Advertisement

Foundations of Physics

, Volume 22, Issue 7, pp 879–948 | Cite as

Quantum/classical correspondence in the light of Bell's inequalities

  • Leonid A. Khalfin
  • Boris S. Tsirelson
Part III. Invited Papers Dedicated To Henry Margenau

Abstract

Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d'Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality.

The article contains a concise survey of some relevant domains: quantum and classical Bell-type inequalities; universal wave function; approaches to quantum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum theory.

Keywords

Quantum Theory Classical Mechanic Reduction Model Sharp Boundary Quantum Dynamic 
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.
    “Invited papers dedicated to John Stewart Bell,”Found. Phys. 20, No. 10 (1990) to21, No. 3 (1991).Google Scholar
  2. 2.
    “Josephson junction, macroscopic quantum tunneling, network,”Jpn. J. Appl. Phys. 26, Suppl. 3, 1378–1429 (1987).Google Scholar
  3. 3.
    G. S. Agarval, “Brownian motion of a quantum oscillator,”Phys. Rev. A 4, 739–747 (1971).Google Scholar
  4. 4.
    David Albert, “On quantum-mechanical automata,”Phys. Lett. A 98, 249–252 (1983).Google Scholar
  5. 5.
    Vinay Ambegaokar, Ulrich Eckern, and Gerd Schon, “Quantum dynamics of tunneling between superconductors,”Phys. Rev. Lett. 48, 1745–1748 (1982).Google Scholar
  6. 6.
    Huzihiro Araki, “A remark on Machida-Namiki theory of measurement,”Prog. Theor. Phys. 64, 719–730 (1980).Google Scholar
  7. 7.
    Alain Aspect, “Experimental tests of Bell's inequalities in atomic physics,”Atomic Physics, Vol. 8, I. Lindgrenet al., ed. (Plenum Press, New York), pp. 103–128.Google Scholar
  8. 8.
    Alain Aspect, Phillipe Grangier, and Gerard Roger, “Experimental tests of realistic local theories via Bell's theorem,”Phys. Rev. Lett. 47, 460–463 (1981); “Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell's inequalities,”Phys. Rev. Lett. 49, 91–94 (1982).Google Scholar
  9. 9.
    Alain Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell's inequalities using time-varying analysers,”Phys. Rev. Lett. 49, 1804–1807 (1982).Google Scholar
  10. 10.
    Alain Aspect and P. Grangier, “About resonant scattering and the other hypothetical effects in the Orsay atomic-cascade experiment tests of Bell inequalities: a discussion and some new experimental data,”Lett. Nuovo Cimento 43, 345–348 (1985).Google Scholar
  11. 11.
    John Baez, “Bell's inequality forC*-algebras,”Lett. Math. Phys. 13, 135–136 (1987).Google Scholar
  12. 12.
    L. Ballentine, “Limitations of the projection postulate,”Found. Phys. 20, 1329–1343 (1990).Google Scholar
  13. 13.
    L. Ballentine, “The statistical interpretation of quantum mechanics,”Rev. Mod. Phys. 42, 358–381 (1970).Google Scholar
  14. 14.
    Thomas Banks, Leonard Susskind, and Michael Peskin, “Difficulties for the evolution of pure states into mixed states,”Nucl. Phys. B 244, 125–134 (1984).Google Scholar
  15. 15.
    K. Baumann, “Quantenmechanik und Objektivierbarkeit,”Z. Naturforsch. A 25, 1954–1956 (1970).Google Scholar
  16. 16.
    John Bell, “Are there quantum jumps?” inSpeakable and Unspeakable in Quantum Mechanics (Cambridge Univ. Press, New York, 1987), pp. 201–212.Google Scholar
  17. 17.
    John Bell, “Introductory Remarks,”Phys. Rep. 137, 7–9 (1986); “Quantum field theory without observers,”Phys. Rep. 137, 49–54 (1986).Google Scholar
  18. 18.
    John Bell, “EPR correlations and EPW distributions,” Ref. 92, pp. 263–266.Google Scholar
  19. 19.
    John Bell, “On wave packet reduction in the Coleman-Hepp model,”Helv. Phys. Acta 48, 93–98 (1975).Google Scholar
  20. 20.
    John Bell, “Introduction to the hidden-variable question,” Ref. 59, pp. 171–181.Google Scholar
  21. 21.
    John Bell, “On the problem of hidden variables in quantum mechanics,”Rev. Mod. Phys. 38, 447–452 (1966).Google Scholar
  22. 22.
    John Bell, “On the Einstein-Podolsky-Rosen paradox,”Physics 1, 195–200 (1964).Google Scholar
  23. 23.
    John Bell, A. Shimony, M. Horne, and J. Clauser, “An exchange on local beables,”Dialectica 39, 85–110 (1985).Google Scholar
  24. 24.
    F. Berezin and M. Shubin,The Schrödinger Equation (Moscow University Press, Moscow, 1983) (in Russian).Google Scholar
  25. 25.
    David Bohm,Quantum theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1952).Google Scholar
  26. 26.
    David Bohm, “A suggested interpretation of the quantum theory in terms of “hidden” variables. I,”Phys. Rev. 85, 166–179 (1952); “A suggested interpretation of the quantum theory in terms of “hidden” variables. II,”Phys. Rev. 85, 180–193 (1952).Google Scholar
  27. 27.
    David Bohm, B. Hiley, and P. Kaloyerou, “An ontological basis for the quantum theory,”Phys. Rep. 144, 321–375 (1987).Google Scholar
  28. 28.
    David Bohm and J. Bub, “A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory,”Rev. Mod. Phys. 38, 453–469 (1966).Google Scholar
  29. 29.
    Niels Bohr, “The quantum postulate and the recent development of atomic theory,”Nature (London) 121, 580–590 (1928).Google Scholar
  30. 30.
    V. Braginsky, V. Mitrofanov, and V. Panov,Systems with small dissipation (Nauka, Moscow, 1981) (in Russian).Google Scholar
  31. 31.
    C. Brans, “Bell's theorem does not eliminate fully causal hidden variables,”Int. J. Theor. Phys. 27, 219–226 (1988).Google Scholar
  32. 32.
    M. Bronstein, “Quantization of gravitational waves,”Zh. Eksp. Teor. Fiz. 6, 195–236 (1936) (in Russian).Google Scholar
  33. 33.
