Advertisement

Bell’s Universe: A Personal Recollection

  • Reinhold BertlmannEmail author
Chapter
Part of the The Frontiers Collection book series (FRONTCOLL)

Abstract

My collaboration and friendship with John Bell is recollected. I will explain his outstanding contributions in particle physics, in accelerator physics, and his joint work with Mary Bell. Mary’s work in accelerator physics is also summarized. I recall our quantum debates, mention some personal reminiscences, and give my personal view on Bell’s fundamental work on quantum theory, in particular, on the concept of contextuality and nonlocality of quantum physics. Finally, I describe the huge influence Bell had on my own work, in particular on entanglement and Bell inequalities in particle physics and their experimental verification, and on mathematical physics, where some geometric aspects of the quantum states are illustrated.

Keywords

Bell inequalities Nonlocality Contextuality Entanglement Factorization algebra Geometry 

PACS number:

03.65.Ud 03.65.Aa 02.10.Yn 03.67.Mn 

Notes

Acknowledgments

First of all, I am grateful to Mary Bell for the generosity of sharing her memories of her scientific career and her life with John. Many thanks, of course, to all my collaborators and friends, to Beatrix Hiesmayr, Nicolai Friis, Walter Grimus, Philipp Köhler, Heide Narnhofer, Gabriele Uchida and Anton Zeilinger, for the exciting and joyful discussions we had together. Last but not least, I would like to thank Renate Bertlmann for her lovingly company and continuous support in all that years.

References

  1. 1.
    J.S. Bell, R.A. Bertlmann, Z. Phys. C 4, 11 (1980)ADSCrossRefGoogle Scholar
  2. 2.
    R.A. Bertlmann, Acta Phys. Aust. 53, 305 (1981)Google Scholar
  3. 3.
    J.J. Sakurai, Phys. Lett. B 46, 207 (1973)ADSCrossRefGoogle Scholar
  4. 4.
    M.A. Shifman, V.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 385, 448, 519 (1979)Google Scholar
  5. 5.
    J.S. Bell, R.A. Bertlmann, Nucl. Phys. B 177, 218 (1981)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    R.A. Bertlmann, Phys. Lett. B 106, 336 (1981)ADSCrossRefGoogle Scholar
  7. 7.
    R.A. Bertlmann, Nucl. Phys. B 204, 387 (1982)ADSCrossRefGoogle Scholar
  8. 8.
    J.S. Bell, R.A. Bertlmann, Phys. Lett. B 137, 107 (1984)ADSCrossRefGoogle Scholar
  9. 9.
    J.S. Bell, letter to R.A. Bertlmann, 14th Nov 1983Google Scholar
  10. 10.
    J.S. Bell, R.A. Bertlmann, Nucl. Phys. B 187, 285 (1981)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    R.A. Bertlmann, J.S. Bell, Nucl. Phys. B 227, 435 (1983)ADSCrossRefGoogle Scholar
  12. 12.
    C. Quigg, J.L. Rosner, Phys. Rep. 56, 167 (1979)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    M. Krammer, H. Krasemann, Acta Phys. Aust. Suppl. 21, 259 (1979)Google Scholar
  14. 14.
    H. Grosse, A. Martin, Phys. Rep. 60, 341 (1980)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    W. Lucha, F.F. Schöberl, D. Gromes, Phys. Rep. 200, 127 (1991)ADSCrossRefGoogle Scholar
  16. 16.
    R.A. Bertlmann, Phys. Lett. B 148, 177 (1984)ADSCrossRefGoogle Scholar
  17. 17.
    H. Leutwyler, Phys. Lett. B 98, 447 (1981)ADSCrossRefGoogle Scholar
  18. 18.
    M.B. Voloshin, Nucl. Phys. B 154, 365 (1979)ADSCrossRefGoogle Scholar
  19. 19.
    R.A. Bertlmann, Nucl. Phys. B (Proc. Suppl.) 23, 307 (1991)Google Scholar
  20. 20.
    J.S. Bell, Proc. R. Soc. A 231, 479 (1955)ADSCrossRefGoogle Scholar
  21. 21.
    G. Lüders, Dan. Mat. Fys. Medd. 28, 5 (1954)Google Scholar
  22. 22.
    W. Pauli, in Niels Bohr and the Development of Physics, ed. by W. Pauli, L. Rosenfeld, V. Weisskopf. (McGraw-Hill, New York and Pergamon Press Ltd., London, 1955)Google Scholar
  23. 23.
    J.S. Bell, T.H.R. Skyrme, Phil. Mag. 1, 1055 (1956)ADSCrossRefGoogle Scholar
  24. 24.
