Skip to main content
Log in

Quantum Locality

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is no reason to suspect any conflict between quantum theory and special relativity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bell, J.S.: Bertlmann’s socks and the nature of reality. J. Phys. (Paris) 42(C2), 41–61 (1981)

    Article  Google Scholar 

  2. Heywood, P., Redhead, M.L.G.: Nonlocality and the Kochen-Specker paradox. Found. Phys. 13, 481–499 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  3. Bell, J.S.: La nouvelle cuisine. In: Sarlemijn, A., Kross, P. (eds.) Between Science and Technology, pp. 97–115. Elsevier, Amsterdam (1990)

    Google Scholar 

  4. Albert, D.Z.: Quantum Mechanics and Experience. Harvard University Press, Cambridge (1992)

    Google Scholar 

  5. Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Found. Phys. 24, 379–384 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  6. Paty, M.: The nature of Einstein’s objections to the Copenhagen interpretation of quantum mechanics. Found. Phys. 25, 183–204 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Goldstein, S.: Quantum philosophy: the flight from reason in science. In: Gross, P.R., Levitt, N., Lewis, M.W. (eds.) The Flight From Science and Reason, pp. 119–125. New York Academy of Sciences, New York (1996)

    Google Scholar 

  8. Suarez, A., Scarani, V.: Does entanglement depend on the timing of the impacts at the beam splitters? Phys. Lett. A 232, 9–14 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  9. Maudlin, T.: Quantum Non-Locality and Relativity, 2nd edn. Wiley/Blackwell, New York (2002)

    Book  Google Scholar 

  10. Shimony, A.: Bell’s theorem. In: Zalta, E.N. (ed.) Stanford Encyclopedia of Philosophy (2004). plato.stanford.edu/entries/bell-theorem/

  11. Elitzur, A.C., Dolev, S.: Quantum phenomena within a new theory of time. In: Elitzur, A., Dolev, S., Kolenda, N. (eds.) Quo Vadis Quantum Mechanics? pp. 325–349. Springer, Berlin (2005)

    Chapter  Google Scholar 

  12. d’Espagnat, B.: On Physics and Philosophy. Princeton University Press, Princeton (2006)

    Google Scholar 

  13. Norsen, T.: Bell locality and the nonlocal character of nature. Found. Phys. Lett. 19, 633–655 (2006) quant-ph/0601205

    Article  MathSciNet  MATH  Google Scholar 

  14. Shimony, A.: Aspects of nonlocality in quantum mechanics. In: Evans, J., Thorndike, A.S. (eds.) Quantum Mechanics at the Crossroads, pp. 107–123. Springer, Berlin (2007)

    Chapter  Google Scholar 

  15. Laudisa, F.: Non-local realistic theories and the scope of the Bell theorem. Found. Phys. 38, 1110–1132 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Berkovitz, J.: Action at a distance in quantum mechanics. Stanford Encyclopedia of Philosophy. (2007). www.plato.stanford.edu/entries/qm-action-distance/

  17. Fine, A.: Joint distributions, quantum correlations, and commuting observables. J. Math. Phys. 23, 1306–1310 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  18. Fine, A.: Do correlations need to be explained? In: Cushing, J.T., McMullin, E. (eds.): Philosophical Consequences of Quantum Theory, pp. 175–194. University of Notre Dame Press, Notre Dame (1989)

    Google Scholar 

  19. de Muynck, W.M.: The Bell inequalities and their irrelevance to the problem of locality in quantum mechanics. Phys. Lett. A 114, 65–67 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  20. de Muynck, W.M., De Baere, W., Martens, H.: Interpretation of quantum mechanics, joint measurement of incompatible observables, and counterfactual definiteness. Found. Phys. 24, 1589–1664 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  21. de Muynck, W.M.: Foundations of Quantum Mechanics, an Empiricist Approach. Kluwer Academic, Dordrecht (2002)

    MATH  Google Scholar 

  22. Mermin, N.D.: What do these correlations know about reality? Nonlocality and the absurd. Found. Phys. 29, 571–587 (1999). arXiv:quant-ph/9807055

    Article  MathSciNet  Google Scholar 

  23. Smerlak, M., Rovelli, C.: Relational EPR. Found. Phys. 37, 427–445 (2007). arXiv:quant-ph/0604064v3

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Brukner, C̆., Żukowski, M.: Bell’s inequalities: foundations and quantum communication. In: Rozenberg, G., Baeck, T.H.W., Kok, J.N. (eds.) Handbook of Natural Computing. Springer, Berlin (2010). arXiv:0909.2611v1