    R. Brout, G. Horwitz, and D. Weil, “On the onset of time and temperature in cosmology,”Phys. Lett. B 192, 318–322 (1987).Google Scholar
  34. 34.
    J. Bub, “The Daneri-Loinger-Prosperi quantum theory of measurement,”Nuovo Cimento B 57, 503–520 (1968).Google Scholar
  35. 35.
    Paul Busch, Marian Grabowski, and Pekka Lahti, “Some remarks on effects, operations, and unsharp measurements,”Found. Phys. 2, 331–345 (1989).Google Scholar
  36. 36.
    A. Caldeira and A. Leggett, “Quantum tunneling in a dissipative system,”Ann. Phys. (N.Y.) 149, 374–456 (1983).Google Scholar
  37. 37.
    A. Caldeira and A. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,”Phys. Rev. Lett. 46, 211–214 (1981).Google Scholar
  38. 38.
    A. Caldeira and A. Leggett, “Influence of damping on quantum interference: An exactly soluble model,”Phys. Rev. A 31, 1059–1066 (1985).Google Scholar
  39. 39.
    Curtis Callan and Sidney Coleman, “Fate of the false vacuum. II. First quantum corrections,”Phys. Rev. D 16, 1762–1768 (1977).Google Scholar
  40. 40.
    Herbert Callen and Theodore Welton, “Irreversibility and generalized noise,”Phys. Rev. 83, 34–40 (1951).Google Scholar
  41. 41.
    Carlton Caves and G. J. Milburn, “Quantum mechanical model for continuous position measurements,”Phys. Rev. A 36, 5543–5555 (1987).Google Scholar
  42. 42.
    Carlton Caves, “Quantum mechanics of measurements distributed in time. II. Connections among formulations,”Phys. Rev. D 35, 1815–1830 (1987).Google Scholar
  43. 43.
    A. Cetto, L. de la Pena, and E. Santos, “A Bell inequality involving position, momentum, and energy,”Phys. Lett. A 113, 304–306 (1985).Google Scholar
  44. 44.
    Sudip Chakravarty and Anthony Leggett, “Dynamics of the two-state system with Ohmic dissipation,”Phys. Rev. Lett. 52, 5–8 (1984).Google Scholar
  45. 45.
    Kai Lai Chung,Markov Chains with Stationary Transition Probabilities (Springer-Verlag, New York, 1967).Google Scholar
  46. 46.
    Christopher Clarke, “Uncertain cosmology,” Ref. 200, pp. 51–60.Google Scholar
  47. 47.
    John F. Clauser and Abner Shimony, “Bell's theorem: experimental tests and implications,”Rep. Prog. Phys. 41, 1881–1927 (1978).Google Scholar
  48. 48.
    J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,”Phys. Rev. Lett. 23, 880–884 (1969).Google Scholar
  49. 49.
    Sidney Coleman, “Black holes as red herrings: topological fluctuations and the loss of quantum coherence,”Nucl. Phys. B 307, 867–882 (1988).Google Scholar
  50. 50.
    Sidney Coleman, “The use of instantons question,”The Whys of Subnuclear Physics, A. Zichichi, ed. (Plenum Press, New York, 1979), pp. 805–916.Google Scholar
  51. 51.
    B. S. Cirel'son, “Quantum generalizations of Bell's inequality,”Lett. Math. Phys. 4, 93–100 (1980).Google Scholar
  52. 52.
    A. Daneri, A. Loinger, and G. Prosperi, “Quantum theory of measurement and ergodicity conditions,”Nucl. Phys. 33, 297–319 (1962).Google Scholar
  53. 53.
    A. Daneri, A. Loinger, and G. Prosperi, “Further remarks on the relations between statistical mechanics and quantum theory of measurement,”Nuovo Cimento B 44, 119–128 (1966).Google Scholar
  54. 54.
    D. Danin,Probabilistic world (Znanie, Moscow, 1981) (in Russian).Google Scholar
  55. 55.
    Amitava Datta and Dipankar Home, “Quantum nonseparability versus local realism: a new test usingB 0939-10 system,”Phys. Lett. A 119, 3–6 (1986).Google Scholar
  56. 56.
    E. Davies, “Quantum stochastic processes,”Commun. Math. Phys. 15, 277–304 (1969); “Quantum stochastic processes. II,”19, 83–105 (1970); and “Quantum stochastic processes. III,”22, 51–70 (1971).Google Scholar
  57. 57.
    E. Davies and J. Lewis, “An operational approach to quantum probability,”Commun. Math. Phys. 17, 239–260 (1970).Google Scholar
  58. 58.
    Bernard D'Espagnat, “Towards a separable ‘empirical reality’?”Found. Phys. 20, 1147–1172 (1990).Google Scholar
  59. 59.
    Bernard D'Espagnat, (ed.), “Foundations of quantum mechanics,”Proc. Int. School of Phys. Enrico Fermi (Academic Press, New York, 1971).Google Scholar
  60. 60.
    W. De Baere, “Einstein-Podolsky-Rosen paradox and Bell's inequalities,”Adv. Electronics Electron Phys. 68, 245–336 (1986).Google Scholar
  61. 61.
    David Deutsch, “Quantum theory as a universal physical theory,”Int. J. Theor. Phys. 24, 1–41 (1985).Google Scholar
  62. 62.
    D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,”Proc. R. Soc. London A 400, 97–117 (1985).Google Scholar
  63. 63.
    Bryce DeWittet al. (ed.),The Many-Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1973).Google Scholar
  64. 64.
    Lajos Diosi, “Relativistic theory for continuous measurement of quantum field,”Phys. Rev. A 42, 5086–5092 (1990).Google Scholar
  65. 65.
    Lajos Diosi, “Continuous quantum measurement and Ito formalism,”Phys. Lett. A 129, 419–423 (1988).Google Scholar
  66. 66.
    Lajos Diosi, “Quantum stochastic processes as models for the state vector reduction,”J. Phys. A 21, 2885–2898 (1988).Google Scholar
  67. 67.
    Lajos Diosi, “On the motion of solids in modified quantum mechanics,”Europhys. Lett. 6, 285–290 (1988).Google Scholar
  68. 68.
    Lajos Diosi, “Exact solution for particle trajectories in modified quantum mechanics,”Phys. Lett. A 122, 221–225 (1987).Google Scholar
  69. 69.
    Lajos Diosi, “A universal master equation for the gravitational violation of quantum mechanics,”Phys. Lett. A 120, 377–381 (1987).Google Scholar
  70. 70.
