Quantum Measurement Paradox

  • Dipankar Home

Abstract

The term measurement in general means a way of determining or reading the value of a particular property associated with an individual system. In classical physics the perturbation induced by the interaction between a measured system and a measuring apparatus can be made as small as desired. In other words the principles of classical physics allow us to know the current state of a system with an arbitrarily small disturbance; this may be called noninvasive measurements in classical physics. This is not true however in quantum physics, essentially because of the following generic feature: If two systems temporarily interact, even after the interaction is over, the composite system described quantum mechanically is inevitably left in an entangled state. This means that the joint wave function is not just a product of wave functions associated with each system. This is true whatever the strength and duration of the interaction in question—even if one of the systems involved is macroscopic (in the usual sense of a system made up of a large number of microphysical constituents). For reasons discussed in this chapter, this feature lies at the heart of a fundamental problem plaguing an attempt to provide a fully coherent quantum mechanical account of a measurement process.

Keywords

Wave Function Wave Packet Pure State Definite Outcome Measurement Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Peres, Phys. Rev. D 22, 879 (1980).ADSGoogle Scholar
  2. 2.
    P. Holland, Quantum Theory of Motion (Cambridge Univer. Press, Cambridge, 1993), pp. sect. 8.3.2.Google Scholar
  3. 3.
    J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932); English translation: Mathematical Foundations of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1955).Google Scholar
  4. 4.
    W. Lamb, in Noise and Chaos in Nonlinear Dynamical Systems (F. Moss et al, eds.) (Cambridge Univer. Press, Cambridge, 1990).Google Scholar
  5. 5.
    M. O. Scully, R. Shea, and J. D. McCullen, Phys. Rep. 43, 485 (1978).ADSGoogle Scholar
  6. 6.
    M. Cini, Nuov. Cim. B 73, 27 (1983).MathSciNetADSGoogle Scholar
  7. M. Cini, in Quantum Theory without Reduction (M. Cini and J. M. Levy-Leblond, eds.) (Adam Hilger, Bristol, UK, 1990).Google Scholar
  8. 7.
    D. F. Walls, M. J. Collet, and G. J. Milburn, Phys. Rev. D 32, 3208 (1985).MathSciNetADSGoogle Scholar
  9. 8.
    P. Busch, P. J. Lahti, and P. Mittelstaedt, Quantum Theory of Measurement (Springer-Verlag, Berlin, 1991).Google Scholar
  10. 9.
    Y. Aharonov and J. L. Safko, Ann. Phys. 91, 279 (1975).ADSGoogle Scholar
  11. 10.
    K. Hepp, Helv. Phys. Acta 45, 237 (1972).Google Scholar
  12. 11.
    A. B. Pippard, Eur. J. Phys. 7, 43 (1986).MathSciNetGoogle Scholar
  13. 12.
    P. W. Anderson, in Lesson of Quantum Theory (J. de Boer et al., eds.) (Elsevier, Amsterdam, 1986).Google Scholar
  14. 13.
    P. Alstrom, P. Hjorth, and R. Mattuck, Am. J. Phys. 50, 697 (1982).ADSGoogle Scholar
  15. 14.
    M. O. Scully, W. E. Lamb, and A. Barut, Found. Phys. 17, 575 (1987).MathSciNetADSGoogle Scholar
  16. 15.
    N. F. Mott, Proc. Roy Soc. A 126, 79 (1929).ADSMATHGoogle Scholar
  17. 16.
    J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), pp. 120–21.MATHGoogle Scholar
  18. 17.
    E. P. Wigner, Annals of the New York Academy of Sciences 480, 5 (1986).MathSciNetADSGoogle Scholar
  19. 18.
    W. V. Quine, in Problems in the Philosophy of Science (I. Lakatos and A. Musgrave, eds.) (North-Holland, Amsterdam, 1968), pp. 200–204.Google Scholar
  20. 19.