    Google Scholar 

  25. Blaylock, G.: The EPR paradox, Bell’s inequality, and the question of locality. Am. J. Phys. 78, 111–120 (2010)

    Article  ADS  Google Scholar 

  26. Maudlin, T.: What Bell proved: A reply to Blaylock. Am J. Phys. 78, 121–125 (2010)

    Article  ADS  Google Scholar 

  27. Albert, D.Z., Galchen, R.: A quantum threat to special relativity. Sci. Am. 300(3), 32–39 (2009)

    Article  Google Scholar 

  28. Di Giuseppe, G., De Martini, F., Boschi, D.: Experimental test of the violation of local realism in quantum mechanics without Bell inequalities. Phys. Rev. A 56, 176–181 (1997)

    Article  ADS  Google Scholar 

  29. Kwiat, P.G., White, A.G., Mitchell, J.R., Nairz, O., Weihs, G., Weinfurter, H., Zeilinger, A.: High-efficiency quantum interrogation measurements via the quantum Zeno effect. Phys. Rev. Lett. 83, 4725–4728 (1999)

    Article  ADS  Google Scholar 

  30. Benenti, G., Casati, G., Strini, G.: Principles of Quantum Computation and Information, vol. I, pp. 88–91. Singapore, World Scientific (2004)

    MATH  Google Scholar 

  31. Walther, P., Aspelmeyer, M., Resch, K.J., Zeilinger, A.: Experimental violation of a cluster state Bell inequality. Phys. Rev. Lett. 95, 020403 (2005)

    Article  ADS  Google Scholar 

  32. Griffiths, D.J.: Introduction to Quantum Mechanics, 2nd edn., pp. 423–428. Prentice Hall, Upper Saddle River (2005)

    Google Scholar 

  33. Yang, T., Zhang, Q., Chen, T.-Y., Lu, S., Yin, J., Pan, J.-W., Wei, Z.-Y., Tian, J.-R., Zhang, J.: Experimental synchronization of independent entangled photon sources. Phys. Rev. Lett. 96, 110501 (2006)

    Article  ADS  Google Scholar 

  34. Gröblacher, S., Paterek, T., Kaltenbaek, R., Brukner, C̆., Żukowski, M., Aspelmeyer, M., Zeilinger, A.: An experimental test of non-local realism. Nature 446, 871–875 (2007). arXiv:0704.2529

    Article  ADS  Google Scholar 

  35. Mullin, W.J., Laloë, F.: Interference of Bose-Einstein condensates: quantum nonlocal effects. Phys. Rev. A 78, 061605 (2008)

    Article  ADS  Google Scholar 

  36. Ghirardi, G.C., Rimini, A., Weber, T.: A general argument against superluminal transmission through the quantum mechanical measurement process. Lett. Nuovo Cimento 27, 293–298 (1980)

    Article  MathSciNet  Google Scholar 

  37. Bruss, D., D’Ariano, G.M., Macchiavello, C., Sacchi, M.F.: Approximate quantum cloning and the impossibility of superluminal information transfer. Phys. Rev. A 62, 062302 (2000)

    Article  ADS  Google Scholar 

  38. Caves, C.M., Fuchs, C.A., Schack, R.: Subjective probability and quantum certainty. Studies Hist. Philos. Mod. Phys. 38, 255–274 (2007). arXiv:quant-ph/0608190

    Article  MathSciNet  MATH  Google Scholar 

  39. Bell, J.S.: Against measurement. In: Miller, A.I. (ed.) Sixty-Two Years of Uncertainty, pp. 17–31. Plenum, New York (1990)

    Google Scholar 

  40. Kuhn, T.S.: The Structure of Scientific Revolutions, 2nd edn. University of Chicago Press, Chicago (1970)

    Google Scholar 

  41. Chang, H., Cartwright, N.: Causality and realism in the EPR experiment. Erkenntnis 38, 169–190 (1993)

    Article  MathSciNet  Google Scholar 

  42. Griffiths, R.B.: Consistent histories and the interpretation of quantum mechanics. J. Stat. Phys. 36, 219–272 (1984)

    Article  ADS  MATH  Google Scholar 

  43. Omnès, R.: Logical reformulation of quantum mechanics I. Foundations. J. Stat. Phys. 53, 893–932 (1988)

    Article  ADS  MATH  Google Scholar 

  44. Gell-Mann, M., Hartle, J.B.: Quantum mechanics in the light of quantum cosmology. In: Zurek, W.H. (ed.) Complexity, Entropy and the Physics of Information, pp. 425–458. Addison-Wesley, Redwood City (1990)

    Google Scholar 

  45. Gell-Mann, M., Hartle, J.B.: Classical equations for quantum systems. Phys. Rev. D 47, 3345–3382 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  46. Griffiths, R.B.: Consistent histories and quantum reasoning. Phys. Rev. A 54, 2759–2774 (1996)