    Albert Einstein, Boris Podolsky, and Nathan Rosen, “Can quantum-mechanical description of physical reality be considered complete?”Phys. Rev. 47, 777–780 (1935).Google Scholar
  71. 71.
    Albert Einstein, “Quanten-Mechanik und Wirklichkeit,”Dialectica 2, 320–323 (1948).Google Scholar
  72. 72.
    Albert Einstein, “Remarks concerning the essays brought together in this cooperative volume,”Albert Einstein, Philosopher-Scientist, P. A. Schillp, ed. (Harper and Row, New York, 1949), pp. 665–688.Google Scholar
  73. 73.
    J. Ellis, J. Hagelin, D. Nanopoulos, and M. Srednicki, “Search for violations of quantum mechanics,”Nucl. Phys. B 241, 381–405 (1984).Google Scholar
  74. 74.
    Hugh Everett, “‘Relative state’ formulation of quantum mechanics,”Rev. Mod. Phys. 29, 454–462 (1957).Google Scholar
  75. 75.
    Paul Fedele and Yong Kim, “Direct measurement of the velocity autocorrelation function for a Brownian test particle,”Phys. Rev. Lett. 44, 691–694 (1980).Google Scholar
  76. 76.
    Richard Feynman, “Quantum mechanical computers,”Found. Phys. 16, 507–531 (1986).Google Scholar
  77. 77.
    P. C. Fishburn and J. A. Reeds, “Bell inequalities, Grothendieck's constant and root two,” to appear (1991).Google Scholar
  78. 78.
    M. Froissart, “Constructive generalization of Bell's inequalities,”Nuovo Cimento B 64, 241–251 (1981).Google Scholar
  79. 79.
    W. Furry, “Note on the quantum-mechanical theory of measurement,”Phys. Rev. 49, 393–399 (1936).Google Scholar
  80. 80.
    C. Gardiner and M. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,”Phys. Rev. A 31, 3761–3774 (1985).Google Scholar
  81. 81.
    C. Gardiner, A. Parkins, and M. Collett, “Input and output in damped quantum systems. II. Methods in non-white-noise situations and application to inhibition of atomic phase decays,” Ref. 246, pp. 1683–1699.Google Scholar
  82. 82.
    Anupam Garg and N. David Mermin, “Farkas's lemma and the nature of reality: statistical implications of quantum correlations,”Found. Phys. 14, 1–39 (1984).Google Scholar
  83. 83.
    A. Garuccio and F. Selleri, “Enhanced photon detection in EPR type experiments,”Phys. Lett. A 103, 99–103 (1984).Google Scholar
  84. 84.
    A. Garuccio and F. Selleri, “Systematic derivation of all the inequalities of Einstein locality,”Found. Phys. 10, 209–216 (1980).Google Scholar
  85. 85.
    Yuval Gefen and Ora Entin-Wohlman, “Noise spectrum and the fluctuation-dissipation theorem in mesoscopic rings,”Ann. Phys. (N.Y.) 206, 68–89 (1991).Google Scholar
  86. 86.
    G. C. Ghirardi, R. Grossi, and P. Pearle, “Relativistic dynamical reduction models: general framework and examples,”Found. Phys. 20, 1271–1316 (1990).Google Scholar
  87. 87.
    G. Ghirardi, A. Rimini, and T. Weber, “The puzzling entanglement of Schrödinger's wave function,”Found. Phys. 18, 1–27 (1988).Google Scholar
  88. 88.
    G. Ghirardi, A. Rimini, and T. Weber, “Unified dynamics for microscopic and macroscopic systems,”Phys. Rev. D 34, 470–491 (1986).Google Scholar
  89. 89.
    S. Giddings and A. Strominger, “Loss of incoherence and determination of coupling constants in quantum gravity,”Nucl. Phys. B 307, 854–866 (1988).Google Scholar
  90. 90.
    N. Giordano, “Evidence for macroscopic quantum tunneling in one-dimensional superconductors,”Phys. Rev. Lett. 61, 2137–2140 (1988).Google Scholar
  91. 91.
    R. Glauber, “Amplifiers, attenuators, and Schrödinger's cat,” Ref. 92, pp. 336–372.Google Scholar
  92. 92.
    Daniel Greenberger (ed.), Proc. of a conference on “New Techniques and Ideas in Quantum Measurement Theory,”Ann. N.Y. Acad. Sci. 480, (1986).Google Scholar
  93. 93.
    Daniel M. Greenberger, Michael A. Horne, Abner Shimony, and Anton Zeilinger, “Bell's theorem without inequalities,”Am. J. Phys. 58, 1131–1143 (1990).Google Scholar
  94. 94.
    Daniel M. Greenberger and Alaine YaSin, “‘Haunted’ measurements in quantum theory,”Found. Phys. 19, 679–704 (1989).Google Scholar
  95. 95.
    A. Grib, “Bell's inequalities and experimental testing of quantum correlations on macroscopic distance,”Usp. Fiz. Nauk 142, 619–634 (1984) (in Russian).Google Scholar
  96. 96.
    F. Guinea, V. Hakim, and A. Muramatsu, “Diffusion and localization of a particle in a periodic potential coupled to a dissipative environment,”Phys. Rev. Lett. 54, 263–266 (1985).Google Scholar
  97. 97.
    F. Guinea, “Friction and particle-hole pairs,”Phys. Rev. Lett. 53, 1268–1271 (1984).Google Scholar
  98. 98.
    Alan Guth and So-Young Pi, “Quantum mechanics of the scalar field in the new inflationary Universe,”Phys. Rev. D 32, 1899–1920 (1985).Google Scholar
  99. 99.
    Rudolf Haag and Daniel Kastler, “An algebraic approach to quantum field theory,”J. Math. Phys. 5, 848–861 (1964).Google Scholar
  100. 100.
    Fritz Haake and Daniel Walls, “Overdamped and amplifying meters in the quantum theory of measurement,”Phys. Rev. A 36, 730–739 (1987).Google Scholar
  101. 101.
    V. Hakim and V. Ambegaokar, “Quantum theory of a free particle interacting with a linearly dissipative environment,”Phys. Rev. A 32, 423–434 (1985).Google Scholar
  102. 102.
    Stephen Hawking, “‘Wormholes in spacetime,”Phys. Rev. D 37, 904–910 (1988).Google Scholar
  103. 103.