    S. Weinberg, Dreams of a Pinal Theory (Vintage, London, 1993), p. 64.Google Scholar
  21. 20.
    W. E. Lamb, in Ta-You Wu Festschrift: Science of Matter (S. Fujita, ed.) (Gordon and Breach, New York, 1979), pp. 7–8.Google Scholar
  22. 21.
    J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), p. 125.MATHGoogle Scholar
  23. 22.
    E. P. Wigner, Am. J. Phys. 31, 6 (1963).MathSciNetADSMATHGoogle Scholar
  24. 23.
    A. J. Leggett, in Lesson of Quantum Theory (J. de Boer, E. Dal, and O. Ulfbeck, eds.) (Elsevier, Amsterdam, 1986), p. 47.Google Scholar
  25. 24.
    N. Bohr, Essays 1958/1962 on Atomic Physics and Human Knowledge (Wiley, New York, 1963), p. 3.MATHGoogle Scholar
  26. 25.
    N. Bohr, Essays 1958/1962 on Atomic Physics and Human Knowledge (Wiley, New York, 1963), p. 60.MATHGoogle Scholar
  27. 26.
    N. Bohr, Dialectica 2, 312 (1948).MATHGoogle Scholar
  28. 27.
    W. Moore, Schrödinger—Life and Thought (Cambridge Univer. Press, Cambridge, 1989), pp. 312–313.Google Scholar
  29. 28.
    N. Bohr, Atomic Physics and Human Knowledge (Wiley, New York, 1958), pp. 32–66.MATHGoogle Scholar
  30. 29.
    P. K. Feyerabend, in Frontiers of Science and Philosophy (R. G. Colodny, éd.) (Univer. of Pittsburgh Press, Pittsburgh, 1962), p. 219.Google Scholar
  31. 30.
    M. Jammer, Philosophy of Quantum Mechanics (Wiley-Interscience, New York, 1974), p. 207.Google Scholar
  32. 31.
    W. Heisenberg, Physical Principles of the Quantum Theory (Univer. of Chicago Press, Chicago, 1930; reprinted Dover, New York), p. 64.MATHGoogle Scholar
  33. 32.
    J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), p. 124.MATHGoogle Scholar
  34. 33.
    L. Rosenfeld, Suppl. Prog. Theo. Phys. 222, 1 (1965).Google Scholar
  35. 34.
    W. Heisenberg, in Niels Bohr and the Development of Physics (W. Pauli, ed.) (Pergamon Press, Oxford, UK, 1955), pp. 12–29.Google Scholar
  36. 35.
    W. Heisenberg, Physics and Philosophy (Harper and Row, New York, 1962), chap. 3.Google Scholar
  37. 36.
    A. Peres and W. H. Zurek, Am. J. Phys. 50, 807 (1982).ADSGoogle Scholar
  38. 37.
    A. Peres, Am. J. Phys. 54, 688 (1986).ADSGoogle Scholar
  39. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, Netherlands, 1993), chap. 12.MATHGoogle Scholar
  40. 38.
    A. B. Pippard, Eur. J. Phys. 7, 43 (1986).MathSciNetGoogle Scholar
  41. 39.
    A. Zeilinger, in Quantum Theory without Reduction (M. Cini and J. M. Levy-Leblond, eds.) (Adam Hilger, Bristol, UK, 1989), pp. 18.Google Scholar
  42. 40.
    R. Peierls, Phys. World, 4, 19 (Jan. 1991).Google Scholar
  43. 41.
    N. G. van Kampen, in Proc. 3d Int. Symp. Foundations of Quantum Mechanics (Physical Society of Japan, Tokyo, 1989), pp. 107–14.Google Scholar
  44. 42.
    L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970).ADSMATHGoogle Scholar
  45. 43.
    D. Home and M. A. B. Whitaker, Phys. Rep. 210, 223 (1992), sects. 5.4 and 6.2.MathSciNetADSGoogle Scholar
  46. 44.
