field Theory

Published online by Cambridge University Press:  01 April 2022

Hans Halvorson
Get access Rights & Permissions [Opens in a new window]

Abstract

Many of the “counterintuitive” features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I. E. Segal and, more recently, G. Fleming (in a paper entitled “Reeh-Schlieder meets Newton-Wigner”) have proposed an alternative “Newton-Wigner” localization scheme that avoids the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner localization scheme and clarify the limited extent to which it avoids the counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that there is no coherent interpretation of the Newton-Wigner localization scheme that renders it free from act-outcome correlations at spacelike separation.

Type
Research Article
Information
Philosophy of Science , Volume 68 , Issue 1 , March 2001 , pp. 111 - 133
Copyright
Copyright © 2001 by 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

†

I would like to thank Jeremy Butterfield, Gordon Fleming, Bernard Kay, David Malament, and especially Rob Clifton for helpful discussions.

References

Araki, Huzihiro (1964), “Types of von Neumann algebras of local observables for the free scalar field”, Progress of Theoretical Physics 32: 956–961.CrossRefGoogle Scholar
Baez, John, Segal, Irving, and Zhou, Zhengfang (1992), Introduction to Algebraic and Constructive Quantum Field Theory, Princeton, N.J.: Princeton University Press.CrossRefGoogle Scholar
Bratteli, Ola and Robinson, Derek (1997), Operator Algebras and Quantum Statistical Mechanics, Vol. 2. NY: Springer.CrossRefGoogle Scholar
Clifton, Rob, Feldman, David, Halvorson, Hans, Redhead, Michael, and Wilce, Alex (1998), “Superentangled states”, Physical Review A 58: 135–145.CrossRefGoogle Scholar
Clifton, Rob and Halvorson, Hans (2000), “Entanglement and open systems in algebraic quantum field theory”, Studies in the History and Philosophy of Modern Physics, forthcoming.CrossRefGoogle Scholar
Fleming, Gordon (2000), “Reeh-Schlieder meets Newton-Wigner”, Philosophy of Science 67 (Proceedings): S495–S515.CrossRefGoogle Scholar
Fleming, Gordon, and Butterfield, Jeremy (1999), “Strange positions”, in Butterfield, Jeremy and Pagonis, Constantine (eds.), From Physics to Philosophy, NY: Cambridge University Press.Google Scholar
Haag, Rudolf (1992), Local Quantum Physics. NY: Springer.CrossRefGoogle Scholar
Halvorson, Hans and Clifton, Rob (2000), “Generic Bell correlation between arbitrary local algebras in quantum field theory”, Journal of Mathematical Physics 41: 1711–1717.CrossRefGoogle Scholar
Horuzhy, Sergei (1988), Introduction to Algebraic Quantum Field Theory. Dordrecht: Kluwer.Google Scholar
Kadison, Richard V. (1970), “Some analytic methods in the theory of operator algebras”, in Taam, C. T. (ed.), Lectures in Modern Analysis and Applications, Vol. II. NY: Springer, 8–29.Google Scholar
Kay, Bernard (1979), “A uniqueness result in the Segal-Weinless approach to linear Bose fields”, Journal of Mathematical Physics 20: 1712–1713.CrossRefGoogle Scholar
Malament, David (1996), “In defense of dogma: Why there cannot be a relativistic quantum mechanics of (localizable) particles”, in Clifton, Rob (ed.), Perspectives on Quantum Reality. Dordrecht: Kluwer, 1–10.Google Scholar
Petz, Dénes (1990), An Invitation to the Algebra of Canonical Commutation Relations. Leuven University Press.Google Scholar
Redhead, Michael (1995a), “More ado about nothing”, Foundations of Physics 25: 123–137.CrossRefGoogle Scholar
Redhead, Michael (1995b), “The vacuum in relativistic quantum field theory”, in Hull, David, Forbes, Micky, and Burian, Richard M. (eds.), PSA 1994, v. 2. East Lansing, MI: Philosophy of Science Association, 77–87.Google Scholar
Saunders, Simon (1992), “Locality, complex numbers, and relativistic quantum theory”, in Hull, David, Forbes, Micky, and Okruhlik, Kathleen (eds.), PSA 1992, v. 1. East Lansing, MI: Philosophy of Science Association, 365–380.Google Scholar
Segal, Irving E. (1964), “Quantum fields and analysis in the solution manifolds of differential equations”, in Martin, William T. and Segal, Irving E., (eds.), Proceedings of a Conference on the Theory and Applications of Analysis in Function Space. Cambridge: MIT Press, 129–153.Google Scholar
Segal, Irving E., and Goodman, Roe W. (1965), “Anti-locality of certain Lorentz-invariant operators”, Journal of Mathematics and Mechanics 14: 629–638.Google Scholar
Summers, Stephen J. and Werner, Reinhard (1985), “The vacuum violates Bell's inequalities”, Physics Letters 110A: 257–259.CrossRefGoogle Scholar