    Stephen Hawking and R. Laflamme, “Baby universes and the nonrenormalizability of gravity,”Phys. Lett. B 209, 39–41 (1988).Google Scholar
  104. 104.
    Stephen Hawking, “Non-trivial topologies in quantum gravity,”Nucl. Phys. B 244, 135–146 (1984).Google Scholar
  105. 105.
    K. Hellwig and K. Kraus, “Formal description of measurements in local quantum field theory,”Phys. Rev. D 1, 566–571 (1970).Google Scholar
  106. 106.
    K. Hellwig and K. Kraus, “Pure operations and measurements,”Commun. Math. Phys. 11, 214–220 (1969); “Operations and measurements. II,”16, 142–147 (1970).Google Scholar
  107. 107.
    Klaus Hepp, “Quantum theory of measurement and macroscopic observables,”Helv. Phys. Acta 45, 237–248 (1972).Google Scholar
  108. 108.
    H. Hoffmann and P. Siemens, “Linear response theory for dissipation in heavy-ion collisions,”Nucl. Phys. A 257, 165–188 (1976).Google Scholar
  109. 109.
    H. Hoffmann and P. Siemens, “On the dynamics of statistical fluctuations in heavy ion collisions,”Nucl. Phys. A 275, 464–486 (1977).Google Scholar
  110. 110.
    A. Holevo,Probabilistic and Statistical Aspects of Quantum Theory (Nauka, Moscow, 1980) (in Russian); English translation: North-Holland, Amsterdam (1982).Google Scholar
  111. 111.
    D. Home and T. Marshall, “A stochastic local realist model for experiment which reproduces the quantum mechanical coincidence rates,”Phys. Lett. A 113, 183–186 (1985).Google Scholar
  112. 112.
    D. Home and F. Selleri, “Bell's theorem and the EPR paradox,”Riv. Nuovo Cimento 14, 1–95 (1991).Google Scholar
  113. 113.
    Michael Horne and Anton Zeilinger, “A Bell-type EPR experiment using linear momenta,” Ref. 157, pp. 435–439.Google Scholar
  114. 114.
    J. M. Jauch, “The problem of measurement in quantum mechanics,”Helv. Phys. Acta 37, 293–316 (1964).Google Scholar
  115. 115.
    J. M. Jauch, Eugene Wigner, and M. Yanase, “Some comments concerning measurements in quantum mechanics,”Nuovo Cimento B 48, 144–151 (1967).Google Scholar
  116. 116.
    E. Joos, “Why do we observe a classical spacetime?”Phys. Lett. A 116, 6–8 (1986)Google Scholar
  117. 117.
    E. Joos, “Quantum theory and the appearance of a classical world,” Ref. 92, pp. 6–13.Google Scholar
  118. 118.
    E. Joos, “Continuous measurement: Watchdog effect versus golden rule,”Phys. Rev. D 29, 1626–1633 (1984).Google Scholar
  119. 119.
    E. Joos and H. Zeh, “The emergence of classical properties through interaction with the environment,”Z. Phys. B 59, 223–243 (1985).Google Scholar
  120. 120.
    S. Kamefuchi (ed.),Proc. Int. Symp. on the Foundations of Quantum Mechanics in the light of New Technology (Phys. Soc. Japan, 1984).Google Scholar
  121. 121.
    T. Kennedy and D. Walls, “Squeezed quantum fluctuations and macroscopic quantum coherence,”Phys. Rev. A 37, 152–157 (1988).Google Scholar
  122. 122.
    Leonid Khalfin, “Quantum-classical correspondence in the light of classical Bell's and quantum Tsirelson's inequalities,” inComplexity, Entropy and the Physics of Information, SFI studies in the Sciences of Complexity, Vol. 9, W. Zurek, ed., (Addison-Wesley, New York, 1990).Google Scholar
  123. 123.
    Leonid Khalfin, “New results on the CP-violation problem,” Tech. Rep. DOE-ER40200-211, Center for Particle Theory, The University of Texas at Austin (February 1990).Google Scholar
  124. 124.
    Leonid Khalfin, “Euclidean approach, Langer-Polyakov-Coleman instanton method and the quantum decay theory,” Invited lecture to the seminar “Gauge Theories of Fundamental Interactions” at the Stefan Banach Int. Math. Centre, Warsaw (september 1988), inProc. of the XXXII Semester in the Stefan Banach Int. Math. Centre (World Scientific, Singapore, 1990), pp. 469–484.Google Scholar
  125. 125.
    Leonid Khalfin, “The problem of foundation of the satistical physics and the quantum decay theory,” Invited lectures at the Stefan Banach Int. Math. Center, Warsaw (September 1988).Google Scholar
  126. 126.
    Leonid Khalfin, “A new effect of the CP-violation for heavy mesons,” Preprint LOMI E-6-87, Leningrad (1987).Google Scholar
  127. 127.
    Leonid Khalfin, “A new effect of the CP-violation for neutral kaons,” Preprint LOMI E-7-87, Leningrad (1987).Google Scholar
  128. 128.
    Leonid Khalfin, “Euclidean approach, Langer-Polyakov-Coleman method and the quantum decay theory,” Report to the Scientific Conference, Nuclear Physics Department USSR Academy of Sciences (April 1987) (unpublished).Google Scholar
  129. 129.
    Leonid Khalfin, “The problem of the foundation of statistical physics, the non-exponentiality of the asymptotic of the correlation functions and the quantum decay theory,”First World Congress Bernoulli Society, Vol. 2 (1986), p. 692.Google Scholar
  130. 130.
    Leonid Khalfin, “Unconditional test of the CPT-invariance and a new effect of the CP-violation forK 0 − K0 mesons,”Proceedings of the III Seminar, Group Theoretical Methods in Physics, Vol. 2, M. Markov, ed. (1986), p. 608 (in Russian).Google Scholar
  131. 131.
    Leonid Khalfin, “The decay of false vacuum, macroscopic tunneling and the quantum decay theory,” Report to the Scientific Conference, Nuclear Physics Department, USSR Academy of Sciences (November 1986) (unpublished).Google Scholar
  132. 132.
    Leonid Khalfin, “A new effect of CP-violation forD 0 − D0,B 0 − B0, (T 0 − T0),” report to the Council of the Nuclear Physics Department, USSR Academy of Sciences (October 1985) (unpublished).Google Scholar
  133. 133.
