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Book cover Time in Quantum Mechanics

Part of the book series: Lecture Notes in Physics ((LNPMGR,volume 72))

Abstract

This chapter is a historical sketch of “time in quantum mechanics”. We have adopted a “physicist’s approach” to history, summarizing in rough chronological order some of the contributions underlying the topics and concepts treated in the book. The account is complemented with comments on later or recent repercussions of the original works, giving certain prominence to some of our own contributions. The time span of this “story” is almost 100 years, so necessarily many of the comments and references will be minimal, and even entire fields are absent, in particular those not related to the topics addressed in the subsequent chapters.

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References

  1. N. Bohr: Philosophical Magazine 26, 1 (1913)

    Google Scholar 

  2. M. Beller: Quantum Dialogue (University of Chicago Press, 1999)

    Google Scholar 

  3. A. Hermann, K.v. Meyen, V.F. Weisskopf, eds.: Wolfgang Pauli, Scientific Correspondence with Bohr, Einstein, Heisenberg (Springer, Berlin, 1979) Letter of Pauli to Bohr, 17 November 1925.

    Google Scholar 

  4. K.v. Meyen, V.F. Weisskopf, eds.: Wolfgang Pauli, Scientific Correspondence with Bohr, Einstein, Heisenberg (Springer, Berlin, 1979) See [3], Letter of Heisenberg to Pauli, 24 November 1925

    Google Scholar 

  5. Heisenberg to Einstein, 30 November 1925, Einstein Archive, Hebrew University of Jerusalem

    Google Scholar 

  6. M. Born: Problems of Atomic Dynamics (MIT Press, Cambridge, Mass., 1926)

    MATH  Google Scholar 

  7. M. Born: Zeitschrift für Physik 37, 863 (1926)

    Article  ADS  Google Scholar 

  8. P. Jordan: Naturwissenschaften 37, 614 (1927)

    Article  ADS  Google Scholar 

  9. W. Pauli: in Handbuch der Physik (Springer, Berlin, 1926), vol. 23, pp. 1–278

    Google Scholar 

  10. W. Heisenberg: Zeitschrift für Physik 43, 172 (1927). Translated in Quantum Theory and Measurement, ed. by J. A. Wheeler, W. H. Zurek (Princeton University Press, Princeton 1983)

    Article  ADS  Google Scholar 

  11. D.M. Appleby: J. Phys. A 31, 6419 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. N. Bohr: Nature 121 (suppl.), 580 (1928)

    Article  MATH  ADS  Google Scholar 

  13. L. Mandelstam, I. Tamm: J. Phys. (USSR) 9, 249 (1945)

    MathSciNet  Google Scholar 

  14. Y. Aharonov, D. Bohm: Phys. Rev. 122, 1649 (1961)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. W. Pauli: in Handbuch der Physik (Springer, Berlin, 1933), vol. 24, pp. 83–272

    Google Scholar 

  16. W. Pauli: in Encyclopedia of Physics, ed. by S. Flugge (Springer, Berlin, 1958), vol. V/1, p. 60

    Google Scholar 

  17. G.R. Allcock: Ann. Phys. (N.Y.) 53, 253 (1969)

    Article  ADS  Google Scholar 

  18. V. Delgado, J.G. Muga: Phys. Rev. A56, 3425 (1997). quant-ph/9704010

    ADS  MathSciNet  Google Scholar 

  19. I.L. Egusquiza, J.G. Muga: Phys. Rev A61, 012104 (2000). See also erratum, Phys. Rev. A 61 (2000) 059901(E). quant-ph/9905023

    ADS  MathSciNet  Google Scholar 

  20. E.A. Galapon: The consistency of a bounded, self-adjoint time operator canonically conjugate to a hamiltonian with non-empty point spectrum (1999). quant-ph/9908033

    Google Scholar 

  21. P. Busch, M. Grabowski, P. Lahti: Operational Quantum Physics (Springer-Verlag, Berlin 1997)

    Google Scholar 

  22. B. Misra: Found. Phys. 25, 1087 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  23. J. von Neumann: Mathematical Foundations of quantum mechanics (Princeton University Press, 1955)

    Google Scholar 

  24. J. Hilgevoord: Am. J. Phys. 64, 1451 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  25. D. Bohm: Quantum Theory (Prentice-Hall, New Jersey, 1951)

