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

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## 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## Preview

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## References

- 1.“Invited papers dedicated to John Stewart Bell,”
*Found. Phys.***20**, No. 10 (1990) to**21**, No. 3 (1991).Google Scholar - 2.“Josephson junction, macroscopic quantum tunneling, network,”
*Jpn. J. Appl. Phys.***26**, Suppl. 3, 1378–1429 (1987).Google Scholar - 3.G. S. Agarval, “Brownian motion of a quantum oscillator,”
*Phys. Rev. A***4**, 739–747 (1971).Google Scholar - 4.
- 5.Vinay Ambegaokar, Ulrich Eckern, and Gerd Schon, “Quantum dynamics of tunneling between superconductors,”
*Phys. Rev. Lett.***48**, 1745–1748 (1982).Google Scholar - 6.Huzihiro Araki, “A remark on Machida-Namiki theory of measurement,”
*Prog. Theor. Phys.***64**, 719–730 (1980).Google Scholar - 7.Alain Aspect, “Experimental tests of Bell's inequalities in atomic physics,”
*Atomic Physics*, Vol. 8, I. Lindgren*et al.*, ed. (Plenum Press, New York), pp. 103–128.Google Scholar - 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.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.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.
- 12.L. Ballentine, “Limitations of the projection postulate,”
*Found. Phys.***20**, 1329–1343 (1990).Google Scholar - 13.L. Ballentine, “The statistical interpretation of quantum mechanics,”
*Rev. Mod. Phys.***42**, 358–381 (1970).Google Scholar - 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.K. Baumann, “Quantenmechanik und Objektivierbarkeit,”
*Z. Naturforsch. A***25**, 1954–1956 (1970).Google Scholar - 16.John Bell, “Are there quantum jumps?” in
*Speakable and Unspeakable in Quantum Mechanics*(Cambridge Univ. Press, New York, 1987), pp. 201–212.Google Scholar - 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.John Bell, “EPR correlations and EPW distributions,” Ref. 92, pp. 263–266.Google Scholar
- 19.John Bell, “On wave packet reduction in the Coleman-Hepp model,”
*Helv. Phys. Acta***48**, 93–98 (1975).Google Scholar - 20.John Bell, “Introduction to the hidden-variable question,” Ref. 59, pp. 171–181.Google Scholar
- 21.John Bell, “On the problem of hidden variables in quantum mechanics,”
*Rev. Mod. Phys.***38**, 447–452 (1966).Google Scholar - 22.
- 23.John Bell, A. Shimony, M. Horne, and J. Clauser, “An exchange on local beables,”
*Dialectica***39**, 85–110 (1985).Google Scholar - 24.F. Berezin and M. Shubin,
*The Schrödinger Equation*(Moscow University Press, Moscow, 1983) (in Russian).Google Scholar - 25.David Bohm,
*Quantum theory*(Prentice-Hall, Englewood Cliffs, New Jersey, 1952).Google Scholar - 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.David Bohm, B. Hiley, and P. Kaloyerou, “An ontological basis for the quantum theory,”
*Phys. Rep.***144**, 321–375 (1987).Google Scholar - 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.Niels Bohr, “The quantum postulate and the recent development of atomic theory,”
*Nature (London)***121**, 580–590 (1928).Google Scholar - 30.V. Braginsky, V. Mitrofanov, and V. Panov,
*Systems with small dissipation*(Nauka, Moscow, 1981) (in Russian).Google Scholar - 31.C. Brans, “Bell's theorem does not eliminate fully causal hidden variables,”
*Int. J. Theor. Phys.***27**, 219–226 (1988).Google Scholar - 32.M. Bronstein, “Quantization of gravitational waves,”
*Zh. Eksp. Teor. Fiz.***6**, 195–236 (1936) (in Russian).Google Scholar - 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.J. Bub, “The Daneri-Loinger-Prosperi quantum theory of measurement,”
*Nuovo Cimento B***57**, 503–520 (1968).Google Scholar - 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.A. Caldeira and A. Leggett, “Quantum tunneling in a dissipative system,”