    J.S. Bell, R.J. Eden, T.H.R. Skyrme, Nucl. Phys. 2, 586 (1956)CrossRefGoogle Scholar
  25. 25.
    J.S. Bell, Nucl. Phys. 4, 295 (1957)CrossRefGoogle Scholar
  26. 26.
    J.S. Bell, T.H.R. Skyrme, Proc. R. Soc. A 242, 129 (1957)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    J.S. Bell, Proc. R. Soc. A 242, 122 (1957)ADSCrossRefGoogle Scholar
  28. 28.
    J.S. Bell, Nucl. Phys. 5, 167 (1957)CrossRefGoogle Scholar
  29. 29.
    J.S. Bell, Proc. Phys. Soc. 73, 118 (1959)ADSCrossRefGoogle Scholar
  30. 30.
    J.S. Bell, Nucl. Phys. 12, 117 (1959)CrossRefGoogle Scholar
  31. 31.
    J.S. Bell, R.J. Blin-Stoyle, Nucl. Phys. 6, 87 (1958)CrossRefGoogle Scholar
  32. 32.
    J.S. Bell, E.J. Squires, Phys. Rev. Lett. 3, 96 (1959)ADSCrossRefGoogle Scholar
  33. 33.
    J.S. Bell, Formal theory of the optical model, in Lectures on the many body problem, ed. by E.R. Caianello (Academic Press, New York, 1962)Google Scholar
  34. 34.
    J.S. Bell, F. Mandl, Proc. Phys. Soc. 71, 272, 867 (1959)Google Scholar
  35. 35.
    D. Bohm, Phys. Rev. 85, 166 (1952). ibid p. 180 (1952)Google Scholar
  36. 36.
    M. Bell, Some Reminiscences, in Quantum [Un]Speakables, eds. by R.A. Bertlmann, A. Zeilinger (Springer, 2002), p. 3Google Scholar
  37. 37.
    J.S. Bell, J. Steinberger, in Proceedings of the Oxford International Conference on Elementary Particles, p. 195 (1965)Google Scholar
  38. 38.
    M. Veltman, Facts and Mysteries in Elementary Particle Physics (World Scientific, Paperback, 2003), p. 212zbMATHCrossRefGoogle Scholar
  39. 39.
    M. Bell, Wellcome address to Quantum [Un]Speakables II (2014). contribution to this bookGoogle Scholar
  40. 40.
    J.S. Bell, J. Løvseth, M. Veltman, in Proceedings of the Siena International Conference on Elementary Particles, p. 584 (1963)Google Scholar
  41. 41.
    J.S. Bell, M. Veltman, Phys. Lett. 5, 94 (1963)ADSCrossRefGoogle Scholar
  42. 42.
    J.S. Bell, M. Veltman, Phys. Lett. 5, 151 (1963)ADSCrossRefGoogle Scholar
  43. 43.
    M. Gell-Mann, Physics 1, 63 (1964)Google Scholar
  44. 44.
    J.S. Bell, Physics 1, 195 (1964)Google Scholar
  45. 45.
    J.S. Bell, Nuovo Cimento 47, 616 (1967)ADSCrossRefGoogle Scholar
  46. 46.
    M. Veltman, Phys. Rev. Lett. 17, 553 (1966)ADSCrossRefGoogle Scholar
  47. 47.
    J.S. Bell, Nuovo Cimento 50, 129 (1967)ADSCrossRefGoogle Scholar
  48. 48.
    D.G. Sutherland, Phys. Lett. 23, 384 (1966)ADSCrossRefGoogle Scholar
  49. 49.
    J.S. Bell, D.G. Sutherland, Nucl. Phys. B 4, 315 (1968)ADSCrossRefGoogle Scholar
  50. 50.
    D.G. Sutherland, Nucl. Phys. B 2, 433 (1967)ADSCrossRefGoogle Scholar
  51. 51.
    M. Veltman, Proc. R. Soc. A 301, 107 (1967)ADSCrossRefGoogle Scholar
  52. 52.
    R. Jackiw, A. Shimony, Phys. Perspect. 4, 78 (2004). arXiv:physics/0105046
  53. 53.
    J. Steinberger, Phys. Rev. 76, 1180 (1949)ADSCrossRefGoogle Scholar
  54. 54.
    M. Gell-Mann, M. Lévy, Nuovo Cimento 16, 705 (1960)CrossRefGoogle Scholar
  55. 55.
    J.S. Bell, R. Jackiw, Nuovo Cimento 60, 47 (1969)ADSCrossRefGoogle Scholar
  56. 56.
    S.L. Adler, Phys. Rev. 177, 2426 (1969)ADSCrossRefGoogle Scholar
  57. 57.