    W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).MathSciNetADSGoogle Scholar
  47. 45.
    K. Gottfried, Phys. World 4, 10, 34 (1991).Google Scholar
  48. 46.
    A. J. Leggett, Contemp. Phys. 25, 583 (1984).ADSGoogle Scholar
  49. 47.
    A. J. Leggett, in Quantum Implications (B. J. Hiley, F. D. Peat, eds.) (Routledge and Kegan Paul, London, 1987), pp. 85–104.Google Scholar
  50. 48.
    A. J. Leggett, in Proc. 1st Int. Symp. Foundations of Quantum Mechanics in the Light of New Technology (Physical Society of Japan, Tokyo, 1984).Google Scholar
  51. A. J. Leggett, Prog. Theor. Phys. Suppl., no. 69, 80 (1980).Google Scholar
  52. 49.
    R. Omnés, Interpretation of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1994), chap. 7.MATHGoogle Scholar
  53. 50.
    N. G. van Kampen, Physica A 153, 97 (1988).MathSciNetADSGoogle Scholar
  54. 51.
    A. J. Leggett, Curr. Sci. 67, 785 (1994).Google Scholar
  55. 52.
    J. S. Bell, Phys. World 3, no. 8, 33 (1990).Google Scholar
  56. J. S. Bell, also in: Sixty-Two Years of Uncertainty (A. I. Miller, ed.) (Plenum, New York, 1990), pp. 17–31.Google Scholar
  57. 53.
    B. d’Espagnat, Veiled Reality—an Analysis of Pre sent-Day Quantum Mechanical Concepts (Addison-Wesley, Reading, MA, 1995), chap. 10.Google Scholar
  58. 54.
    R. Omnés, Found. Phys. 25, 605 (1995).MathSciNetADSGoogle Scholar
  59. 55.
    K. Gottfried, Quantum Mechanics (W. A. Benjamin, New York, 1966), chap. 4.Google Scholar
  60. 56.
    C. F von Weizsäcker and Th. Görnitz, Found. Phys. 21, 311 (1991).Google Scholar
  61. 57.
    R. B. Griffiths, J. Stat. Phys. 36, 219 (1984).ADSMATHGoogle Scholar
  62. R. B. Griffiths, in New Techniques and Ideas in Quantum Measurement Theory (D. M. Greenberger, ed.) (New York Academy of Sciences, New York, 1986).Google Scholar
  63. R. B. Griffiths, Found. Phys. 23, 1601 (1993).MathSciNetADSGoogle Scholar
  64. 58.
    R. Omnés, J. Stat. Phys. 53, 893 (1988).ADSMATHGoogle Scholar
  65. R. Omnés, Rev. Mod. Phys. 64, 339 (1992).ADSGoogle Scholar
  66. 59.
    M. Gell-Mann and J. B. Hartle, in Complexity, Entropy, and the Physics of Information (W. Zurek, ed.) (Addison-Wesley, Reading, MA, 1990).Google Scholar
  67. M. Gell-Mann and J. B. Hartle, in Proc. 3d Int. Symp. Foundations of Quantum Mechanics in the Light of New Technology (S. Kobayashi et al, eds.) (Phys. Soc. of Japan, Tokyo, 1990).Google Scholar
  68. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).MathSciNetADSGoogle Scholar
  69. 60.
    B. d’Espagnat, J. Stat. Phys. 56, 747 (1989).MathSciNetADSGoogle Scholar
  70. B. d’Espagnat, Found. Phys. 20, 1147 (1990).MathSciNetADSGoogle Scholar
  71. 61.
    M. Gell-Mann, Quark and the Jaguar (Little Brown and Co., London, 1994), pp. 153–54.MATHGoogle Scholar
  72. 62.