*Ann. Phys. (N.Y.)***149**, 374–456 (1983).Google Scholar - 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.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.Curtis Callan and Sidney Coleman, “Fate of the false vacuum. II. First quantum corrections,”
*Phys. Rev. D***16**, 1762–1768 (1977).Google Scholar - 40.Herbert Callen and Theodore Welton, “Irreversibility and generalized noise,”
*Phys. Rev.***83**, 34–40 (1951).Google Scholar - 41.Carlton Caves and G. J. Milburn, “Quantum mechanical model for continuous position measurements,”
*Phys. Rev. A***36**, 5543–5555 (1987).Google Scholar - 42.Carlton Caves, “Quantum mechanics of measurements distributed in time. II. Connections among formulations,”
*Phys. Rev. D***35**, 1815–1830 (1987).Google Scholar - 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.Sudip Chakravarty and Anthony Leggett, “Dynamics of the two-state system with Ohmic dissipation,”
*Phys. Rev. Lett.***52**, 5–8 (1984).Google Scholar - 45.Kai Lai Chung,
*Markov Chains with Stationary Transition Probabilities*(Springer-Verlag, New York, 1967).Google Scholar - 46.Christopher Clarke, “Uncertain cosmology,” Ref. 200, pp. 51–60.Google Scholar
- 47.John F. Clauser and Abner Shimony, “Bell's theorem: experimental tests and implications,”
*Rep. Prog. Phys.***41**, 1881–1927 (1978).Google Scholar - 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.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.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.B. S. Cirel'son, “Quantum generalizations of Bell's inequality,”
*Lett. Math. Phys.***4**, 93–100 (1980).Google Scholar - 52.A. Daneri, A. Loinger, and G. Prosperi, “Quantum theory of measurement and ergodicity conditions,”
*Nucl. Phys.***33**, 297–319 (1962).Google Scholar - 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.D. Danin,
*Probabilistic world*(Znanie, Moscow, 1981) (in Russian).Google Scholar - 55.Amitava Datta and Dipankar Home, “Quantum nonseparability versus local realism: a new test using
*B*^{0}939-1^{0}system,”*Phys. Lett. A***119**, 3–6 (1986).Google Scholar - 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.E. Davies and J. Lewis, “An operational approach to quantum probability,”
*Commun. Math. Phys.***17**, 239–260 (1970).Google Scholar - 58.Bernard D'Espagnat, “Towards a separable ‘empirical reality’?”
*Found. Phys.***20**, 1147–1172 (1990).Google Scholar - 59.Bernard D'Espagnat, (ed.), “Foundations of quantum mechanics,”
*Proc. Int. School of Phys. Enrico Fermi*(Academic Press, New York, 1971).Google Scholar - 60.W. De Baere, “Einstein-Podolsky-Rosen paradox and Bell's inequalities,”
*Adv. Electronics Electron Phys.***68**, 245–336 (1986).Google Scholar - 61.David Deutsch, “Quantum theory as a universal physical theory,”
*Int. J. Theor. Phys.***24**, 1–41 (1985).Google Scholar - 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.Bryce DeWitt
*et al.*(ed.),*The Many-Worlds Interpretation of Quantum Mechanics*(Princeton University Press, Princeton, New Jersey, 1973).Google Scholar - 64.Lajos Diosi, “Relativistic theory for continuous measurement of quantum field,”
*Phys. Rev. A***42**, 5086–5092 (1990).Google Scholar - 65.Lajos Diosi, “Continuous quantum measurement and Ito formalism,”
*Phys. Lett. A***129**, 419–423 (1988).Google Scholar - 66.Lajos Diosi, “Quantum stochastic processes as models for the state vector reduction,”
*J. Phys. A***21**, 2885–2898 (1988).Google Scholar - 67.Lajos Diosi, “On the motion of solids in modified quantum mechanics,”
*Europhys. Lett.***6**, 285–290 (1988).Google Scholar - 68.Lajos Diosi, “Exact solution for particle trajectories in modified quantum mechanics,”
*Phys. Lett. A***122**, 221–225 (1987).Google Scholar - 69.Lajos Diosi, “A universal master equation for the gravitational violation of quantum mechanics,”
*Phys. Lett. A***120**, 377–381 (1987).Google Scholar - 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.