    R.A. Bertlmann, Anomalies in Quantum Field Theory (Oxford University Press, Paperback, 2000)zbMATHCrossRefGoogle Scholar
  58. 58.
    R.A. Bertlmann, E. Kohlprath, Ann. Phys. 288, 137 (2001)ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    R. Jackiw, letter to R.A. Bertlmann, 17th May 1996Google Scholar
  60. 60.
    R.A. Bertlmann, letter to R. Jackiw, 21st July 1996Google Scholar
  61. 61.
    J.S. Bell, E. de Rafael, Nucl. Phys. B 11, 611 (1969)ADSCrossRefGoogle Scholar
  62. 62.
    J.S. Bell, C.H.L. Smith, Nucl. Phys. B 24, 285 (1970)ADSCrossRefGoogle Scholar
  63. 63.
    J.S. Bell, C.H.L. Smith, Nucl. Phys. B 28, 317 (1971)ADSCrossRefGoogle Scholar
  64. 64.
    J.S. Bell, Acta Phys. Austriaca Suppl. XIII, 395 (1974)Google Scholar
  65. 65.
    J.S. Bell, A.J.G. Hey, Phys. Lett. 51B, 365 (1974)ADSCrossRefGoogle Scholar
  66. 66.
    J.S. Bell, H. Ruegg, Nucl. Phys. B 93, 12 (1975)ADSCrossRefGoogle Scholar
  67. 67.
    J.S. Bell, H. Ruegg, Nucl. Phys. B 104, 245 (1976)ADSCrossRefGoogle Scholar
  68. 68.
    P.G. Burke, I.C. Percival, John Stewart Bell. Biogr. Mems. Fellows R. Soc. Lond. 45, 1 (1999)CrossRefGoogle Scholar
  69. 69.
    J.S. Bell, W. Walkinshaw, A variational approach to disc loaded waveguides. AERE G/R 680 (1950)Google Scholar
  70. 70.
    J.S. Bell, W. Walkinshaw, Review of theory of dielectric loaded linear accelerators. AERE G/R 544 (1950)Google Scholar
  71. 71.
    J.S. Bell, Scattering by focussing foils in a proton linear accelerators. AERE T/M 62 (1952)Google Scholar
  72. 72.
    J.S. Bell, Phase debunching by focussing foils in a proton linear accelerators. AERE T/M 68 (1952)Google Scholar
  73. 73.
    J.S. Bell, Basic algebra of the strong focussing system. AERE T/R 1114 (1953)Google Scholar
  74. 74.
    M. Bell, K. Gottfried, M. Veltman (eds.), Quantum Mechanics, High Energy Physics and Accelerators, Selected Papers of John S. Bell (World Scientific, 1995)Google Scholar
  75. 75.
    J.S. Bell, Nature 171, 167 (1953)ADSCrossRefGoogle Scholar
  76. 76.
    J.S. Bell, Proc. Phys. Soc. B 66, 802 (1953)ADSCrossRefGoogle Scholar
  77. 77.
    J.S. Bell, Linear accelerator phase oscillations. AERE T/M 114 (1954)Google Scholar
  78. 78.
    W.G. Unruh, Phys. Rev. D 14, 870 (1976)ADSCrossRefGoogle Scholar
  79. 79.
    S. Hawking, Nature 248, 30 (1974). Commun. Math. Phys. 43, 199 (1975)Google Scholar
  80. 80.
    J.D. Jackson, Rev. Mod. Phys. 48, 417 (1976)ADSCrossRefGoogle Scholar
  81. 81.
    J.S. Bell, J.M. Leinaas, Nucl. Phys. B 212, 131 (1983)ADSCrossRefGoogle Scholar
  82. 82.
    J.S. Bell, J.M. Leinaas, Nucl. Phys. B 284, 488 (1987)ADSMathSciNetCrossRefGoogle Scholar
  83. 83.
    J.S. Bell, R.J. Hughes, J.M. Leinaas, Z. Phys. C 28, 75 (1985)ADSCrossRefGoogle Scholar
  84. 84.
    J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, 1987)Google Scholar
  85. 85.
    M. Bell, The secret service agent, in Kingussie Secondary School Magazine, p. 5 (1939–1940)Google Scholar
  86. 86.
    M. Bell, letter to R.A. Bertlmann, 16th Feb 2015Google Scholar
  87. 87.
    M. Bell, letter to R.A. Bertlmann, 23rd May 2013Google Scholar
  88. 88.
    M. Ross, Slow neutron absorption cross-section of elements. Rep. Prog. Phys. XII, 291 (1949)Google Scholar
  89. 89.
    M. Ross, W. Walkinshaw, Effect of corrugation pitch on performance of M.R.C. linear accelerator. AERE T/M 55 (1952)Google Scholar
  90. 90.
