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Volumn 34, Issue 6, 2004, Pages 891-935

Foundations of quantum mechanics: The connection between QM and the Central limit theorem

Author keywords

Central limit theorem; Classical and quantum mechanics; Interpretation of quantum mechanics

Indexed keywords


EID: 3142661280     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:FOOP.0000034222.65544.26     Document Type: Article
Times cited : (13)

References (50)
  • 5
    • 36149002446 scopus 로고
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1964) Phys. Rev. B , vol.136
    • Kershaw, D.1
  • 6
    • 0041336647 scopus 로고
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1965) Phys. Rev. B , vol.138
    • Comisar, G.G.1
  • 7
    • 84932502092 scopus 로고
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1965) Proc. Cambridge Philos. Soc. , vol.61 , pp. 537
    • Marshall, T.W.1
  • 8
    • 36049058883 scopus 로고
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1966) Phys. Rev. , vol.150 , pp. 1079
    • Nelson, E.1
  • 9
    • 11744314767 scopus 로고
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1969) J. Math. Phys. , vol.10 , pp. 1620
    • De La Peña, L.1
  • 10
    • 24244465434 scopus 로고
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1970) Phys. Lett. A , vol.31 , pp. 403
    • De La Peña, L.1
  • 11
    • 4243400043 scopus 로고
    • to cite but a few
    • D. Kershaw, Phys. Rev. B 136, B1850 (1964), G. G. Comisar, Phys. Rev. B 138, B1332 (1965). T. W. Marshall, Proc. Cambridge Philos. Soc. 61, 537 (1965). E. Nelson, Phys. Rev. 150, 1079 (1966), L. de la Peña, J. Math. Phys. 10, 1620 (1969), L. de la peña, Phys. Lett. A 31, 403 (1970). L. de la Peña and A. M. Cetto, Phys. Rev. D 3, 795 (1971), to cite but a few.
    • (1971) Phys. Rev. D , vol.3 , pp. 795
    • De La Peña, L.1    Cetto, A.M.2
  • 15
    • 0009500786 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1945) Rev. Mod. Phys. , vol.17 , pp. 195
    • Dirac, P.A.M.1
  • 16
    • 0000441472 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1954) Prog. Theor. Phys. , vol.11 , pp. 341
    • Takabayasi, T.1
  • 17
    • 0002379655 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1966) J. Math. Phys. , vol.7 , pp. 66
    • Pool, J.C.T.1
  • 18
    • 0141582037 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1966) J. Math. Phys. , vol.7 , pp. 781
    • Cohen, L.1
  • 19
    • 0001177654 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1968) J. Math. Phys. , vol.9 , pp. 299
    • Misra, S.P.1    Shankara, T.S.2
  • 20
    • 0001031543 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1970) Phys. Rev. D , vol.2 , pp. 2161
    • Agarwal, G.S.1    Wolf, E.2
  • 21
    • 49649138458 scopus 로고
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1976) Physica A , vol.83 , pp. 210
    • Cartwright, N.D.1
  • 22
    • 0000406855 scopus 로고
    • and many others
    • P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945). T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954). J. C. T. Pool, J. Math. Phys. 7, 66 (1966). L. Cohen, J. Math. Phys. 7, 781 (1966). S. P. Misra and T. S. Shankara, J. Math. Phys. 9, 299 (1968). G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970). N. D. Cartwright, Physica A 83, 210 (1976). R. F. O'Connell and E. P. Wigner, Phys. Lett. A 85, 121 (1981), and many others.
    • (1981) Phys. Lett. A , vol.85 , pp. 121
    • O'Connell, R.F.1    Wigner, E.P.2
  • 24
    • 0003496256 scopus 로고
    • (Dover, New York), translated from the Russian by G. Gamow (we changed slightly Khinchin's notation to fit our own)
    • A. I. Kinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York, 1949) pp. 84, 85, translated from the Russian by G. Gamow (we changed slightly Khinchin's notation to fit our own).
    • (1949) Mathematical Foundations of Statistical Mechanics , pp. 84
    • Kinchin, A.I.1
  • 25
    • 0004203380 scopus 로고
    • (Addison-Wesley, New York), (where the restricted case we are considering is better explained)
    • P. L. Meyer, Introductory Probability and Statistical Applications (Addison-Wesley, New York, 1965), p. 270ff (where the restricted case we are considering is better explained).
    • (1965) Introductory Probability and Statistical Applications
    • Meyer, P.L.1
  • 26
    • 3142686813 scopus 로고
    • in Oeuvres de Paul Levy (Ecole Polytechnique, France)
    • P. Levy, Théorie des erreurs. La loi de Gauss et les lois exceptionelles. in Oeuvres de Paul Levy (Ecole Polytechnique, France, 1976), pp. 14-49 P. Levy shows in his own derivation that it is not necessary to make the hypothesis that the characteristic function may be decomposable into a Taylor series; indeed, his derivation is much more general than the one presented by us here. However, the present derivation has the advantage of being known to the great majority of physicists, since it is part of usual statistical mechanics' manuals.
    • (1976) Théorie des Erreurs. La Loi de Gauss et les Lois Exceptionelles , pp. 14-49