- 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.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.Hugh Everett, “‘Relative state’ formulation of quantum mechanics,”
*Rev. Mod. Phys.***29**, 454–462 (1957).Google Scholar - 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.
- 77.P. C. Fishburn and J. A. Reeds, “Bell inequalities, Grothendieck's constant and root two,” to appear (1991).Google Scholar
- 78.M. Froissart, “Constructive generalization of Bell's inequalities,”
*Nuovo Cimento B***64**, 241–251 (1981).Google Scholar - 79.W. Furry, “Note on the quantum-mechanical theory of measurement,”
*Phys. Rev.***49**, 393–399 (1936).Google Scholar - 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.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.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.A. Garuccio and F. Selleri, “Enhanced photon detection in EPR type experiments,”
*Phys. Lett. A***103**, 99–103 (1984).Google Scholar - 84.A. Garuccio and F. Selleri, “Systematic derivation of all the inequalities of Einstein locality,”
*Found. Phys.***10**, 209–216 (1980).Google Scholar - 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.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.G. Ghirardi, A. Rimini, and T. Weber, “The puzzling entanglement of Schrödinger's wave function,”
*Found. Phys.***18**, 1–27 (1988).Google Scholar - 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.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.N. Giordano, “Evidence for macroscopic quantum tunneling in one-dimensional superconductors,”
*Phys. Rev. Lett.***61**, 2137–2140 (1988).Google Scholar - 91.R. Glauber, “Amplifiers, attenuators, and Schrödinger's cat,” Ref. 92, pp. 336–372.Google Scholar
- 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.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.Daniel M. Greenberger and Alaine YaSin, “‘Haunted’ measurements in quantum theory,”
*Found. Phys.***19**, 679–704 (1989).Google Scholar - 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.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.
- 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.Rudolf Haag and Daniel Kastler, “An algebraic approach to quantum field theory,”
*J. Math. Phys.***5**, 848–861 (1964).Google Scholar - 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.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.
- 103.Stephen Hawking and R. Laflamme, “Baby universes and the nonrenormalizability of gravity,”
*Phys. Lett. B***209**, 39–41 (1988).Google Scholar - 104.Stephen Hawking, “Non-trivial topologies in quantum gravity,”
*Nucl. Phys. B***244**, 135–146 (1984).Google Scholar - 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.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.Klaus Hepp, “Quantum theory of measurement and macroscopic observables,”
*Helv. Phys. Acta***45**, 237–248 (1972).Google Scholar - 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.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.A. Holevo,
*Probabilistic and Statistical Aspects of Quantum Theory*(Nauka, Moscow, 1980) (in Russian); English translation: North-Holland, Amsterdam (1982).Google Scholar - 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.D. Home and F. Selleri, “Bell's theorem and the EPR paradox,”
*Riv. Nuovo Cimento***14**, 1–95 (1991).Google Scholar - 113.Michael Horne and Anton Zeilinger, “A Bell-type EPR experiment using linear momenta,” Ref. 157, pp. 435–439.Google Scholar
- 114.J. M. Jauch, “The problem of measurement in quantum mechanics,”
*Helv. Phys. Acta***37**, 293–316 (1964).Google Scholar - 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.