    Article  ADS  Google Scholar 

  47. Griffiths, R.B.: Choice of consistent family, and quantum incompatibility. Phys. Rev. A 57, 1604–1618 (1998). arXiv:quant-ph/9708028

    Article  ADS  Google Scholar 

  48. Omnès, R.: Understanding Quantum Mechanics. Princeton University Press, Princeton (1999)

    MATH  Google Scholar 

  49. Griffiths, R.B.: Consistent Quantum Theory. Cambridge University Press, Cambridge (2002). http://quantum.phys.cmu.edu/CQT/

    MATH  Google Scholar 

  50. Gell-Mann, M., Hartle, J.B.: Quasiclassical coarse graining and thermodynamic entropy. Phys. Rev. A 76, 022104 (2007). arXiv:quant-ph/0609190

    Article  ADS  Google Scholar 

  51. Wigner, E.P.: The problem of measurement. Am. J. Phys. 31, 6–15 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. Busch, P., Shimony, A.: Insolubility of the quantum measurement problem for unsharp observables. Stud. Hist. Phil. Mod. Phys. 27, 397–404 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  53. Mittelstaedt, P.: The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  54. Griffiths, R.B.: EPR, Bell, and Quantum Locality (2010). arXiv:1007.4281

  55. Griffiths, R.B.: Consistent histories. In: Greenberger, D., Hentschel, K., Weinert, F. (eds.) Compendium of Quantum Physics, pp. 117–122. Springer, Berlin (2009)

    Chapter  Google Scholar 

  56. Hohenberg, P.C.: An introduction to consistent quantum theory (2010). arXiv:0909.2359v3

  57. Bohm, D.: Quantum Theory. Englewood Cliffs, Prentice Hall (1951), chapter 22

    Google Scholar 

  58. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

  59. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  60. Greenberger, D.M., Horne, M., Zeilinger, A.: Going beyond Bell’s theorem. In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory and Conceptions of the Universe, pp. 69–72. Kluwer, Dordrecht (1989)

    Google Scholar 

  61. Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58, 1131–1143 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  62. Hardy, L.: Quantum mechanics, local realistic theories and Lorentz-invariant realistic theories. Phys. Rev. Lett. 68, 2981–2984 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  63. Stapp, H.P.: Comments on Shimony’s “An analysis of Stapp’s ‘A Bell-type theorem without hidden variables”. Found. Phys. 36, 73–82 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  64. Griffiths, R.B.: Consistent resolution of some relativistic quantum paradoxes. Phys. Rev. A 66, 062101 (2002). arXiv:quant-ph/0207015

    Article  MathSciNet  ADS  Google Scholar 

  65. Feller, W.: An Introduction to probability Theory and Its Applications, vol. 1, 3rd edn. Wiley, New York (1968)

    MATH  Google Scholar 

  66. DeGroot, M.H., Schervish, M.J.: Probability and Statistics, 3rd edn. Addison-Wesley, Boston (2002)

    Google Scholar 

  67. Mermin, N.D.: Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s. Phys. Rev. D 22, 356–361 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  68. Garg, A., Mermin, N.D.: Local realism and measured correlations in the spin-s Einstein-Podolsky-Rosen experiment. Phys. Rev. D 27, 339–348 (1983)

    Article  ADS  Google Scholar 

  69. Singh, C., Belloni, M., Christian, W.: Improving students’ understanding of quantum mechanics. Phys. Today 59(8), 43–49 (2006)

    Article  Google Scholar 

  70. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  71. Mermin, N.D.: Quantum Computer Science. Cambridge University Press, New York (2007)

    MATH  Google Scholar 

  72. Griffiths, R.B., Niu, C.-S.: Semiclassical Fourier transform for quantum computation. Phys. Rev. Lett. 76, 3228–3231 (1996)

    Article  ADS  Google Scholar 

  73. von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)

    MATH  Google Scholar 

  74. Mermin, N.D.: The Ithaca interpretation of quantum mechanics. Pramana 51, 549–565 (1998)

    Article  ADS  Google Scholar 

  75. Einstein, A.: Autobiographical notes. In: Schilpp, P.A. (ed.) Albert Einstein: Philosopher-Scientist, 2nd edn., pp. 1–95. Tudor Publishing Co., New York (1951)

    Google Scholar 

  76. Goldstein, S.: Bohmian mechanics. In: Stanford Encyclopedia of Philosophy (2006)

  77. Bassi, A., Ghirardi, G.C.: Dynamical reduction models. Phys. Rep. 379, 257 (2003). arXiv:quant-ph/0302164

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robert B. Griffiths.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Griffiths, R.B. Quantum Locality. Found Phys 41, 705–733 (2011). https://doi.org/10.1007/s10701-010-9512-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-010-9512-5

Keywords

Navigation