    Leonid Khalfin, “Non-exponential decreasing of the correlation functions, the divergence of the kinetic coefficients and the quantum decay theory,”IV Int. Symp. on Inform. Theory (Tashkent), Vol. 3 (1984), p. 213.Google Scholar
  134. 134.
    Leonid Khalfin, “Bell's inequalities, Tsirelson's inequalities andK 0 − K0 0K 0 mesons,” Report to the session of Nuclear Physics Department, USSR Academy of Sciences (April 1983) (unpublished).Google Scholar
  135. 135.
    Leonid Khalfin, “The asymptotic dependence of the correlation functions and the divergence of the kinetic coefficients,”III Int. Vilnius Conf. on Prob. Theory and Math. Stat., Vol. 2 (1981), p. 215.Google Scholar
  136. 136.
    Leonid Khalfin, “Theory ofK 0 − K0,D 0 − d0,B 0 − b0, (T 0 − t0) mesons outside the Wigner-Weisskopf approximation and the CP-invariance problem,” Preprint LOMI P-4-80, Leingrad (1980).Google Scholar
  137. 137.
    Leonid Khalfin, “On Boltzman's H theorem,”Theor. Math. Phys. 35, 555–558 (1978).Google Scholar
  138. 138.
    Leonid Khalfin, “Modern situation with the mathematical foundation of statistical physics,”Usp. Mat. Nauk 33, 243 (1978) (in Russian).Google Scholar
  139. 139.
    Leonid Khalfin, “Investigations on the quantum theory of the unstable particles,” dissertation, Lab. Theor. Phys. JINR (1973) (unpublished).Google Scholar
  140. 140.
    Leonid Khalfin, “The CPT-invariance of the CP-noninvariant theory ofK 0 − 943-100 mesons and admissible mass distributions ofK S andK L mesons,”Pis'ma Zh. Eksp. Teor. Fiz. 15, 348 (1972) (in Russian).Google Scholar
  141. 141.
    Leonid Khalfin, “The problem of the foundations of statistical physics and the quantum decay theory,”Dokl. Akad. Nauk 162, 1273–1276 (1965) (in Russian).Google Scholar
  142. 142.
    Leonid Khalfin, “Quantum theory of the decay of the physical systems,” dissertation, Lebedev Phys. Inst., USSR Academy of Sciences (1960) (unpublished).Google Scholar
  143. 143.
    Leonid Khalfin, “On the decay theory of a quasi-stationary state,”Zh. Eksp. Teor. Fiz. 33, 1371 (1958) (in Russian).Google Scholar
  144. 144.
    Leonid Khalfin, “On the decay theory of a quasi-stationary state,”Dokl. Akad. Nauk SSSR 115, 277–280 (1957) (in Russian).Google Scholar
  145. 145.
    Leonid Khalfin and Boris Tsirelson, “Quantum/classical correspondence in the light of Bell's inequalities,” technical report MIT/LCS/TM/420, Massachusetts Institute of Technology (November 1990).Google Scholar
  146. 146.
    Leonid Khalfin and Boris Tsirelson, “A quantitative criterion of the applicability of the classical description within the quantum theory,” Ref. 156, pp. 369–401.Google Scholar
  147. 147.
    Leonid Khalfin and Boris Tsirelson, “Quantum and quasi-classical analogs of Bell inequalities,” Ref. 157, pp. 441–460.Google Scholar
  148. 148.
    S. Khoruzhy,Introduction to Algebraic Quantum Field Theory (Nauka, Moscow, 1986) (in Russian).Google Scholar
  149. 149.
    R. Koch, D. Van Harlingen, and J. Clarke, “Quantum-noise theory for the resistively shunted Josephson junction,”Phys. Rev. Lett. 45, 2132–2135 (1980); “Observation of zero-point fluctuations in a resistively shunted Josephson tunnel junction,”47, 1216–1219 (1981).Google Scholar
  150. 150.
    S. Kochen, “A new interpretation of quantum mechanics,” Ref. 157, pp 151–169.Google Scholar
  151. 151.
    Karl Kraus, “General state changes in quantum theory,”Ann. Phys. (N.Y.) 64, 311–335 (1971).Google Scholar
  152. 152.
    N. Krylov, “Works on foundations of statistical physics,” USSR Academy of Sciences Moscow and Leningrad (1950) (in Russian).Google Scholar
  153. 153.
    N. Krylov and V. Fock, “On the two main interpretations of the energy-time uncertainty relation,”Zh. Eksp. Teor. Fiz. 17, 93–107 (1947) (in Russian).Google Scholar
  154. 154.
    O. Kübler and H. Zeh, “Dynamics of quantum correlations,”Ann. Phys. (N.Y.) 76, 405–418 (1973).Google Scholar
  155. 155.
    R. Kubo, “The fluctuation-dissipation theorem,”Rep. Prog. Phys. 29, 255–284 (1966).Google Scholar
  156. 156.
    P. Lahtiet al. (ed.),Symposium on the Foundations of Modern Physics 1987 (World Scientific, Singapore, 1987).Google Scholar
  157. 157.
    P. Lahtiet al. (ed.),Symposium on the Foundations of Modern Physics 1985 (World Scientific, Singapore, 1985).Google Scholar
  158. 158.
    Lawrence Landau, “Empirical two-point correlation functions,”Found. Phys. 18, 449–460 (1988).Google Scholar
  159. 159.
    Lawrence Landau, “Gaussian quantum fields and stochastic electrodynamics,”Phys. Rev. A 37, 4449–4460 (1988).Google Scholar
  160. 160.
    Lawrence Landau, “On the violation of Bell's inequality in quantum theory,”Phys. Lett. A 120, 54–56 (1987).Google Scholar
  161. 161.
    Lawrence Landau, “Experimental tests of general quantum theories,”Lett. Math. Phys. 14, 33–40 (1987).Google Scholar
  162. 162.
    Lawrence Landau, “On the non-classical structure of the vacuum,”Phys. Lett. A 123, 115–118 (1987).Google Scholar
  163. 163.
    J. Langer, “Theory of the condensation point,”Ann. Phys. 41, 108–157 (1967); “Statistical theory of the decay of metastable states,”54, 258–275 (1969).Google Scholar
  164. 164.
    G. Lavrelashvili, V. Rubakov, and P. Tinyakov, “On the loss of quantum coherence via changing of space topology in quantum gravity,Pis'ma Zh. Eksp. Teor. Fiz. 46, 134–136 (1987) (in Russian).Google Scholar
  165. 165.