- 117.E. Joos, “Quantum theory and the appearance of a classical world,” Ref. 92, pp. 6–13.Google Scholar
- 118.E. Joos, “Continuous measurement: Watchdog effect versus golden rule,”
*Phys. Rev. D***29**, 1626–1633 (1984).Google Scholar - 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.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.T. Kennedy and D. Walls, “Squeezed quantum fluctuations and macroscopic quantum coherence,”
*Phys. Rev. A***37**, 152–157 (1988).Google Scholar - 122.Leonid Khalfin, “Quantum-classical correspondence in the light of classical Bell's and quantum Tsirelson's inequalities,” in
*Complexity, 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.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.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), in
*Proc. of the XXXII Semester in the Stefan Banach Int. Math. Centre*(World Scientific, Singapore, 1990), pp. 469–484.Google Scholar - 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.Leonid Khalfin, “A new effect of the CP-violation for heavy mesons,” Preprint LOMI E-6-87, Leningrad (1987).Google Scholar
- 127.Leonid Khalfin, “A new effect of the CP-violation for neutral kaons,” Preprint LOMI E-7-87, Leningrad (1987).Google Scholar
- 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.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.Leonid Khalfin, “Unconditional test of the CPT-invariance and a new effect of the CP-violation for
*K*^{0}− K^{0}mesons,”*Proceedings of the III Seminar, Group Theoretical Methods in Physics*, Vol. 2, M. Markov, ed. (1986), p. 608 (in Russian).Google Scholar - 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.Leonid Khalfin, “A new effect of CP-violation for
*D*^{0}− D^{0},*B*^{0}− B^{0}, (*T*^{0}− T^{0}),” report to the Council of the Nuclear Physics Department, USSR Academy of Sciences (October 1985) (unpublished).Google Scholar - 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.Leonid Khalfin, “Bell's inequalities, Tsirelson's inequalities and
*K*^{0}− K^{0}^{0}−*K*^{0}mesons,” Report to the session of Nuclear Physics Department, USSR Academy of Sciences (April 1983) (unpublished).Google Scholar - 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.Leonid Khalfin, “Theory of
*K*^{0}− K^{0},*D*^{0}− d^{0},*B*^{0}− b^{0}, (*T*^{0}− t^{0}) mesons outside the Wigner-Weisskopf approximation and the CP-invariance problem,” Preprint LOMI P-4-80, Leingrad (1980).Google Scholar - 137.
- 138.Leonid Khalfin, “Modern situation with the mathematical foundation of statistical physics,”
*Usp. Mat. Nauk***33**, 243 (1978) (in Russian).Google Scholar - 139.Leonid Khalfin, “Investigations on the quantum theory of the unstable particles,” dissertation, Lab. Theor. Phys. JINR (1973) (unpublished).Google Scholar
- 140.Leonid Khalfin, “The CPT-invariance of the CP-noninvariant theory of
*K*^{0}− 943-10^{0}mesons and admissible mass distributions of*K*_{S}and*K*_{L}mesons,”*Pis'ma Zh. Eksp. Teor. Fiz.***15**, 348 (1972) (in Russian).Google Scholar - 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.Leonid Khalfin, “Quantum theory of the decay of the physical systems,” dissertation, Lebedev Phys. Inst., USSR Academy of Sciences (1960) (unpublished).Google Scholar
- 143.Leonid Khalfin, “On the decay theory of a quasi-stationary state,”
*Zh. Eksp. Teor. Fiz.***33**, 1371 (1958) (in Russian).Google Scholar - 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.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.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.Leonid Khalfin and Boris Tsirelson, “Quantum and quasi-classical analogs of Bell inequalities,” Ref. 157, pp. 441–460.Google Scholar
- 148.S. Khoruzhy,
*Introduction to Algebraic Quantum Field Theory*(Nauka, Moscow, 1986) (in Russian).Google Scholar - 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.S. Kochen, “A new interpretation of quantum mechanics,” Ref. 157, pp 151–169.Google Scholar
- 151.Karl Kraus, “General state changes in quantum theory,”
*Ann. Phys. (N.Y.)***64**, 311–335 (1971).Google Scholar - 152.N. Krylov, “Works on foundations of statistical physics,” USSR Academy of Sciences Moscow and Leningrad (1950) (in Russian).Google Scholar
- 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.O. Kübler and H. Zeh, “Dynamics of quantum correlations,”
*Ann. Phys. (N.Y.)***76**, 405–418 (1973).Google Scholar - 155.