    M. Ross, Series impedance of double ridged wave guides. AERE T/M 58 (1952)Google Scholar
  91. 91.
    M. Ross, Note on the prebunching for proton linear accelerator. AERE T/M 66 (1952)Google Scholar
  92. 92.
    J.S. Bell, M. Ross, Heating of focussing foils by a proton beam. AERE T/M 70 (1952)Google Scholar
  93. 93.
    M. Ross, A strong focussing electrostatic lens. AERE T/M 83 (1953)Google Scholar
  94. 94.
    M. Bell, Shunt impedance of rod-loaded wave guides. AERE T/M 99 (1954)Google Scholar
  95. 95.
    M. Bell, A note on gaps at proton energies of 10 and 50 MeV in the proton linear accelerator. AERE T/M 101 (1954)Google Scholar
  96. 96.
    M. Bell, Focussing system for the 600 MeV proton linear accelerator. AERE T/M 112 (1954)Google Scholar
  97. 97.
    M. Bell, Nonlinear equations of motion in the synchrotron. AERE T/M 125 (1955)Google Scholar
  98. 98.
    M. Bell, Focussing in the proton linear accelerator. II, AERE T/M 128 (1955)Google Scholar
  99. 99.
    M. Bell, Perturbation formulae for Hill’s equation. AERE T/M 139 (1956)Google Scholar
  100. 100.
    M. Bell, Twist resonances. AERE T/R 2077 (1956)Google Scholar
  101. 101.
    M. Bell, An analytic treatment of nonlinear effects in the spiral ridged cyclotron. AERE T/R 2209 (1957)Google Scholar
  102. 102.
    M. Bell, Injection into the 7 GeV synchrotron. AERE T/M 155 (1957)Google Scholar
  103. 103.
    M. Bell, A note on Mathieu functions. Proc. Glasg. Math. Assoc. III, Part III, 132 (1957)Google Scholar
  104. 104.
    M. Bell, The effect of a second harmonic in a 4-ridged spiral cyclotron, AERE R-3326 (1960)Google Scholar
  105. 105.
    G.I. Budker, At. Energy 22, 346 (1967)Google Scholar
  106. 106.
    G.I. Budker, N.S. Dikansky, V.I. Kudelainen, I.N. Meshkov, V.V. Parkhomchuk, D.V. Pestrikov, A.N. Skrinsky, B.N. Sukhina, Part. Accel. 7, 197 (1976)Google Scholar
  107. 107.
    M. Bell, Part. Accel. 10, 101 (1980)Google Scholar
  108. 108.
    M. Bell et al., Phys. Lett. 87B, 275 (1979)ADSCrossRefGoogle Scholar
  109. 109.
    M. Bell, J. Chaney, H. Herr, F. Krienen, P. Møller-Petersen, G. Petrucci, Nucl. Instrum. Methods 190, 237 (1981)ADSCrossRefGoogle Scholar
  110. 110.
    J.S. Bell, M. Bell, Part. Accel. 11, 233 (1981)Google Scholar
  111. 111.
    M. Bell, J.S. Bell, Part. Accel. 12, 49 (1982)Google Scholar
  112. 112.
    M. Bell, J.S. Bell, Part. Accel. 13, 13 (1983)Google Scholar
  113. 113.
    M. Bell, J.S. Bell, Part. Accel. 22, 301 (1988)Google Scholar
  114. 114.
    R. Bankenbecler, S.D. Drell, Phys. Rev. D 36, 277 (1987)ADSCrossRefGoogle Scholar
  115. 115.
    A.A. Sokolov, I.M. Ternov, Synchrotron Radiation, Pergamon (1971)Google Scholar
  116. 116.
    A.I. Nikishov, V.I. Ritus, Sov. Phys. JETP 25, 1135 (1967)ADSGoogle Scholar
  117. 117.
    A.N. Matveev, ZETF 31, 479 (1956). Sov. Phys. JETP 4, 409 (1957)Google Scholar
  118. 118.
    V.N. Baier, V.M. Katkov, Sov. Phys. JETP 26, 854 (1968). Sov. Phys. JETP 28, 807 (1969)Google Scholar
  119. 119.
    M. Bell, J.S. Bell, Part. Accel. 24, 1 (1988)Google Scholar
  120. 120.
    M. Bell, J.S. Bell, Nucl. Instrum. Methods Phys. Res. A 275, 258 (1989)Google Scholar
  121. 121.
    J.S. Bell, Bertlmann’s socks and the nature of reality, CERN preprint Ref.TH.2926-CERN, 18 July 1980Google Scholar
  122. 122.