    • Levy, P.1
  • 27
    • 85139747524 scopus 로고    scopus 로고
    • note
    • δx = 0 = 0, but this restriction is not necessary.
  • 28
    • 0041319340 scopus 로고
    • L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). W. Heisenberg, "The development of the interpretation of the quantum theory," in Niels Bohr and the Development of Physics. W. Pauli, ed. (McGraw-Hill, New York, 1955), p. 12. T. Brody, The Philosophy behind Physics (Springer, Berlin, 1993). A. Landé, From Dualism to Unity in Quantum Mechanics (Cambridge University Press, Cambridge, 1960), and many others (cf. the references in Ballentine's paper, for instance).
    • (1970) Rev. Mod. Phys. , vol.42 , pp. 358
    • Ballentine, L.E.1
  • 29
    • 0041319340 scopus 로고
    • The development of the interpretation of the quantum theory
    • W. Pauli, ed. (McGraw-Hill, New York)
    • L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). W. Heisenberg, "The development of the interpretation of the quantum theory," in Niels Bohr and the Development of Physics. W. Pauli, ed. (McGraw-Hill, New York, 1955), p. 12. T. Brody, The Philosophy behind Physics (Springer, Berlin, 1993). A. Landé, From Dualism to Unity in Quantum Mechanics (Cambridge University Press, Cambridge, 1960), and many others (cf. the references in Ballentine's paper, for instance).
    • (1955) Niels Bohr and the Development of Physics , pp. 12
    • Heisenberg, W.1
  • 30
    • 0041319340 scopus 로고
    • Springer, Berlin
    • L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). W. Heisenberg, "The development of the interpretation of the quantum theory," in Niels Bohr and the Development of Physics. W. Pauli, ed. (McGraw-Hill, New York, 1955), p. 12. T. Brody, The Philosophy behind Physics (Springer, Berlin, 1993). A. Landé, From Dualism to Unity in Quantum Mechanics (Cambridge University Press, Cambridge, 1960), and many others (cf. the references in Ballentine's paper, for instance).
    • (1993) The Philosophy behind Physics
    • Brody, T.1
  • 31
    • 0041319340 scopus 로고
    • (Cambridge University Press, Cambridge), and many others (cf. the references in Ballentine's paper, for instance)
    • L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). W. Heisenberg, "The development of the interpretation of the quantum theory," in Niels Bohr and the Development of Physics. W. Pauli, ed. (McGraw-Hill, New York, 1955), p. 12. T. Brody, The Philosophy behind Physics (Springer, Berlin, 1993). A. Landé, From Dualism to Unity in Quantum Mechanics (Cambridge University Press, Cambridge, 1960), and many others (cf. the references in Ballentine's paper, for instance).
    • (1960) From Dualism to Unity in Quantum Mechanics
    • Landé, A.1
  • 45
    • 84858291384 scopus 로고
    • N. R. Hanson, Am. J. Phys. 27, 1 (1959). A. Shimony, Am. J. Phys. 31, 755 (1963). E. E. Witmer, Am. J. Phys. 35, 40 (1963). E. P. Wigner, Am. J. Phys. 31, 6 (1963). P. Pearle, Am. J. Phys. 35, 742 (1967). J. P. Wesley, Found. Phys. 14, 155 (1984), and many others.
    • (1959) Am. J. Phys. , vol.27 , pp. 1
    • Hanson, N.R.1
  • 46
    • 84953396305 scopus 로고
    • N. R. Hanson, Am. J. Phys. 27, 1 (1959). A. Shimony, Am. J. Phys. 31, 755 (1963). E. E. Witmer, Am. J. Phys. 35, 40 (1963). E. P. Wigner, Am. J. Phys. 31, 6 (1963). P. Pearle, Am. J. Phys. 35, 742 (1967). J. P. Wesley, Found. Phys. 14, 155 (1984), and many others.
    • (1963) Am. J. Phys. , vol.31 , pp. 755
    • Shimony, A.1
  • 47
    • 84910840761 scopus 로고
    • N. R. Hanson, Am. J. Phys. 27, 1 (1959). A. Shimony, Am. J. Phys. 31, 755 (1963). E. E. Witmer, Am. J. Phys. 35, 40 (1963). E. P. Wigner, Am. J. Phys. 31, 6 (1963). P. Pearle, Am. J. Phys. 35, 742 (1967). J. P. Wesley, Found. Phys. 14, 155 (1984), and many others.
    • (1963) Am. J. Phys. , vol.35 , pp. 40
    • Witmer, E.E.1
  • 48
    • 84945060063 scopus 로고
    • N. R. Hanson, Am. J. Phys. 27, 1 (1959). A. Shimony, Am. J. Phys. 31, 755 (1963). E. E. Witmer, Am. J. Phys. 35, 40 (1963). E. P. Wigner, Am. J. Phys. 31, 6 (1963). P. Pearle, Am. J. Phys. 35, 742 (1967). J. P. Wesley, Found. Phys. 14, 155 (1984), and many others.
    • (1963) Am. J. Phys. , vol.31 , pp. 6
    • Wigner, E.P.1
  • 49
    • 0040619513 scopus 로고
    • N. R. Hanson, Am. J. Phys. 27, 1 (1959). A. Shimony, Am. J. Phys. 31, 755 (1963). E. E. Witmer, Am. J. Phys. 35, 40 (1963). E. P. Wigner, Am. J. Phys. 31, 6 (1963). P. Pearle, Am. J. Phys. 35, 742 (1967). J. P. Wesley, Found. Phys. 14, 155 (1984), and many others.
    • (1967) Am. J. Phys. , vol.35 , pp. 742
    • Pearle, P.1
  • 50
    • 0011328478 scopus 로고
    • and many others
    • N. R. Hanson, Am. J. Phys. 27, 1 (1959). A. Shimony, Am. J. Phys. 31, 755 (1963). E. E. Witmer, Am. J. Phys. 35, 40 (1963). E. P. Wigner, Am. J. Phys. 31, 6 (1963). P. Pearle, Am. J. Phys. 35, 742 (1967). J. P. Wesley, Found. Phys. 14, 155 (1984), and many others.
    • (1984) Found. Phys. , vol.14 , pp. 155
    • Wesley, J.P.1


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