    T. D. Lee and C. N. Yang, unpublished; D. Inglis, “Completeness of quantum mechanics and charge-conjugation correlations of theta particles,”Rev. Mod. Phys. 33, 1–7 (1961).Google Scholar
  166. 166.
    T. D. Lee and C. S. Wu,Annu. Rev. Nucl. Sci. 15, 381–476 (1965);16, 471–599 (1966).Google Scholar
  167. 167.
    A. J. Leggett, “Schrödinger's cat and her laboratory cousins,”Contemp. Phys. 25, 583–598 (1984).Google Scholar
  168. 168.
    A. Leggett, “Macroscopic quantum systems and the quantum theory of measurement,”Prog. Theor. Phys. Suppl., No. 69, 80–100 (1980).Google Scholar
  169. 169.
    A. Leggett, “Quantum mechanics and realism at the macroscopic level. Is an experimental discrimination feasible?” Ref. 92, pp. 21–24.Google Scholar
  170. 170.
    A. Leggett, S. Chakravarty, A. Dorsey, M. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,”Rev. Mod. Phys. 59, 1–85 (1987).Google Scholar
  171. 171.
    A. J. Leggett and A. Garg, “Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?,”Phys. Rev. Lett. 54, 857–860 (1985).Google Scholar
  172. 172.
    A. J. Leggett and F. Sols, “On the concept of spontaneously broken gauge symmetry in condensed matter physics,”Found. Phys. 21, 353–364 (1991).Google Scholar
  173. 173.
    V. L. Lepore, “New inequalities from local realism,”Found Phys. Lett. 2, 15–26 (1989).Google Scholar
  174. 174.
    K. K. Likharev, “Really-quantum macroscopic effects in weak superconductivity,”Usp. Fiz. Nauk 139, 169–184 (1983) (in Russian).Google Scholar
  175. 175.
    A. Loinger, “Comments on a recent paper concerning the quantum theory of measurement,”Nucl. Phys. A 108, 245–249 (1968).Google Scholar
  176. 176.
    H. McKean,Stochastic Integrals (Academic Press, New York, 1969).Google Scholar
  177. 177.
    S. Machida and M. Namiki, “Theory of measurement in quantum mechanics. Mechanism of reduction of wave packet. I,”Prog. Theor. Phys. 63, 1457–1473 (1980); “Theory of measurement in quantum mechanics. Mechanism of reduction of wave packet. II,”Prog. Theor. Phys. 63, 1833–1847 (1980).Google Scholar
  178. 178.
    L. Mandelstam, “Lectures on foundations of quantum mechanics (the theory of indirect measurements),”Complete Collected Scientific Works, Vol. 5 (Academy of Sciences USSR, Moscow, 1950), pp. 345–415.Google Scholar
  179. 179.
    Norman Margolus, “Parallel quantum computation,” manuscript (1989).Google Scholar
  180. 180.
    T. Marshall, E. Santos, and F. Selleri, “Local realism has not been refuted by atomic cascade experiments,”Phys. Lett. A 98, 5–9 (1983).Google Scholar
  181. 181.
    T. Marshall, “The distance separating quantum theory from reality,”Phys. Lett. A 99, 163–166 (1983).Google Scholar
  182. 182.
    T. Marshall and E. Santos,Phys. Lett. A 108, 373–376 (1985).Google Scholar
  183. 183.
    John Martinis, Michel Devoret, and John Clarke, “Experimental tests for the quantum behavior of a macroscopic degree of freedom: the phase difference across a Josephson junction,”Phys. Rev. B 35, 4682–4698 (1987).Google Scholar
  184. 184.
    G. Milburn and D. Walls, “Effect of dissipation on interference in phase space,”Phys. Rev. A 38, 1087–1090 (1988).Google Scholar
  185. 185.
    N. Mott, “The wave mechanics of α-ray tracks,”Proc. R. Soc. London A 126, 79–84 (1929).Google Scholar
  186. 186.
    M. Namikiet al. (ed.),Proc. Second Int. Symp. on the Foundation of Quantum Mechanics in the Light of New Technology (Phys. Soc. Japan, 1987).Google Scholar
  187. 187.
    E. Nelson, “The locality problem in stochastic mechanics,” Ref. 92, pp. 533–538.Google Scholar
  188. 188.
    Z. Ou and L. Mandel, “Violation of Bell's inequality and classical probability in a two-photon correlation experiment,”Phys. Rev. Lett. 61, 50–53 (1988).Google Scholar
  189. 189.
    D. Palatnik, private communication.Google Scholar
  190. 190.
    S. Pascazio and J. Reignier, “On emission lifetimes in atomic cascade tests of the Bell inequality,”Phys. Lett. A 126, 163–167 (1987).Google Scholar
  191. 191.
    Wolfgang Pauli,Festschrift zum 60. Geburtstage A. Sommerfelds, Leipzig (1928).Google Scholar
  192. 192.
    Philip Pearle, “Alternative to the orthodox interpretation of quantum theory,”Am. J. Phys. 35, 742–753 (1967).Google Scholar
  193. 193.
    Asher Peres, “Existence of ‘free will’ as a problem of physics,”Found. Phys. 16, 573–584 (1986).Google Scholar
  194. 194.
    Asher Peres, “Reversible logic and quantum computers,”Phys. Rev. A 32, 3266–3276 (1985).Google Scholar
  195. 195.
    Asher Peres, “On quantum-mechanical automata,”Phys. Lett. A 101, 249–250 (1984).Google Scholar
  196. 196.
    Asher Peres, “When is a quantum measurement?” Ref. 92, pp. 438–448.Google Scholar
  197. 197.
    Asher Peres and Nathan Rosen, “Quantum limitations on the measurement of gravitational fields,”Phys. Rev. 118, 335–336 (1960).Google Scholar
  198. 198.
    W. Perrie, A. Duncan, H. Beyer, and H. Kleinpoppen, “Polarization correlation of the two photons emitted by metastable atomic deuterium: a test of Bell's inequality,”Phys. Rev. Lett. 54, 1790–1793 (1985).Google Scholar
  199. 199.
    A. M. Polyakov, “Hidden symmetry of the two-dimensional chiral fields,”Phys. Lett. B 72, 224–226 (1977).Google Scholar
  200. 200.
    W. C. Priceet al. (ed.)The Uncertainty Principle and Foundations of Quantum Mechanics: A Fifty Year's Survey (Wiley, New York, 1977).Google Scholar
  201. 201.