    A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)ADSCrossRefGoogle Scholar
  123. 123.
    J.S. Bell, J. de Phys., Colloque C2, Suppl. 3, Tome 42, C2-41 (1981)Google Scholar
  124. 124.
    A. Aspect, J. Dalibard, G. Roger, Phys. Rev. Lett. 49, 1804 (1982)ADSMathSciNetCrossRefGoogle Scholar
  125. 125.
    N.D. Mermin, Rev. Mod. Phys. 65, 803 (1993)ADSMathSciNetCrossRefGoogle Scholar
  126. 126.
    J.S. Bell, Rev. Mod. Phys. 38, 447 (1966)ADSCrossRefGoogle Scholar
  127. 127.
    J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin 1932). Princeton University Press, English translation (1955)Google Scholar
  128. 128.
    G. Hermann, Die naturphilosophischen Grundlagen der Quantenmechanik. Abhandlungen der Fries’schen Schule 6, 69 (1935)Google Scholar
  129. 129.
    J. Conway, S.B. Kochen, The geometry of quantum paradoxes, in Quantum [Un]speakables, eds. by R.A. Bertlmann, A. Zeilinger (Springer, 2002), p. 257Google Scholar
  130. 130.
    A.M. Gleason, J. Math. Mech. 6, 885 (1957)MathSciNetGoogle Scholar
  131. 131.
    S.B. Kochen, E. Specker, J. Math. Mech. 17, 59 (1967)MathSciNetGoogle Scholar
  132. 132.
    E. Amselem, M. Bourennane, C. Budroni, A. Cabello, O. Gühne, M. Kleinmann, J.-Å. Larsson, M. Wieśniak, Phys. Rev. Lett. 110, 078901 (2013)ADSCrossRefGoogle Scholar
  133. 133.
    G. Cañas, S. Etcheverry, E.S. Gómez, C. Saavedra, G.B. Xavier, G. Lima, A. Cabello, Phys. Rev. A 90, 012119 (2014)ADSCrossRefGoogle Scholar
  134. 134.
    A. Cabello, S. Severini, A. Winter, Phys. Rev. Lett. 112, 040401 (2014)ADSCrossRefGoogle Scholar
  135. 135.
    A. Cabello, P. Badziag, M.T. Cunha, Phys. Rev. Lett. 111, 180404 (2013)ADSCrossRefGoogle Scholar
  136. 136.
    O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, J.-Å. Larsson, Phys. Rev. A 89, 062107 (2014)ADSCrossRefGoogle Scholar
  137. 137.
    A. Acín, T. Fritz, A. Leverrier, A.B. Sainz, Commun. Math. Phys. 334, 533 (2015)ADSCrossRefGoogle Scholar
  138. 138.
    A. Cabello, The unspeakable why, talk at Quantum [Un]Speakables II (2014). Contribution in this bookGoogle Scholar
  139. 139.
    D. Bohm, Y. Aharonov, Phys. Rev. 108, 1070 (1957)ADSMathSciNetCrossRefGoogle Scholar
  140. 140.
    J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)ADSCrossRefGoogle Scholar
  141. 141.
    G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, A. Zeilinger, Phys. Rev. Lett. 81, 5039 (1998)ADSMathSciNetCrossRefGoogle Scholar
  142. 142.
    G. Weihs, Ein Experiment zum Test der Bellschen Ungleichung unter Einstein Lokalität, Ph.D. Thesis, University of Innsbruck (1998)Google Scholar
  143. 143.
    E.P. Wigner, Am. J. Phys. 38, 1005 (1970)ADSCrossRefGoogle Scholar
  144. 144.
    J.F. Clauser, M.A. Horne, Phys. Rev. D 10, 526 (1974)ADSCrossRefGoogle Scholar
  145. 145.
    H.M. Wiseman, E.G. Cavalcanti, Causarum Investigatio and the Two Bells Theorems of John Bell, talk at Quantum [Un]Speakables II (2014). Contribution in this bookGoogle Scholar
  146. 146.
    N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, S. Wehner, Rev. Mod. Phys. 86, 419 (2014)ADSCrossRefGoogle Scholar
  147. 147.
    O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009)ADSMathSciNetCrossRefGoogle Scholar
  148. 148.
    W. Pauli, M. Born, 31st March 1954, in Wolfgang Pauli, Scientific Correspondence with Bohr, Einstein, Heisenberg, vol. IV, ed. by von K. Meyenn (Springer, 1999), Part II, pp. 1953–1954Google Scholar
  149. 149.
    J.F. Clauser, Early history of Bell’s theorem, in Quantum [Un]speakables, eds. by R.A. Bertlmann, A. Zeilinger (Springer, 2002), p. 61Google Scholar
  150. 150.