    P. A. M. Dirac, in Electrons et Photons—Rapports et Discussions du Cinquième Conseil de Physique tenu à Bruxelles 1927 (Gauthier-Villars, Paris, 1928).Google Scholar
  73. 63.
    P. A. M. Dirac, Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1930), p. 36.MATHGoogle Scholar
  74. 64.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, UK, 1977), p. 22.Google Scholar
  75. 65.
    L. E. Ballentine, Found. Phys. 20, 1329 (1990).MathSciNetADSGoogle Scholar
  76. 66.
    L. E. Ballentine, Quantum Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1990), chap. 9.Google Scholar
  77. 67.
    L. D. Landau and R. Peierls, Z. Phys. 69, 56 (1931).ADSGoogle Scholar
  78. 68.
    L. E. Ballentine, in Fundamental Questions in Quantum Mechanics (L. M. Roth and A. Inomata, eds.) (Gordon and Breach, New York, 1986), pp. 65–75.Google Scholar
  79. 69.
    H. Everett, Rev. Mod. Phys. 29, 454 (1957).MathSciNetADSGoogle Scholar
  80. 70.
    E. J. Squires, in Quantum Theory without Reduction (M. Cini and J. M. Levy-Leblond, eds.) (Adam-Hilger, Bristol, UK, 1989).Google Scholar
  81. 71.
    E. J. Squires, Synthese 97, 109 (1993).MathSciNetGoogle Scholar
  82. 72.
    B. S. Dewitt and N. Graham, Many-Worlds Interpretation of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1973), pp. 155–65.Google Scholar
  83. 73.
    L. E. Ballentine, Found. Phys. 3, 229 (1973).ADSGoogle Scholar
  84. 74.
    D. Deutsch, Int. J. Theor. Phys. 24, 1 (1985).MathSciNetGoogle Scholar
  85. 75.
    M. Lockwood, Mind, Brain, and the Quantum (Basil Blackwell, Oxford, UK, 1989), chap. 13.Google Scholar
  86. 76.
    D. Albert and B. Loewer, Synthese 77, 195 (1988).MathSciNetGoogle Scholar
  87. 77.
    H. P. Stapp, Mind, Matter, and Quantum Mechanics (Springer-Verlag, Berlin, 1993).MATHGoogle Scholar
  88. 78.
    H. Primas, Chemistry, Quantum Mechanics, and Reductionism (Springer-Verlag, Berlin, 1981), pp. sect. 3.6.Google Scholar
  89. 79.
    D. Bohm and B. J. Hiley, Undivided universe (Routledge, London, 1993), p. 311.Google Scholar
  90. 80.
    H. Everett, in Many-Worlds Interpretation of Quantum Mechanics (B. S. DeWitt and N. Graham, eds.) (Princeton Univer. Press, Princeton, NJ, 1973), pp. 100.Google Scholar
  91. 81.
    J. Schwinger, M. O. Scully, and B. G. Englert, Z. Phys. D 10, 135 (1988).ADSGoogle Scholar
  92. B. G. Englert, J. Schwinger, and M. O. Scully, Found. Phys. 18, 1045 (1988).MathSciNetADSGoogle Scholar
  93. 82.
    B. d’Espagnat, Veiled Reality—an Analysis of Present-Day Quantum Mechanical Concepts (Addison-Wesley, Reading, MA, 1995), pp. 282–83.Google Scholar
  94. 83.
    N. Gisin, Phys. Lett. A 143, 1 (1990).ADSGoogle Scholar
  95. 84.
    J. Polchinski, Phys. Rev. Lett. 66, 397 (1991).MathSciNetADSMATHGoogle Scholar
  96. 85.
    S. Weinberg, Dreams of a Final Theory (Vintage, London, 1993), pp. 69–70.Google Scholar
  97. 86.
    G. C. Ghirardi, A. Rimini, and T. Weber, in Quantum Probability and Applications (L. Accardi and W. von Waldenfels, eds.) (Springer-Verlag, Berlin, 1985), pp. 223–32.Google Scholar
  98. 87.