    201.Ilya Prigogine,From Being to Becoming: Time and Complexity in the Physical Sciences (W. H. Freeman, San Francisco, 1980).Google Scholar
  202. 202.
    H. Primas, “Contextual quantum objects and their ontic interpretation,” Ref. 156, pp. 251–275.Google Scholar
  203. 203.
    G. Prosperi, “The quantum measurement process and the observation of continuous trajectories,”Lect. Notes Math. 1055, 301–326 (1984).Google Scholar
  204. 204.
    Peter Rastall, “Locality, Bell's theorem, and quantum mechanics,”Found. Phys. 15, 963–972 (1985).Google Scholar
  205. 205.
    Michael Redhead, “Relativity and quantum mechanics—conflict or peaceful coexistence?” Ref. 92, pp. 14–20.Google Scholar
  206. 206.
    T. Regge, “Gravitational fields and quantum mechanics,”Nuovo Cimento 7, 215–221 (1958).Google Scholar
  207. 207.
    P. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantummechanical harmonic oscillator,”Phys. Rev. A 31, 471–478 (1985).Google Scholar
  208. 208.
    L. Rosenfeld, “The measuring process in quantum mechanics,”Prog. Theor. Phys. Supp., extra number, 222–231 (1965); “Questions of method in the consistency problem of quantum mechanics,”Nucl. Phys. A 108, 241–244 (1968).Google Scholar
  209. 209.
    S. M. Roy and V. Singh, “Hidden variable theories without non-local signalling and their experimental tests,”Phys. Lett. A 139, 437–441 (1989).Google Scholar
  210. 210.
    S. M. Roy and V. Singh, “Generalized beable quantum field theory,”Phys. Lett. B 234, 117–120 (1990).Google Scholar
  211. 211.
    C. Savage and D. Walls, “Damping of quantum conherence: the master-equation approach,”Phys. Rev. A 32, 2316–2323 (1985); “Quantum coherence and interference of damped free particles,”Phys. Rev. A 32, 3487–3492 (1985).Google Scholar
  212. 212.
    Erwin Schrödinger, “Die gegenwartige Situation in der Quantenmechanik,”Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).Google Scholar
  213. 213.
    S. Schlieder, “Einige Bemerkungen zur Zustandsänderung von relativistischen quantenmechanischen Systemen durch Messungen und zur Lokalitätsforderung,”Commun. Math. Phys. 7, 305–331 (1968).Google Scholar
  214. 214.
    A. Schmid, “Diffusion and localization in a dissipative quantum system,”Phys. Rev. Lett. 51, 1506–1509 (1983).Google Scholar
  215. 215.
    Albert Schmid, “On a quasiclassical Langevin equation,”J. Low Temp. Phys. 49, 609–626 (1982).Google Scholar
  216. 216.
    F. Selleri, “Realism and the wave-function of quantum mechanics,” Ref. 59, pp. 398–406.Google Scholar
  217. 217.
    F. Selleri, “Einstein locality and theK 0946-10 system,”Lett. Nuovo Cimento 36, 521–526 (1983).Google Scholar
  218. 218.
    I. Senitzky, “Dissipation in quantum mechanics. The harmonic oscillator,”Phys. Rev. 119, 670–679 (1960).Google Scholar
  219. 219.
    Y. Shih and C. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,”Phys. Rev. Lett. 61, 2921–2924 (1988).Google Scholar
  220. 220.
    A. Shimony, “Role of the observer in quantum theory,”Am. J. Phys. 31, 755–773 (1963).Google Scholar
  221. 221.
    Y. Sinai, “On foundations of the ergodic conjecture for one dynamical system of statistical mechanics,”Dokl. Akad. Nauk 153, 1261–1264 (1963); “Dynamical systems with elastic reflexion,”Usp. Mat. Nauk 25, 141–192 (1970) (in Russian).Google Scholar
  222. 222.
    J. Six, “Test of the nonseparability of theK 0946-20 system,”Phys. Lett. B 114, 200–202 (1982).Google Scholar
  223. 223.
    B. Spassky and A. Moskovsky, “On non-locality in quantum physics,”Usp. Fiz. Nauk 142, 599–617 (1984) (in Russian).Google Scholar
  224. 224.
    S. Srivastava, Vishwamittar, and I. S. Minhas, “On the quantization of linearly damped harmonic oscillator,”J. Math. Phys. 32, 1510–1515 (1991).Google Scholar
  225. 225.
    P. Stamp, “Influence of paramagnetic and Kondo impurities on macroscopic quantum tunneling in SQUID's,”Phys. Rev. Lett. 61, 2905–2908 (1988).Google Scholar
  226. 226.
    Henry Stapp, “Gauge-fields and integrated quantum-classical theory,” Ref. 92, pp. 326–335.Google Scholar
  227. 227.
    Stephen Summers and Reinhold Werner, “The vacuum violates Bell's inequalties,”Phys. Lett. A 110, 257–259 (1985).Google Scholar
  228. 228.
    Stephen Summers and Reinhold Werner, “Bell's inequalities and quantum field theory. I. General setting,”J. Math. Phys. 28, 2440–2447 (1987).Google Scholar
  229. 229.
    Stephen Summers and Reinhold Werner, “Bell's inequalities and quantum field theory. II. Bell inequaltities are maximally violated in the vacuum,”J. Math. Phys. 28, 2448–2456 (1987).Google Scholar
  230. 230.
    Stephen Summers and Reinhold Werner, “Maximal violation of Bell's inequalities is generic in quantum field theory,”Commun. Math. Phys. 110, 247–259 (1987).Google Scholar
  231. 231.
    G. Svetlichny, “Distinguishing three-body from two-body nonseparability by a Bell-type inequality,”Phys. Rev. D 35, 3066–3069 (1987).Google Scholar
  232. 232.
    Paola Tombesi and Antonio Mecozzi, “Generation of macroscopically distinguishable quantum states and detection by the squeezed-vacuum technique,” Ref. 246, pp. 1700–1709.Google Scholar
  233. 233.
    H. Treder, inAstrofisica e Cosmologia, Gravitazione, Quanti e Relatività (Giunti Barbera, Firenze, 1979).Google Scholar
  234. 234.
    Boris Tsirelson, “In comparison to what is the Planck constant small?” (to appear).Google Scholar
  235. 235.
