Abstract
The Everett-interpretation description of isolated measurements, i.e., measurements involving interaction between a measuring apparatus and a measured system but not interaction with the environment, is shown to be unambiguous, claims in the literature to the contrary notwithstanding. The appearance of ambiguity in such measurements is engendered by the fact that, in the Schrödinger picture, information on splitting into Everett copies must be inferred from the history of the combined system. In the Heisenberg picture this information is contained in mathematical quantities associated with a single time.
Similar content being viewed by others
REFERENCES
H. Everett III, “\lsRelative state\rs formulation of quantum mechanics,” Rev. Mod. Phys. 29, 454–462 (1957); reprinted in [2].
B. S. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics (Princeton University, Princeton, NJ, 1973).
M. C. Price, “The Everett FAQ,” http://www.hedweb.com/manworld.htm (1995).
L. Vaidman, “Many-worlds interpretation of quantum mechanics,” in Stanford Encyclopedia of Philosophy (Summer 2002 edn.), E. N. Zalta, ed.; http://plato.stanford.edu/archives/sum2002/entries/qm-manyworlds.
W. H. Zurek, “Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?,” Phys. Rev. D 24, 1516–1525 (1981).
W. H. Zurek, “Environment-induced superselection rules,” Phys. Rev. D 26, 1862–1880 (1982).
H. P. Stapp, “The basis problem in many-worlds theories,” Can. J. Phys. 86, 1043–1052 (2002); quant-ph/0110148.
W. H. Zurek, “Decoherence and the transition from quantum to classical\3-revisited,” Los Alamos Science 27, 2–25 (2002); quant-ph/0306072.
J. Barrett, “Everett's relative-state formulation of quantum mechanics”, in Stanford Encyclopedia of Philosophy (Spring 2003 Edition), E. N. Zalta, ed.; http://plato.stanford.edu/archives/spr2003/entries/qm-everett/.
W. H. Zurek, “Quantum Darwinism and envariance,” quant-ph/0308163 (2003).
B. DeWitt, “The quantum mechanics of isolated systems,” Int. J. Mod. Phys. A 13, 1881–1916 (1998).
B. S. DeWitt, “The many-universes interpretation of quantum mechanics,” in Proceedings of the International School of Physics “Enrico Fermi” Course IL: Foundations of Quantum Mechanics (Academic Press, New York, 1972). Reprinted in [2].
L. E. Ballentine, “Can the statistical postulate of quantum theory be derived?\3-a critique of the many-universes interpretation,” Found. Phys. 3, 229–240 (1973).
L. Vaidman, “On schizophrenic experiences of the neutron or why we should believe in the many-worlds interpretation of quantum theory,” Int. Stud. Phil. Sci. 12, 245–261 (1998); quant-ph/9609006.
D. Deutsch, and P. Hayden, “Information flow in entangled quantum systems,” Proc. R. Soc. Lond. A 456, 1759–1774 (2000); quant-ph/9906007.
M. A. Rubin, “Locality in the Everett interpretation of Heisenberg-picture quantum mechanics,” Found. Phys. Lett. 14, 301–322 (2001); quant-ph/0103079.
M. A. Rubin, “Relative frequency and probability in the Everett interpretation of Heisenberg-picture quantum mechanics,” Found. Phys. 33, 379–405 (2003); quant-ph/0209055.
B. d'Espagnat, Conceptual Foundations of Quantum Mechanics, 2nd edn. (Benjamin, Reading, MA, 1976).
C. Kiefer and E. Joos, “Decoherence: Concepts and Examples,” in P. Blanchard and A. Jadczyk, eds., Quantum Future (Springer, Berlin, 1998); quant-ph/9803052.
M. A. Rubin, “Locality in the Everett interpretation of quantum field theory,” Found. Phys. 32, 1495–1523 (2002); quant-ph/0204024.
E. Joos and H. D. Zeh, “The emergence of classical properties through interaction with the environment,” Z. Phys. B59, 223–243 (1985).
K. Hornberger and J. E. Sipe, “Collisional decoherence reexamined,” Phys. Rev. A 68, 012105 (2003); quant-ph/0303094.
K. Hornberger, S. Uttenhaler, B. Brezger, L. Hackermueller, M. Arndt and A. Zeilinger, “Collisional decoherence observed in matter wave interferometry,” Phys. Rev. Lett. 90, 160401 (2003); quant-ph/0303093.
L. Hackermueller, K. Hornberger, B. Brezger, A. Zeilinger, and M. Arndt, “Decoherence in a Talbot-Lau interferometer: the influence of molecular scattering,” Appl. Phys. B 77, 781–787 (2003); quant-ph/0307238.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (University Press, Cambridge, 2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rubin, M.A. There Is No Basis Ambiguity in Everett Quantum Mechanics. Found Phys Lett 17, 323–341 (2004). https://doi.org/10.1023/B:FOPL.0000035668.37005.e0
Published:
Issue Date:
DOI: https://doi.org/10.1023/B:FOPL.0000035668.37005.e0