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A Dissolution of the Problem of Locality

Published online by Cambridge University Press:  28 February 2022

Simon Saunders
Simon Saunders*
Affiliation:
Harvard University
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Extract

Relativistic quantum theory poses a number of conceptual problems over and above the non-relativistic mechanics. From a purely mathematical point of view it is also much more sophisticated. Even the kinematic theory poses considerable difficulties: locality, antimatter, negative energy, and charge are already systematically linked in ways that cannot simply be paraphrased. A further complication is that in the midst of this structure we have what is usually called the Newton-Wigner representation (or, in the case of the Dirac theory, the Foldy-Wouthuysen representation), in which fields and states are no longer covariantly described and where the “local” self-adjoint quantities (NW-local observables) do not obey microcausality, but only satisfy equal-time commutators with respect to a particular inertial frame. If we pass to this represenation, we obtain at a stroke the basic structure of non-relativistic quantum field theory; it is not too hard to descend from that to a many-particle mechanics, and to recover the usual definitions of localization.

Type
Part III. Fields, Particles and Quantum Theories
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1994 , Issue 2: Volume Two: Symposia and Invited Papers 1994 , 1994 , pp. 88 - 98
Copyright
Copyright © 1995 by the Philosophy of Science Association

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Footnotes

1

I would like to thank David Malement and Gordon Fleming for a number of illuminating discussions.

References

Emch, G. (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York: Wiley Interscience.Google Scholar
Enss, V. (1975), “Characterization of Particles by Means of Local Observables”, Communications in Mathematical Physics 45: 35–52.10.1007/BF01609864CrossRefGoogle Scholar
Fleming, G. (1988), “Lorentz Invariant State Reduction, and Localization”, Proceedings of the Philosophy of Science Association 2: 112-26.Google Scholar
Hergerfelt, G.C. (1974), “Remark on Causality and Particle Localization”, Physical Review D22: 377.Google Scholar
Haag, R. (1992), Local Quantum Physics. Berlin: Springer-Verlag.10.1007/978-3-642-97306-2CrossRefGoogle Scholar
Hylton, P. (1990), Russell, Idealism, and the Emergence of Analytic Philosophy. Oxford: Clarendon Press.Google Scholar
Lüders, G. (1951), “Über die Zustandsänderung durch den Messprozess”, Annalen der Physik 8: 322-28.Google Scholar
Malement, D. (1995), “In Defence of Orthodoxy”, in Clifton, R., (ed.), Reality and Experience. Dordrecht: Kluwer.Google Scholar
Newton, T. and Wigner, E. (1949), “Localized States for Elementary Systems”, Reviews of Modern Physics 21: 400–406.10.1103/RevModPhys.21.400CrossRefGoogle Scholar
Post, H. (1970), “Correspondence, Invariance, and Heuristics: In Praise of Conservative Induction”, Studies in History and Philosophy of Science 2: 213-55.10.1016/0039-3681(71)90042-2CrossRefGoogle Scholar
Quine, W.V. (1990), In Pursuit of Truth. Cambridge: Harvard University Press.Google Scholar
Saunders, S. (1992) “Locality, Complex Numbers, and Relativistic Quantum Theory”, Proceedings of the Philosophy of Science Association 1: 365-80.Google Scholar
Saunders, S. (1991), “The Negative-energy Sea”, in Saunders, S. and Brown, H., (eds.), The Philosophy of Vacuum. Oxford: Clarendon Press.Google Scholar
Segal, I. (1964), “Quantum Fields and Analysis in the Solution Manifolds of Differential Equations”, in Martin, W. and Segal, I., (eds.), Analysis in Function Space. Cambridge, MIT Press.Google Scholar
Streater, R. and Wightman, A. (1964), PCT, Spin and Statistics, and All That. Reading: Addison-Wesley.Google Scholar
Varadarajan, V. (1970), Geometry of Quantum Theory, Vol.2. Princeton: Van Nostrand.Google Scholar
Wightman, A. (1962), ‘Localizability of Quantum Mechanical Systems’, Reviews of Modern Physics 34: 845-72.10.1103/RevModPhys.34.845CrossRefGoogle Scholar
Wald, R. (1994), Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago: University of Chicago Press.Google Scholar