    J.F. Clauser, Bull. Am. Phys. Soc. 14, 578 (1969)Google Scholar
  151. 151.
    S.J. Freedman, J.F. Clauser, Phys. Rev. Lett. 28, 938 (1972)ADSCrossRefGoogle Scholar
  152. 152.
    S.J. Freedman, LBL Rep. 191 (1972). Lawrence Berkeley National LaboratoryGoogle Scholar
  153. 153.
    E.S. Fry, R.C. Thompson, Phys. Rev. Lett. 37, 465 (1976)ADSCrossRefGoogle Scholar
  154. 154.
    A. Pais, Subtle is the Lord, The Science and Life of Albert Einstein (Oxford University Press, 1982)Google Scholar
  155. 155.
    A. Aspect, Phys. Rev. D 14, 1944 (1976)ADSCrossRefGoogle Scholar
  156. 156.
    A. Aspect, P. Grangier, G. Roger, Phys. Rev. Lett. 47, 460 (1981)ADSCrossRefGoogle Scholar
  157. 157.
    A. Aspect, P. Grangier, G. Roger, Phys. Rev. Lett. 49, 91 (1982)ADSCrossRefGoogle Scholar
  158. 158.
    A. Aspect, P. Grangier, Lett. Nuovo Cimento 43, 345 (1985)CrossRefGoogle Scholar
  159. 159.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000)Google Scholar
  160. 160.
    R.A. Bertlmann, A. Zeilinger (eds.), Quantum [Un]speakables (Springer, 2002)Google Scholar
  161. 161.
    J. Brendel, E. Mohler, W. Martienssen, Eur. Phys. Lett. 20, 575 (1992)ADSCrossRefGoogle Scholar
  162. 162.
    P.R. Tapster, J.G. Rarity, P.C.M. Owens, Phys. Rev. Lett. 73, 1923 (1994)ADSCrossRefGoogle Scholar
  163. 163.
    W. Tittel, J. Brendel, H. Zbinden, N. Gisin, Phys. Rev. Lett. 81, 3563 (1998)ADSCrossRefGoogle Scholar
  164. 164.
    D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Nature 390, 575 (1997)ADSCrossRefGoogle Scholar
  165. 165.
    X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, A. Zeilinger, Nature 489, 269 (2012)ADSCrossRefGoogle Scholar
  166. 166.
    T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000)ADSCrossRefGoogle Scholar
  167. 167.
    N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002)ADSCrossRefGoogle Scholar
  168. 168.
    K.J. Resch, M. Lindenthal, B. Blauensteiner, H.J. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, A. Zeilinger, Opt. Express 13, 202 (2005)ADSCrossRefGoogle Scholar
  169. 169.
    R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, A. Zeilinger, Nat. Phys. 3, 481 (2007)CrossRefGoogle Scholar
  170. 170.
    M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S.W. Nam, R. Ursin, A. Zeilinger, Nature 497, 227 (2013)ADSCrossRefGoogle Scholar
  171. 171.
    P.H. Eberhard, Phys. Rev. A 47, 747 (1993)ADSCrossRefGoogle Scholar
  172. 172.
    M.A. Rowe, D. Kielpinsky, V. Meyer, C.A. Sackett, W.M. Itano, D.J. Wineland, Nature 409, 791 (2001)ADSCrossRefGoogle Scholar
  173. 173.
    Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, H. Rauch, Nature 425, 45 (2003)ADSCrossRefGoogle Scholar
  174. 174.
    Y. Hasegawa, K. Durstberger-Rennhofer, S. Sponar, H. Rauch, Kochen-Specker theorem studied with neutron interferometer (2010). arXiv:1004.2836
  175. 175.
    H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, Y. Hasegawa, Phys. Rev. Lett. 103, 040403 (2009)ADSCrossRefGoogle Scholar
  176. 176.
    J.S. Bell, La nouvelle cuisine, in Between Science and Technology, eds. by A. Sarlemijn, P. Kroes (Elsevier Science Publishers, 1990)Google Scholar
  177. 177.
    J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edn. (Cambridge University Press, 2004)Google Scholar
  178. 178.
    A. Einstein, Ann. Phys. 23, 371 (1907)CrossRefGoogle Scholar
  179. 179.
    R.A. Bertlmann, Bell’s theorem and the nature of reality, preprint University of Vienna, 1988. Found. Phys. 20, 1191 (1990)ADSMathSciNetCrossRefGoogle Scholar
  180. 180.
    D. Greenberger, Interview given at Quantum [Un]Speakables II (Vienna, 2014). https://vimeo.com/113838670
  181. 181.
    A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001)ADSCrossRefGoogle Scholar
  182. 182.
