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Spatial Degrees of Freedom in Everett Quantum Mechanics

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Abstract

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a “core basis problem.” To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus.

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References

  1. Everett H. III, (1957). “ ‘Relative state’ formulation of quantum mechanics”. Rev. Mod. Phys. 29, 454–462 Reprinted in Ref. 2

    Article  MathSciNet  ADS  Google Scholar 

  2. DeWitt B.S., Graham N. ed. (1973). The Many Worlds Interpretation of Quantum Mechanics. Princeton University, Princeton, NJ

    Google Scholar 

  3. M. C. Price, “The Everett FAQ,” http://www.hedweb.com/manworld.htm (1995).

  4. L. Vaidman, “Many-worlds interpretation of quantum mechanics,” in Stanford Encyclopedia of Philosophy (Summer 2002 Edition), E. N. Zalta, ed., http://plato. stanford.edu/archives/sum2002/entries/qm-manyworlds.

  5. Zurek W.H. (1981). “Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?”. Phys. Rev. D 24, 1516–1525

    Article  MathSciNet  ADS  Google Scholar 

  6. Zurek W.H. (1982). “Environment-induced superselection rules”. Phys. Rev. D 26, 1862–1880

    Article  MathSciNet  ADS  Google Scholar 

  7. Zurek W.H. (2002) “Decoherence and the transition from quantum to classical—revisited”. Los Alamos Science 27, 2–25 quant-ph/0306072

    Google Scholar 

  8. 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/.

  9. W. H. Zurek “Quantum Darwinism and envariance,” quant-ph/0308163 (2003).

  10. Rubin M.A. (2004) “There is no basis ambiguity in Everett quantum mechanics”. Found. Phys. Lett. 17, 323–341 quant-ph/0310186

    Article  MATH  MathSciNet  Google Scholar 

  11. 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, B. d’Espagnat, ed. (Academic, New York, 1972). Reprinted in Ref. 2.

  12. DeWitt B. (1998). “The quantum mechanics of isolated systems”. Int. J. Mod. Phys. A 13, 1881–1916

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. Schlosshauer M. (2004) “Decoherence, the measurement problem, and interpretations of quantum mechanics”. Rev. Mod. Phys 76, 1267–1305 quant-ph/0312059

    Article  ADS  Google Scholar 

  14. Stapp H.P. (2002) “The basis problem in many-worlds theories”. Can. J. Phys. 86, 1043–1052 quant-ph/0110148

    Article  ADS  Google Scholar 

  15. Rubin M.A. (2001) “Locality in the Everett interpretation of Heisenberg-picture quantum mechanics”. Found. Phys. Lett. 14, 301–322 quant-ph/0103079

    Article  MathSciNet  Google Scholar 

  16. Rubin M.A. (2003) “Relative frequency and probability in the Everett interpretation of Heisenberg-picture quantum mechanics”. Found. Phys. 33, 379–405 quant-ph/ 0209055

    Article  MathSciNet  Google Scholar 

  17. Rubin M.A. (2002) “Locality in the Everett interpretation of quantum field theory”. Found. Phys. 32, 1495–1523 quant-ph/0204024

    Article  MathSciNet  Google Scholar 

  18. d’Espagnat B. (1976). Conceptual Foundations of Quantum Mechanics, 2nd edn. Benjamin, Reading, MA

    Google Scholar 

  19. F. J. Tipler, “Does quantum nonlocality exist? Bell’s theorem and the many-worlds interpretation,” quant-ph/0003146.

  20. Deutsch D., Hayden P. (2000) “Information flow in entangled quantum systems”. Proc. R. Soc. Lond. A 456, 1759–1774 quant-ph/9906007

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Cramér H. (1946). Mathematical Methods of Statistics. Princeton University, Princeton, NJ

    MATH  Google Scholar 

  22. Pólya G. (1968). Mathematics and Plausible Reasoning, Vol. II, 2nd. edn. Princeton University, Princeton, NJ

    MATH  Google Scholar 

  23. Halliwell J.J. (1999) “Somewhere in the universe: Where is the information stored when histories decohere?”. Phys. Rev. D 60, 105031 quant-ph/9902008

    Article  MathSciNet  ADS  Google Scholar 

  24. Ballentine L.E. (1998). Quantum Mechanics: A Modern Development. World Scientific, Singapore

    MATH  Google Scholar 

  25. Rosenlicht M. (1986). Introduction to Analysis. Dover, Mineola, NY

    MATH  Google Scholar 

  26. d’Espagnat B. (2001). “A note on measurement”. Phys. Lett. A 282, 133–137

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. D. N. Page,“Probabilities don’t matter,” in Proceedings of the 7th Marcel Grossmann Meeting on General Relativity, M. Keiser and R. T. Jantsen, eds. (World Scientific, Singapore, 1995); gr-qc/9411004.