    Google Scholar 

  26. K.R. Popper: British Journal for the Philosophy of Science 10, 25 (1959)

    Article  ADS  Google Scholar 

  27. E. Nelson: Phys. Rev. 150, 1079 (1966)

    Article  ADS  Google Scholar 

  28. D. Bohm, J.P. Vigier: Phys. Rev. 96, 208 (1954)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. D. Bohm, B.J. Hiley: Phys. Rep. 172, 93 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  30. M.Q. Chen, M.S. Wang: Phys. Lett. A 149, 441 (1990)

    Article  ADS  Google Scholar 

  31. K. Imafaku, I. Ohba, Y. Yamanaka: Phys. Lett. A 204, 329 (1995)

    Article  ADS  Google Scholar 

  32. L. Marchildon: No contradictions between Bohmian and quantum mechanics (2000). quant-ph/0007068

    Google Scholar 

  33. A. Neumaier: Bohmian mechanics contradicts quantum mechanics (2000). quant-ph/0001011

    Google Scholar 

  34. P. Ghose: Incompatibility of the de Broglie-Bohm theory with quantum mechanics (2000). quant-ph/0001024

    Google Scholar 

  35. P. Ghose: An experiment to distinguish between de Broglie-Bohm and standard quantum mechanics (2000). quant-ph/0003037

    Google Scholar 

  36. P. Ghose: Reply to’ No contradictions between Bohmian and quantum mechanics’ (2000). quant-ph/0008007

    Google Scholar 

  37. M. Golshani, O. Akhavan: A two-slit experiment which distinguishes between the standard and bohmian quantum mechanics (2000). quant-ph/0009040

    Google Scholar 

  38. M. Golshani, O. Akhavan: Experiment can decide between the standard and Bohmian quantum mechanics (2001). quant-ph/0103100

    Google Scholar 

  39. M. Golshani, O. Akhavan: Bohmian prediction about a two double-slit experiment and its disagreement with the standard quantum mechanics (2001). quant-ph/0103101

    Google Scholar 

  40. W. Struyve, W.D. Baere: Comments on some recently proposed experiments that should distinguish Bohmian mechanics from quantum mechanics (2001). quant-ph/0108038

    Google Scholar 

  41. P.R. Holland: The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993)

    Google Scholar 

  42. D. Bohm, B. Hiley: The Undivided Universe: An Ontological Interpretation of Quantum Mechanics (Routledge, London, 1993)

    Google Scholar 

  43. J.R. Barker: Semicond. Sci. Technol. 9, 911 (1994)

    Article  ADS  Google Scholar 

  44. C.R. Leavens: Phys. Rev. A 58, 840 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  45. M. Daumer: in Bohmian mechanics and quantum theory: an appraisal, ed. by J.T. Cushing, A. Fine, S. Goldstein (Kluwer, Dordrecht, 1996), pp. 87–98

    Google Scholar 

  46. X. Oriols, F. Martín, J. Suñé: Phys. Rev. A 54, 2594 (1996)

    Article  ADS  Google Scholar 

  47. Y. Nogami, F.M. Toyama, W. van Dijk: Phys. Lett. A270, 279 (2000)

    ADS  Google Scholar 

  48. E. Schrödinger: British Journal for the Philosophy of Science 3, 109 (1952)

    Article  Google Scholar 

  49. M. Born: British Journal for the Philosophy of Science 4 (1953)

    Google Scholar 

  50. H.D. Zeh: Phys. Lett. A 174, 189 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  51. H. Everett: Rev. Mod. Phys. 29, 454 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  52. P. Szriftgiser, D. Guéry-Odelin, M. Arndt, J. Dalibard: Phys. Rev. Lett. 77, 4 (1996)

    Article  ADS  Google Scholar 

  53. M. Moshinsky: Phys. Rev. 88, 625 (1952)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  54. H. Salecker, E.P. Wigner: Phys. Rev. 109, 571 (1958)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  55. A. Peres: Am. J. Phys. 48, 552 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  56. Y. Aharonov, J. Oppenheim, S. Popescu, B. Reznik, W.G. Unruh: Phys. Rev. A 57, 4130 (1998). quant-ph/9709031

    Article  ADS  MathSciNet  Google Scholar 

  57. F.T. Smith: Phys. Rev. 118, 349 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  58. L. Eisenbud: Ph.D. thesis, Princeton Univ. (1948). Unpublished

    Google Scholar 

  59. E.P. Wigner: Phys. Rev. 98, 145 (1955)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  60. J.G. Muga, C.R. Leavens, J.P. Palao: Phys. Rev. A 58, 4336 (1998). quant-ph/9807066