- 156.P. Lahti
*et al.*(ed.),*Symposium on the Foundations of Modern Physics 1987*(World Scientific, Singapore, 1987).Google Scholar - 157.P. Lahti
*et al.*(ed.),*Symposium on the Foundations of Modern Physics 1985*(World Scientific, Singapore, 1985).Google Scholar - 158.Lawrence Landau, “Empirical two-point correlation functions,”
*Found. Phys.***18**, 449–460 (1988).Google Scholar - 159.Lawrence Landau, “Gaussian quantum fields and stochastic electrodynamics,”
*Phys. Rev. A***37**, 4449–4460 (1988).Google Scholar - 160.Lawrence Landau, “On the violation of Bell's inequality in quantum theory,”
*Phys. Lett. A***120**, 54–56 (1987).Google Scholar - 161.Lawrence Landau, “Experimental tests of general quantum theories,”
*Lett. Math. Phys.***14**, 33–40 (1987).Google Scholar - 162.Lawrence Landau, “On the non-classical structure of the vacuum,”
*Phys. Lett. A***123**, 115–118 (1987).Google Scholar - 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.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.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.
- 167.A. J. Leggett, “Schrödinger's cat and her laboratory cousins,”
*Contemp. Phys.***25**, 583–598 (1984).Google Scholar - 168.A. Leggett, “Macroscopic quantum systems and the quantum theory of measurement,”
*Prog. Theor. Phys. Suppl.*, No. 69, 80–100 (1980).Google Scholar - 169.A. Leggett, “Quantum mechanics and realism at the macroscopic level. Is an experimental discrimination feasible?” Ref. 92, pp. 21–24.Google Scholar
- 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.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.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.V. L. Lepore, “New inequalities from local realism,”
*Found Phys. Lett.***2**, 15–26 (1989).Google Scholar - 174.K. K. Likharev, “Really-quantum macroscopic effects in weak superconductivity,”
*Usp. Fiz. Nauk***139**, 169–184 (1983) (in Russian).Google Scholar - 175.A. Loinger, “Comments on a recent paper concerning the quantum theory of measurement,”
*Nucl. Phys. A***108**, 245–249 (1968).Google Scholar - 176.H. McKean,
*Stochastic Integrals*(Academic Press, New York, 1969).Google Scholar - 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.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.Norman Margolus, “Parallel quantum computation,” manuscript (1989).Google Scholar
- 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.T. Marshall, “The distance separating quantum theory from reality,”
*Phys. Lett. A***99**, 163–166 (1983).Google Scholar - 182.
- 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.G. Milburn and D. Walls, “Effect of dissipation on interference in phase space,”
*Phys. Rev. A***38**, 1087–1090 (1988).Google Scholar - 185.N. Mott, “The wave mechanics of α-ray tracks,”
*Proc. R. Soc. London A***126**, 79–84 (1929).Google Scholar - 186.M. Namiki
*et 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.E. Nelson, “The locality problem in stochastic mechanics,” Ref. 92, pp. 533–538.Google Scholar
- 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.D. Palatnik, private communication.Google Scholar
- 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.Wolfgang Pauli,
*Festschrift zum 60. Geburtstage A. Sommerfelds*, Leipzig (1928).Google Scholar - 192.Philip Pearle, “Alternative to the orthodox interpretation of quantum theory,”
*Am. J. Phys.***35**, 742–753 (1967).Google Scholar - 193.Asher Peres, “Existence of ‘free will’ as a problem of physics,”
*Found. Phys.***16**, 573–584 (1986).Google Scholar - 194.Asher Peres, “Reversible logic and quantum computers,”
*Phys. Rev. A***32**, 3266–3276 (1985).Google Scholar - 195.