    Catalogue of the exhibition Action at a Distance: The Life and Legacy of John Stewart Bell, The Naughton Gallery, Queen’s University Belfast, 2014; Video of the exhibition. http://www.mediator.qub.ac.uk/ms/BellExb.mp4
  183. 183.
    Announcement of Quantum [Un]Speakables III. https://www.youtube.com/watch?v=BgUtWihTvDM
  184. 184.
    R.A. Bertlmann, W. Grimus, Phys. Lett. B 392, 426 (1997)ADSCrossRefGoogle Scholar
  185. 185.
    R.A. Bertlmann, W. Grimus, Phys. Rev. D 58, 034014 (1998)ADSCrossRefGoogle Scholar
  186. 186.
    A. Apostolakis et al., CPLEAR Collection. Phys. Lett. B 422, 339 (1998)ADSCrossRefGoogle Scholar
  187. 187.
    R.A. Bertlmann, W. Grimus, B.C. Hiesmayr, Phys. Rev. D 60, 114032 (1999)ADSCrossRefGoogle Scholar
  188. 188.
    R.A. Bertlmann, Entanglement, Bell inequalities and decoherence in particle physics, in Quantum Coherence: From Quarks to Solids, vol. 689, eds. by W. Pötz, J. Fabian, U. Hohensteiner. Lecture Notes in Physics (Springer, 2006), pp. 1–45Google Scholar
  189. 189.
    C. Schuler, Entanglement, Bell inequalities and decoherence in neutral K-meson systems, Bachelor Thesis, University of Vienna (2014)Google Scholar
  190. 190.
    G. Amelino-Camelia et al., Eur. Phys. J. C 68, 619 (2010)ADSCrossRefGoogle Scholar
  191. 191.
    G. Lindblad, Commun. Math. Phys. 48, 119 (1976)ADSMathSciNetCrossRefGoogle Scholar
  192. 192.
    V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976)ADSMathSciNetCrossRefGoogle Scholar
  193. 193.
    R.A. Bertlmann, W. Grimus, Phys. Rev. D 64, 056004 (2001)ADSCrossRefGoogle Scholar
  194. 194.
    C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)ADSMathSciNetCrossRefGoogle Scholar
  195. 195.
    S. Hill, W.K. Wootters, Phys. Rev. Lett. 78, 5022 (1997)ADSCrossRefGoogle Scholar
  196. 196.
    W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  197. 197.
    W.K. Wootters, Quantum Inf. Comput. 1, 27 (2001)MathSciNetGoogle Scholar
  198. 198.
    R.A. Bertlmann, K. Durstberger, B.C. Hiesmayr, Phys. Rev. A 68, 012111 (2003)ADSCrossRefGoogle Scholar
  199. 199.
    R.A. Bertlmann, B.C. Hiesmayr, Phys. Rev. A 63, 062112 (2001)ADSCrossRefGoogle Scholar
  200. 200.
    R.A. Bertlmann, A. Bramon, G. Garbarino, B.C. Hiesmayr, Phys. Lett. A 332, 355 (2004)ADSCrossRefGoogle Scholar
  201. 201.
    F. Uchiyama, Phys. Lett. A 231, 295 (1997)ADSCrossRefGoogle Scholar
  202. 202.
    R.A. Bertlmann, W. Grimus, B.C. Hiesmayr, Phys. Lett. A 289, 21 (2001)ADSCrossRefGoogle Scholar
  203. 203.
    B.C. Hiesmayr, A. Di Domenico, C. Curceanu, A. Gabriel, M. Huber, J.-A. Larsson, P. Moskal, Eur. Phys. J. C 72, 1856 (2012)ADSCrossRefGoogle Scholar
  204. 204.
    A. Di Domenico, privat communication to R.A. Bertlmann (2014)Google Scholar
  205. 205.
    A. Bramon, R. Escribano, G. Garbarino, Found. Phys. 36, 563 (2006)ADSMathSciNetCrossRefGoogle Scholar
  206. 206.
    A. Bramon, R. Escribano, G. Garbarino, A review on Bell inequality tests with neutral kaons, ed. by A. Di Domenico. Frascati Physics Series, vol. XLIII, p. 217 (2007)Google Scholar
  207. 207.
    A. Bramon, G. Garbarino, Phys. Rev. Lett. 88, 040403 (2002)ADSCrossRefGoogle Scholar
  208. 208.
    A. Bramon, G. Garbarino, Phys. Rev. Lett. 89, 160401 (2002)ADSCrossRefGoogle Scholar
  209. 209.
    H. Tataroglu, Nichtlokale Korrelation in Kaonischen Systemen, Diploma Thesis, University of Vienna (2009)Google Scholar
  210. 210.