    Boris Tsirelson, “Quantum analogs of Bell's inequalities: the case of two spacelike separated domains,” inProblems of the Theory of Probability Distributions IX, Math. Inst. Steklov (LOMI), Vol. 142 (1985), pp. 174–194 (in Russian).Google Scholar
  236. 236.
    Boris Tsirelson, “On a formal description of quantum systems that are similar to systems of stochastic automata,” inProceedings II School-Seminar on Locally Interacting Systems and Their Application in Biology, R. L. Dobrushin, V. I. Kryukov, and A. L. Toom, ed., (Biological Centre Acad. Sci. USSR, Pushchino, Moscow Region, 1979), pp. 100–138 (in Russian).Google Scholar
  237. 237.
    W. G. Unruh, “Quantum coherence, wormholes, and the cosmological constant,”Phys. Rev. D 40, 1053–1063 (1989).Google Scholar
  238. 238.
    W. G. Unruh and Wojciech H. Zurek, “Reduction of a wave packet in quantum Brownian motion,”Phys. Rev. D 40, 1071–1094 (1989).Google Scholar
  239. 239.
    Leon Van Hove, “Quantum-mechanical perturbations giving rise to a statistical transport equation,”Physica 21, 517–540 (1955).Google Scholar
  240. 240.
    Leon Van Hove, “Energy corrections and persistent perturbation effects in continuous spectra 2. The perturbed stationary states,”Physica 22, 343–354 (1956); “The approach to equilibrium in quantum statistics”23, 411–480 (1957); “The ergodic behavior of quantum many-body systems,”25, 268–276 (1959).Google Scholar
  241. 241.
    A. M. Vershik and B. S. Tsirelson, “Formulation of Bell-type problems and ‘noncommutative’ convex geometry,” to appear in:Ad. Sov. Math. 9, 95–114 AMS.Google Scholar
  242. 242.
    John von Neumann,Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, New York, 1932). English translation:Mathematical foundations of quantum mechanics (Princeton University Press, Princeton, New Jersey, 1955).Google Scholar
  243. 243.
    Milan Vujičic and Fedor Herbut, “Distant correlations in quantum mechanics,” Ref. 157, pp. 677–689.Google Scholar
  244. 244.
    H. Wakita, “Measurement in quantum mechanics,”Prog. Theor. Phys. 23, 32–40 (1960); “Measurement in quantum mechanics. II. Reduction of a wave packet,”27, 139–144 (1962); “Measurement in quantum mechanics. III. Macroscopic measurement and statistical operators,”27, 1156–1164 (1962).Google Scholar
  245. 245.
    D. Walls and G. Milburn, “Effect of dissipation on quantum coherence,”Phys. Rev. A 31, 2403–2408 (1985).Google Scholar
  246. 246.
    W. H. Weber (ed.), “Squeezed States of the Electromagnetic Field,”J. Opt. Soc. Am. B 4(10) (1987).Google Scholar
  247. 247.
    Carl Weizsacker, “Heisenberg's philosophy,” Ref. 156, pp. 277–293.Google Scholar
  248. 248.
    Carl Weizsacker, “Quantum theory and space-time,” Ref. 157, pp. 223–237.Google Scholar
  249. 249.
    John Archibald Wheeler, “Assessment of Everett's ‘relative state’ formulation of quantum theory,”Rev. Mod. Phys. 29, 463–465 (1957).Google Scholar
  250. 250.
    M. Whitaker, “The relative states and many-worlds interpretations of quantum mechanics and the EPR problem,”J. Phys. A 18, 253–264 (1985).Google Scholar
  251. 251.
    Eugene Wigner, “Remarks on the mind-body question,” inThe Scientist Speculates, I. J. Good, ed. (Heinemann, London 1962).Google Scholar
  252. 252.
    C. H. Woo, “Why the classical-quantal dualism is still with us,”Am. J. Phys. 54, 923–928 (1986).Google Scholar
  253. 253.
    William Wootters and Wojciech Zurek, “Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle,”Phys. Rev. D 19, 473–484 (1979).Google Scholar
  254. 254.
    B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,”Phys. Rev. Lett. 57, 13–16 (1986).Google Scholar
  255. 255.
    H. Zeh, “Measurement in Bohm's versus Everetts's quantum theory,”Found. Phys. 18, 723–730 (1988).Google Scholar
  256. 256.
    H. Zeh, “Emergence of classical time from a universal wavefunction,”Phys. Lett. A 116, 9–12 (1986).Google Scholar
  257. 257.
    H. Zeh, “Quantum theory and time asymmetry,”Found. Phys. 9, 803–818 (1979).Google Scholar
  258. 258.
    H. Zeh, “Toward a quantum theory of observation,”Found. Phys. 3, 109–116 (1973).Google Scholar
  259. 259.
    H. Zeh, “On the irreversibility of time and observation in quantum theory,” Ref. 59, pp. 263–273.Google Scholar
  260. 260.
    H. Zeh, “On the interpretation of measurement in quantum theory,”Found. Phys. 1, 69–76 (1970).Google Scholar
  261. 261.
    V. Zelevinsky, “Some problems of dynamics of heavy ions interactions,”Proceedings of XII Winter LIN Ph School, Leningrad, 1977, pp. 53–96 (in Russian).Google Scholar
  262. 262.
    Wojciech Zurek, “Quantum measurements and the environment induced transition from quantum to classical,” Preprint LA-UR-89-25, Los Alamos (1988).Google Scholar
  263. 263.
    Wojciech Zurek, “Reduction of the wavepacket: How long does it take?”Frontiers of Nonequilibrium Statistical Physics, G. T. Moore,et al., ed. (Plenum Press, New York 1986), pp. 145–151.Google Scholar
  264. 264.
    Wojciech Zurek, “Reduction of the wave packet and environment-induced superselection,” Ref. 92, pp. 89–97.Google Scholar
  265. 265.
    Wojciech Zurek, “Environment-induced superselection rules,”Phys. Rev. D 26, 1862–1880 (1982).Google Scholar
  266. 266.
    Wojciech Zurek, “Pointer basis of quantum apparatus: into what mixture does the wave packet collapse?,”Phys. Rev. D 24, 1516–1525 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Leonid A. Khalfin
    • 1
  • Boris S. Tsirelson
    • 2
  1. 1.Steklov Mathematical InstituteRussian Academy of Sciences, Leningrad DivisionLeningradRussia
  2. 2.School of MathematicsTel Aviv UniversityTel AvivIsrael

Personalised recommendations