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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.

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