    Article  ADS  Google Scholar 

  61. G.R. Allcock: Ann. Phys. (N.Y.) 53, 286 (1969)

    Article  ADS  Google Scholar 

  62. G.R. Allcock: Ann. Phys. (N.Y.) 53, 311 (1969)

    Article  ADS  Google Scholar 

  63. E.P. Wigner: in Aspects of quantum theory, ed. by A. Salam, E. P. Wigner (Cambridge University Press, London, 1972)

    Google Scholar 

  64. A.D. Baute, I.L. Egusquiza, J.G. Muga: J. Phys. A 34, 4289 (2000). quant-ph/0007066

    Article  ADS  MathSciNet  Google Scholar 

  65. J.G. Muga, R. Leavens: Phys. Rep. 338, 353 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  66. J.G. Muga, S. Brouard, D. Macías: Ann. Phys. (N.Y.) 240, 351 (1995)

    Article  ADS  Google Scholar 

  67. J.P. Palao, J.G. Muga, R. Sala: Phys. Rev. Lett. 80, 5469 (1998). quant-ph/9805035

    Article  ADS  Google Scholar 

  68. J.P. Palao: Teoría cuántica de colisiones con potenciales complejos en una dimensión. Ph.D. thesis, Universidad de La Laguna (1999)

    Google Scholar 

  69. A.J. Bracken, G.F. Melloy: J. Phys. A: Math. Gen. 27, 2197 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  70. G.F. Melloy, A.J. Bracken: Ann. Phys. (Leipzig) 7, 726 (1998)

    Article  MATH  ADS  Google Scholar 

  71. J.G. Muga, J.P. Palao, C.R. Leavens: Phys. Lett. A 253, 21 (1999). quant-ph/9803087

    Article  ADS  Google Scholar 

  72. Y. Aharonov, P.G. Bergmann, J.L. Lebowitz: Phys. Rev. B 134, 1410 (1964)

    ADS  MathSciNet  Google Scholar 

  73. Y. Aharonov, D. Albert, A. Casher, L. Vaidman: Phys. Lett. A 124, 199 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  74. J. Kijowski: Rept. Math. Phys. 6, 361 (1974)

    ADS  Google Scholar 

  75. R. Giannitrapani: Int. J. Theor. Phys. 36, 1575 (1997). quant-ph/9611015

    Article  MATH  MathSciNet  Google Scholar 

  76. P. Busch, M. Grabowski, P.J. Lahti: Phys. Lett. A 191, 357 (1994)

    Article  ADS  Google Scholar 

  77. N.I. Akhiezer, I.M. Glazman: Theory of linear operators in Hilbert space (Dover, New York, 1963)

    Google Scholar 

  78. A.D. Baute, I.L. Egusquiza, J.G. Muga: Phys. Rev. A 64, 012501 (2001)

    Article  ADS  Google Scholar 

  79. J. León: J. Phys. A 30, 4791 (1997). quant-ph/9608013

    Article  MATH  ADS  MathSciNet  Google Scholar 

  80. J.G. Muga, A.D. Baute, J.A. Damborenea, I.L. Egusquiza: Model for the arrival-time distribution in fluorescence time-of-flight experiments (2000). quant-ph/0009111

    Google Scholar 

  81. B. Misra, E.C.G. Sudarshan: J. Math. Phys. 18, 756 (1977)

    Google Scholar 

  82. D. Home, M.A.B. Whitaker: Ann. Phys. (N.Y.) 258, 237 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  83. M.D. Srinivas, R. Vijayalakshmi: Pramana 16, 173 (1981)

    Article  ADS  Google Scholar 

  84. C.W. Helstrom: Int. J. Theor. Phys. 11, 357 (1974)

    Article  MathSciNet  Google Scholar 

  85. A.S. Holevo: Rep. Math. Phys. 13, 379 (1978)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  86. S. Kochen, E. P. Specker: J. Math. Mech. 17, 59 (1967)

    MATH  MathSciNet  Google Scholar 

  87. J.S. Bell: Rev. Mod. Phys. 38, 447 (1966)

    Article  MATH  ADS  Google Scholar 

  88. R.I.G. Hughes: The structure and interpretation of quantum mechanics (Harvard University Press, Cambridge, 1989)

    Google Scholar 

  89. G.C. Ghirardi, A. Rimini, T. Weber: Phys. Rev. D 34, 470 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  90. P. Blanchard, A. Jadczyk: Helv. Phys. Acta 69, 613 (1996). quant-ph/9602010

