Abstract
An introductory outline of measurements in relativistic quantum theory is given. Following the ideas of Aharonov and Albert, the apparent paradoxes of causality for nonlocal measurements and of the instantaneity of the state vector reduction are discussed. A relativistically covariant prescription for measurements of local and nonlocal observables is presented. The selective measurement of nonlocal observables is formulated in terms of the state vectors of the quantum object and of the corresponding quantum probe. Finally, some general conclusions concerning the constraints imposed by causality on the measurability of operators and states are drawn.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1968).
Y. Aharonov and D.Z. Albert, Phys. Rev. D 24, 359 (1981).
L. Landau and R. Peierls, Z. Phys. 69, 56 (1931).
N. Bohr and L. Rosenfeld, Zur Frage der Meßbarkeit der elektromagnetischen Feldgrößen, Kopenhagen, 1933.
K.-E. Hellwig and K. Kraus, Phys. Rev. D 1, 566 (1970).
Y. Aharonov and D. Z. Albert, Phys. Rev. D 21, 3316 (1980).
O. Cohen and B. J. Hiley, Foundations of Physics 25, 1669 (1995).
Y. Aharonov and D. Z. Albert, Phys. Rev. D 29, 228 (1984).
V.B. Braginsky and F. Ya. Khalili, Quantum Measurement (Cambridge University Press, Cambridge, 1992).
Y. Aharonov, David Z. Albert, and L. Vaidman, Phys. Rev. D 34, 1805 (1986).
S. Popescu and L. Vaidman, Phys. Rev. A 49, 4331 (1994).
C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter and Anton Zeilinger, Nature 390, 575 (1997).
L. Vaidman, Phys. Rev. A 49, 1473 (1994).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this paper
Cite this paper
Breuer, HP., Petruccione, F. (1999). State vector reduction in relativistic quantum mechanics: An introduction. In: Breuer, HP., Petruccione, F. (eds) Open Systems and Measurement in Relativistic Quantum Theory. Lecture Notes in Physics, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104397
Download citation
DOI: https://doi.org/10.1007/BFb0104397
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65978-5
Online ISBN: 978-3-540-48808-8
eBook Packages: Springer Book Archive