    G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986).MathSciNetADSMATHGoogle Scholar
  99. 88.
    E. J. Squires, Phys. Lett. A 158, 431 (1991).ADSGoogle Scholar
  100. 89.
    P. Pearle and E. Squires, Phys. Rev. Lett. 73, 1 (1994).ADSGoogle Scholar
  101. 90.
    D. Z. Albert and B. Loewer, in Perspectives on Quantum Reality (R. Clifton, ed.) (Kluwer, Dordrecht, Netherlands, 1996), pp. 81–92.Google Scholar
  102. 91.
    D. Z. Albert and B. Loewer, in Proc. Philosophy of Science Association, vol. 1 (A. Fine et al., eds.), pp. 277-85.Google Scholar
  103. 92.
    D. Z. Albert and L. Vaidman, Phys. Lett. A 139, 1 (1989). D. Z. Albert and L. Vaidman, 171, 438 (1992).MathSciNetADSGoogle Scholar
  104. 93.
    F. Aicardi, A. Borsellino, G. C. Ghirardi, and R. Grassi, Found. Phys. Lett. 4, 109 (1991).Google Scholar
  105. 94.
    C. Dove and E. J. Squires, Symmetric Versions of Explicit Wave Function Collapse Models (Univer. of Durhan, Preprint DTP/94/45, 1994).Google Scholar
  106. 95.
    P. Pearle, Phys. Rev. A 39, 2277 (1989).ADSGoogle Scholar
  107. 96.
    G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).MathSciNetADSGoogle Scholar
  108. 97.
    G. C. Ghirardi and A. Rimini, in Sixty-Two Years of Uncertainty (A. Miller, ed.) (Plenum, New York, 1990), pp. 167–91.Google Scholar
  109. 98.
    G. C. Ghirardi in Fundamental Problems in Quantum Theory (D. M. Greenberger and A. Zeilinger, eds.) (New York Academy of Sciences, New York, 1995).Google Scholar
  110. 99.
    G. C. Ghirardi, R. Grassi, and A. Rimini, Phys. Rev. A 42, 1057 (1990).ADSGoogle Scholar
  111. 100.
    A. Rimini, in International Course on Advances on Quantum Phenomena (E. Beltrametti and J. M. Levy-Leblond, eds.) (Plenum, New York, 1994).Google Scholar
  112. 101.
    A. Shimony, in Proc. Philosophy of Science Association, vol. 2 (A. Fine et al., eds.).Google Scholar
  113. 102.
    G. C. Ghirardi, R. Grassi, and F. Benatti, Found. Phys. 25, 5 (1995).MathSciNetADSMATHGoogle Scholar
  114. 103.
    J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), p. 117.MATHGoogle Scholar
  115. 104.
    G. C. Ghirardi and R. Grassi, in Bohmian Mechanics and Quantum Theory: An Appraisal (J. T. Cushing, A. Fine, and S. Goldstein, eds.) (Kluwer, Dordrecht, Netherlands, 1996), pp. 353–77.Google Scholar
  116. 105.
    D. Bohm and B. J. Hiley, Undivided Universe (Routledge, London, 1993), pp. 326–28.Google Scholar
  117. 106.
    P. Holland, Found. Phys., to be published.Google Scholar
  118. 107.
    S. Machida and M. Namiki, Prog Theor. Phys. 63, 1457, 1833 (1980).ADSGoogle Scholar
  119. M. Namiki, Ann. NY Acad. Sci. 480, 78 (1986).ADSGoogle Scholar
  120. M. Namiki, Found. Phys. 18, 29 (1988).MathSciNetADSGoogle Scholar
  121. 108.
    M. Namiki and S. Pascazio, Phys. Rep. 232, 301 (1993).MathSciNetADSGoogle Scholar
  122. 109.