    MATH  MathSciNet  Google Scholar 

  91. P. Blanchard, A. Jadczyk: EEQT: A way out of the quantum trap (1998). quant-ph/9812081

    Google Scholar 

  92. P. Pearle: in Open systems and measurement in relativistic quantum theory, ed. by F. Petruccione, H.P. Breuer (Springer Verlag, 1999). quant-ph/9901077

    Google Scholar 

  93. R.B. Griffiths: J. Stat. Phys. 36, 219 (1984)

    Article  MATH  ADS  Google Scholar 

  94. M. Gell-Mann, J.B. Hartle: in Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, ed. by S. Kobayashi, H. Ezawa, Y. Murayama, S. Nomura (Physical Society of Japan, Tokyo, 1990)

    Google Scholar 

  95. M. Gell-Mann, J.B. Hartle: in 25th International Conference on High Energy Physics, ed. by K. K. Phua, Y. Yamaguchi (World Scientific, Singapore, 1991)

    Google Scholar 

  96. R. Omnès: Rev. Mod. Phys. 64, 339 (1992)

    Article  ADS  Google Scholar 

  97. R. Omnès: The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994)

    MATH  Google Scholar 

  98. J.B. Hartle: Phys. Rev. D 37, 2818 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  99. J.B. Hartle: Phys. Rev. D 44, 3173 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  100. O. Rudolph: Int. J. Theor. Phys. 35, 1581 (1996). quant-ph/9512024

    Article  MATH  MathSciNet  Google Scholar 

  101. O. Rudolph: J. Math. Phys. 37, 5368 (1996). quant-ph/9605037

    Article  MATH  ADS  MathSciNet  Google Scholar 

  102. A. Kent: Phys. Scripta T76, 78 (1998) gr-qc/9809026

    Article  ADS  MathSciNet  Google Scholar 

  103. N. Yamada, S. Takagi: Prog. Theor. Phys. 85, 985 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  104. N. Yamada, S. Takagi: Prog. Theor. Phys. 86, 599 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  105. N. Yamada, S. Takagi: Prog. Theor. Phys. 87, 77 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  106. I.L. Egusquiza, J.G. Muga: Phys. Rev. A 62, 032103 (2000). quant-ph/0003041

    Article  ADS  MathSciNet  Google Scholar 

  107. J.J. Halliwell, E. Zafiris: Phys. Rev. D 57, 3351 (1998). quant-ph/9706045

    Article  ADS  MathSciNet  Google Scholar 

  108. J. Dalibard, Y. Castin, K. Molmer: Phys. Rev. Lett. 68, 580 (1992)

    Article  ADS  Google Scholar 

  109. H. Carmichael: An open systems approach to quantum optics (Sringer-Verlag Berlin, 1993)

    MATH  Google Scholar 

  110. G.C. Hegerfeldt: Phys. Rev. A 47, 449 (1993)

    Article  ADS  Google Scholar 

  111. M.B. Plenio, P.L. Knight: Rev. Mod. Phys. 70, 101 (1998). quant-ph/9702007

    Article  ADS  Google Scholar 

  112. R.J. Cook: Progress in Optics 28, 361 (1990)

    Article  Google Scholar 

  113. S. Stenholm: Physica Scripta 47, 724 (1993)

    Article  ADS  Google Scholar 

  114. T.A. Brun: Phys. Rev. Lett. 78, 1833 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  115. M. Büttiker, R. Landauer: Phys. Rev. Lett. 49, 1739 (1982)

    Article  ADS  Google Scholar 

  116. R.Y. Chiao: (1998). quant-ph/9811019

    Google Scholar 

  117. S. Brouard, R. Sala Mayato, J.G. Muga: Phys. Rev. A 49, 4312 (1994)

    Article  ADS  Google Scholar 

  118. P. Balcou, L. Dutriaux: Phys. Rev. Lett. 78, 851 (1997)

    Article  ADS  Google Scholar 

  119. E.H. Hauge, J.A. Stovneng: Rev. Mod. Phys. 61, 917 (1989)

    Article  ADS  Google Scholar 

  120. M. Büttiker: in Electronic Properties of Multilayers and Low-dimensional Semiconductor Structures, ed. by J.C. et al. (Plenum, New York, 1990), p. 297