    B.C. Hiesmayr, Weak Interaction Processes: Which Quantum Information is revealed? (2014). arXiv:1410.1707
  211. 211.
    B.C. Hiesmayr, Bringing Bells Theorem Back to the Domain of Particle Physics and Cosmology (2015). Contribution to this bookGoogle Scholar
  212. 212.
    J.-L. Li, C.-F. Qiao, Sci. China G 53, 870 (2010)CrossRefGoogle Scholar
  213. 213.
    Y.-B. Ding, J.-L. Li, C.-F. Qiao, High Energy Phys. Nucl. Phys. 31, 1086 (2007)Google Scholar
  214. 214.
    J.-L. Li, C.-F. Qiao, Phys. Lett. A 373, 4311 (2009)ADSCrossRefGoogle Scholar
  215. 215.
    N. Friis, R.A. Bertlmann, M. Huber, B.C. Hiesmayr, Phys. Rev. A 81, 042114 (2010)ADSCrossRefGoogle Scholar
  216. 216.
    I. Fuentes-Schuller, R.B. Mann, Phys. Rev. Lett. 95, 120404 (2005)ADSMathSciNetCrossRefGoogle Scholar
  217. 217.
    D.E. Bruschi, J. Louko, E. Martín-Martínez, A. Dragan, I. Fuentes, Phys. Rev. A 82, 042332 (2010)ADSCrossRefGoogle Scholar
  218. 218.
    N. Friis, P. Köhler, E. Martín-Martínez, R.A. Bertlmann, Phys. Rev. A 84, 062111 (2011)ADSCrossRefGoogle Scholar
  219. 219.
    N. Gisin, Phys. Lett. A 154, 201 (1991)ADSMathSciNetCrossRefGoogle Scholar
  220. 220.
    R.A. Bertlmann, J. Phys. A: Math. Theor. 47, 424007 (2014)ADSMathSciNetCrossRefGoogle Scholar
  221. 221.
    R.F. Werner, Phys. Rev. A 40, 4277 (1989)ADSCrossRefGoogle Scholar
  222. 222.
    A. Peres, Phys. Rev. Lett. 77, 1413 (1996)ADSMathSciNetCrossRefGoogle Scholar
  223. 223.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)ADSMathSciNetCrossRefGoogle Scholar
  224. 224.
    R. Horodecki, P. Horodecki, M. Horodecki, Phys. Lett. A 200, 340 (1995)ADSMathSciNetCrossRefGoogle Scholar
  225. 225.
    R.A. Bertlmann, H. Narnhofer, W. Thirring, Phys. Rev. A 66, 032319 (2002)ADSMathSciNetCrossRefGoogle Scholar
  226. 226.
    B.M. Terhal, Phys. Lett. A 271, 319 (2000)ADSMathSciNetCrossRefGoogle Scholar
  227. 227.
    R.A. Bertlmann, P. Krammer, Ann. Phys. 324, 1388 (2009)ADSMathSciNetCrossRefGoogle Scholar
  228. 228.
    K.G.H. Vollbrecht, R.F. Werner, Phys. Rev. A 64, 062307 (2000)ADSCrossRefGoogle Scholar
  229. 229.
    R. Horodecki, M. Horodecki, Phys. Rev. A 54, 1838 (1996)ADSMathSciNetCrossRefGoogle Scholar
  230. 230.
    W. Thirring, R.A. Bertlmann, P. Köhler, H. Narnhofer, Eur. Phys. J. D 64, 181 (2011)ADSCrossRefGoogle Scholar
  231. 231.
    P. Zanardi, Phys. Rev. Lett. 87, 077901 (2001)ADSCrossRefGoogle Scholar
  232. 232.
    M. Kuś, K. Życzkowski, Phys. Rev. A 63, 032307 (2001)ADSMathSciNetCrossRefGoogle Scholar
  233. 233.
    K. Życzkowski, I. Bengtsson, An Introduction to Quantum Entanglement: a Geometric Approach. arXiv:quant-ph/0606228
  234. 234.
    I. Bengtsson, K. Życzkowski, Geometry of Quantum states: An Introduction to Quantum Entanglement (Cambridge University Press, 2006)Google Scholar
  235. 235.
    R.A. Bertlmann, H. Narnhofer, W. Thirring, Eur. Phys. J. D 67, 62 (2013)ADSCrossRefGoogle Scholar
  236. 236.
    G. Uchida, R.A. Bertlmann, B.C. Hiesmayr, Phys. Lett. A 379, 2698 (2015)Google Scholar
  237. 237.
    G. Krenn, A. Zeilinger, Phys. Rev. A 54, 1793 (1996)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of ViennaViennaAustria

Personalised recommendations