  28. D. N. Page,“Sensible quantum mechanics: Are only perceptions probabilistic?” quant-ph/9506010.

  29. Page D.N. (1996) “Sensible quantum mechanics: Are probabilities only in the mind?”. Int. J. Mod. Phys. D 5, 583–596 gr-qc/9507042

    Article  MathSciNet  ADS  Google Scholar 

  30. Gaillard M.K., Grannis P.D., Sciulli F.J. (1999). “The standard model of particle physics”. Rev. Mod. Phys. 71, S96–S111

    Article  Google Scholar 

  31. Brown L. (1992). Quantum Field Theory. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  32. Weinberg S. (1995). The Quantum Theory of Fields: Vol. I, Foundations. Cambridge University Press, Cambridge

    Google Scholar 

  33. Joos E. (1987). “Comment on ‘Unified dynamics for microscopic and macroscopic systems”’. Phys Rev. D 36, 3285–3286

    Article  MathSciNet  ADS  Google Scholar 

  34. Kandel E.R., Schwartz J.H., Jessell T.M. (2000). Principles of Neural Science, 4th edn. McGraw-Hill, New York

    Google Scholar 

  35. A. Shimony, “Comments on Legett’s ‘macroscopic realism’,” in Quantum Measurement: Beyond Paradox R. A. Healey and G. Hellman, eds. (University of Minnesota Press, Minneapolis, 1998).

  36. P. St. Hilaire, D. Bierman, and S. Hameroff, “Quantum states in the retina,”http://www.quantumconsciousness.org/views/QuantumStatesRetina.html (2002).

  37. Schlosshauer M. (2006) “Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics”. Ann. Phys. 321, 112–149 quant-ph/0506199

    Article  MATH  ADS  Google Scholar 

  38. Thaheld F.T. (2005) “Does consciousness really collapse the wave function? A possible objective biophysical resolution to the measurement problem”. BioSystems 81, 113–124 quant-ph/050942

    Article  Google Scholar 

  39. F. T. Thaheld, “Comment on ‘Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics’,” quant-ph/0602190.

  40. P. van Esch, “On the Everett programme and the Born rule,” quant-ph/0505059.

  41. Friedman J.R., Patel V., Chen W., Tolpygo S.K., Lukens J.E. (2000) “Detection of a Schrödinger’s cat state in an rf-SQUID”. Nature 406, 43–46 cond-mat/0004293

    Article  ADS  Google Scholar 

  42. J. J. Halliwell, “Some recent developments in the decoherent histories approach to quantum theory,” in Decoherence and Entropy in Complex Systems: Selected Lectures from DICE 2002 H.-T. Elze, ed. (Springer, Berlin, 2004); quant-ph/0301117.

  43. Joos E., Zeh H.D. (1985). “The emergence of classical properties through interaction with the environment”. Z. Phys. B 59, 223–243

    Article  ADS  Google Scholar 

  44. Hornberger K., Sipe J.E. (2003) “Collisional decoherence reexamined”. Phys. Rev. A 68, 012105 quant-ph/0303094

    Article  ADS  Google Scholar 

  45. Hornberger K., Uttenhaler S., Brezger B., Hackermueller L., Arndt M., Zeilinger A. (2003) “Collisional decoherence observed in matter wave interferometry”. Phys. Rev. Lett. 90, 160401 quant-ph/0303093

    Article  ADS  Google Scholar 

  46. Hackermueller L., Hornberger K., Brezger B., Zeilinger A., Arndt M. (2003) “Decoherence in a Talbot-Lau interferometer: the influence of molecular scattering”. Appl. Phys. B 77, 781–787 quant-ph/0307238

    Article  ADS  Google Scholar 

  47. Hackermueller L., Uttenthaler S., Hornberger K., Reiger E., Brezger B., Zeilinger A., Arndt M. (2003) “The wave nature of biomolecules and fluorofullerenes”. Phys. Rev. Lett. 91, 090408 quant-ph/0309016

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Lincoln Laboratory, Massachusetts Institute of Technology, 244 Wood Street, Lexington, MA, 02420-9185, USA

    Mark A. Rubin

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  1. Mark A. Rubin
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Correspondence to Mark A. Rubin.

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This work was sponsored by the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the U.S. Government.

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Rubin, M.A. Spatial Degrees of Freedom in Everett Quantum Mechanics. Found Phys 36, 1115–1159 (2006). https://doi.org/10.1007/s10701-006-9062-z

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  • DOI: https://doi.org/10.1007/s10701-006-9062-z

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