    Google Scholar 

  121. R. Landauer: Ber. Bunsenges. Phys. Chem. 95, 404 (1991)

    Google Scholar 

  122. C.R. Leavens, G.C. Aers: in Scanning Tunneling Microscopy and Related Techniques, ed. by R. J. Behm, N. García, H. Rohrer (Kluwer, Dordrecht, 1990)

    Google Scholar 

  123. M. Jonson: ‘Tunneling times in quantum mechanical tunneling’. In: Quantum Transport in Semiconductors, ed. by D.K. Ferry, C. Jacoboni (Plenum, New York, 1991)

    Google Scholar 

  124. V.S. Olkhovsky, E. Recami: Phys. Rep. 214, 339 (1992)

    Article  ADS  Google Scholar 

  125. R. Landauer, Th. Martin: Rev. Mod. Phys. 66, 217 (1994)

    Article  ADS  Google Scholar 

  126. C.R. Leavens, G.C. Aers: Solid State Commun. 63, 1101 (1987)

    Article  ADS  Google Scholar 

  127. D. Sokolovski, L.M. Baskin: Phys. Rev. A 36, 4604 (1987)

    Article  ADS  Google Scholar 

  128. D. Sokolovski, J.N.L. Connor: Phys. Rev. A 42, 6512 (1990)

    Article  ADS  Google Scholar 

  129. D. Sokolovski, J.N.L. Connor: Phys. Rev. A 47, 4677 (1993)

    Article  ADS  Google Scholar 

  130. E. Pollak, W.H. Miller: Phys. Rev. Lett. 53, 115 (1984)

    Article  ADS  Google Scholar 

  131. E. Pollak: J. Chem. Phys. 83, 1111 (1985)

    Article  ADS  Google Scholar 

  132. J.G. Muga, S. Brouard, R. Sala: Phys. Lett. A 167, 24 (1992)

    Article  ADS  Google Scholar 

  133. B.A. van Tiggelen, A. Tip, A. Lagendijk: J. Phys. A 26, 1731 (1993)

    Article  ADS  Google Scholar 

  134. S. Brouard, R. Sala, J.G. Muga: Europhys. Lett. 22, 159 (1993)

    Article  ADS  Google Scholar 

  135. Y. Aharonov, L. Vaidman: Phys. Rev. A 41, 11 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  136. A.M. Steinberg: Phys. Rev. Lett. 74, 2405 (1995)

    Article  ADS  Google Scholar 

  137. C. Grupen: Particle Detectors (Cambridge University Press, Cambridge, 1996)

    Google Scholar 

  138. J.P. Palao, J.G. Muga, S. Brouard, A. Jadczyk: Phys. Lett. A233, 227 (1997). quant-ph/9901040

    ADS  Google Scholar 

  139. T.E. Hartman: J. Appl. Phys. 33, 3427 (1962)

    Article  ADS  Google Scholar 

  140. V. Delgado, J.G. Muga: Ann. Phys. (N.Y.) 248, 122 (1996)

    Article  ADS  Google Scholar 

  141. A.M. Steinberg, P.G. Kwiat, R.Y. Chiao: Phys. Rev. Lett. 71, 708 (1993)

    Article  ADS  Google Scholar 

  142. A. Enders, G. Nimtz: J. Phys. I France 3, 1089 (1993)

    Article  Google Scholar 

  143. A. Ranfagni, P. Fabeni, G.P. Pazzi, D. Mugnai: Phys. Rev. E 48, 1453 (1993)

    Article  ADS  Google Scholar 

  144. P. Mittelstädt, G. Nimtz, eds.: Workshop on Superluminal? Velocities, vol. 7 (1998)

    Google Scholar 

  145. R.Y. Chiao, A.M. Steinberg: in Progress in Optics XXXVII, ed. by E. Wolf (Elsevier, Amsterdam, 1997), pp. 347–406

    Google Scholar 

  146. G. Hegerfeldt: ‘Particle localization and the notion of Einstein causality’. In: Extensions of Quantum Theory, ed. by A. Horzela, E. Kapuscik (Apeiron, Mintreal 2001) pp. 9–16. quant-ph/0109044.

    Google Scholar 

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Muga, J.G., Mayato, R.S., Egusquiza, I.L. (2002). Introduction. In: Muga, J.G., Mayato, R.S., Egusquiza, I.L. (eds) Time in Quantum Mechanics. Lecture Notes in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45846-8_1

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