    R. Penrose, Shadows of the Mind (Oxford Univer. Press, Oxford, UK, 1994), chap. 6.Google Scholar
  123. 110.
    I. Prigogine and C. George, Proc. Nat. Acad. Sci. (USA) 80, 4590 (1983).MathSciNetADSMATHGoogle Scholar
  124. T. Petrosky and I. Prigogine, Liouville Space Extension of Quantum Mechanics, to appear in Adv. Chem. Phys. (1997).Google Scholar
  125. 111.
    B. Misra, I. Prigogine, and M. Courbage, Proc. Nat. Acad. Sci. (USA) 76, 4768 (1979).MathSciNetADSGoogle Scholar
  126. I. Prigogine and I. Stengers, Order out of Chaos (Bantam Books, New York, 1984).Google Scholar
  127. 112.
    D. Home and S. Bose, Phys. Lett. A (1996).Google Scholar
  128. 113.
    W. H. Zurek, in Conceptual Problems of Quantum Gravity (A. Ashtekar and J. Stachel, eds.) (Birhauser, Boston, 1991).Google Scholar
  129. W. H. Zurek, Phys. Today 44, 36 (1991).Google Scholar
  130. 114.
    W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).MathSciNetADSGoogle Scholar
  131. 115.
    D. M. Greenberger and A. Yasin, in Proc. 2d Int. Symp. Foundations of Quantum Mechanics (M. Namiki et al, eds.) (Phys. Soc. Japan, Tokyo, 1987), pp. 18–24.Google Scholar
  132. 116.
    D. Home and R. Chattopadhyaya, Phys. Rev. Lett. 76, 2836 (1996).MathSciNetADSMATHGoogle Scholar
  133. 117.
    A. Rae, Quantum Physics: Illusion or Reality? (Cambridge Univer. Press, Cambridge, 1986), p. 61.Google Scholar
  134. 118.
    A. Shimony, in Philosophical Consequences of Quantum Theory (J. T. Cushing and E. Mcmullin, eds.) (Univer. of Notre Dame Press, Notre Dame, IN, 1989), p. 36.Google Scholar
  135. 119.
    I. Percival, Nature 351, 357 (1991).ADSGoogle Scholar
  136. 120.
    I. Husain and A. Sancar, Nucleic Acids Res. 15, 1109 (1987).Google Scholar
  137. 121.
    G. B. Sancar, F. W. Smith, R. Reid, G. Payne, M. Levy, and A. Sancar, J. Biol. Chem. 262, 478 (1987).Google Scholar
  138. 122.
    G. B. Sancar, F. W. Smith, and A. Sancar, Biochemistry 24, 1849 (1985).Google Scholar
  139. 123.
    N. Gisin and I. Percival, J. Phys. A 26, 2245 (1993).MathSciNetADSGoogle Scholar
  140. 124.
    F. Aicardi, A. Borsellino, G. C. Ghirardi, and R. Grassi, Found. Phys. Lett. 4, 116 (1991).Google Scholar
  141. 125.
    A. Venugopalan, Phys. Rev. A 50, 2742 (1994).ADSGoogle Scholar
  142. 126.
    I. Husain, J. Griffith, and A. Sancar, Proc. Nat. Acad. Sci (USA) 85, 2558 (1988).ADSGoogle Scholar
  143. 127.
    J. S. Bell, in Ghost in the Atom (P. C. W. Davies and J. R. Brown, eds.) (Cambridge Univer. Press, Cambridge, 1986), p. 54.Google Scholar
  144. 128.
    A. J. Leggett, Curr. Sci. 67, 785 (1994).Google Scholar
  145. 129.
    R. P. Feynman, in Feynman Lectures on Gravitation (F. B. Morinigo, W. G. Wagner, and B. Hatfield, eds.), pp. 12 and 15, Addison-Wesley, Massachusetts (1995).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Dipankar Home
    • 1
  1. 1.Bose InstituteCalcuttaIndia

Personalised recommendations