- 196.Asher Peres, “When is a quantum measurement?” Ref. 92, pp. 438–448.Google Scholar
- 197.Asher Peres and Nathan Rosen, “Quantum limitations on the measurement of gravitational fields,”
*Phys. Rev.***118**, 335–336 (1960).Google Scholar - 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.A. M. Polyakov, “Hidden symmetry of the two-dimensional chiral fields,”
*Phys. Lett. B***72**, 224–226 (1977).Google Scholar - 200.W. C. Price
*et al.*(ed.)*The Uncertainty Principle and Foundations of Quantum Mechanics: A Fifty Year's Survey*(Wiley, New York, 1977).Google Scholar - 201.201.Ilya Prigogine,
*From Being to Becoming: Time and Complexity in the Physical Sciences*(W. H. Freeman, San Francisco, 1980).Google Scholar - 202.H. Primas, “Contextual quantum objects and their ontic interpretation,” Ref. 156, pp. 251–275.Google Scholar
- 203.G. Prosperi, “The quantum measurement process and the observation of continuous trajectories,”
*Lect. Notes Math.***1055**, 301–326 (1984).Google Scholar - 204.Peter Rastall, “Locality, Bell's theorem, and quantum mechanics,”
*Found. Phys.***15**, 963–972 (1985).Google Scholar - 205.Michael Redhead, “Relativity and quantum mechanics—conflict or peaceful coexistence?” Ref. 92, pp. 14–20.Google Scholar
- 206.T. Regge, “Gravitational fields and quantum mechanics,”
*Nuovo Cimento***7**, 215–221 (1958).Google Scholar - 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.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.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.S. M. Roy and V. Singh, “Generalized beable quantum field theory,”
*Phys. Lett. B***234**, 117–120 (1990).Google Scholar - 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.Erwin Schrödinger, “Die gegenwartige Situation in der Quantenmechanik,”
*Naturwissenschaften***23**, 807–812, 823–828, 844–849 (1935).Google Scholar - 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.A. Schmid, “Diffusion and localization in a dissipative quantum system,”
*Phys. Rev. Lett.***51**, 1506–1509 (1983).Google Scholar - 215.Albert Schmid, “On a quasiclassical Langevin equation,”
*J. Low Temp. Phys.***49**, 609–626 (1982).Google Scholar - 216.F. Selleri, “Realism and the wave-function of quantum mechanics,” Ref. 59, pp. 398–406.Google Scholar
- 217.F. Selleri, “Einstein locality and the
*K*^{0}946-1^{0}system,”*Lett. Nuovo Cimento***36**, 521–526 (1983).Google Scholar - 218.I. Senitzky, “Dissipation in quantum mechanics. The harmonic oscillator,”
*Phys. Rev.***119**, 670–679 (1960).Google Scholar - 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.
- 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.J. Six, “Test of the nonseparability of the
*K*^{0}946-2^{0}system,”*Phys. Lett. B***114**, 200–202 (1982).Google Scholar - 223.B. Spassky and A. Moskovsky, “On non-locality in quantum physics,”
*Usp. Fiz. Nauk***142**, 599–617 (1984) (in Russian).Google Scholar - 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.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.Henry Stapp, “Gauge-fields and integrated quantum-classical theory,” Ref. 92, pp. 326–335.Google Scholar
- 227.Stephen Summers and Reinhold Werner, “The vacuum violates Bell's inequalties,”
*Phys. Lett. A***110**, 257–259 (1985).Google Scholar - 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.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.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.G. Svetlichny, “Distinguishing three-body from two-body nonseparability by a Bell-type inequality,”
*Phys. Rev. D***35**, 3066–3069 (1987).Google Scholar - 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.H. Treder, in
*Astrofisica e Cosmologia, Gravitazione, Quanti e Relatività*(Giunti Barbera, Firenze, 1979).Google Scholar - 234.Boris Tsirelson, “In comparison to what is the Planck constant small?” (to appear).Google Scholar
- 235.Boris Tsirelson, “Quantum analogs of Bell's inequalities: the case of two spacelike separated domains,” in
*Problems of the Theory of Probability Distributions IX*, Math. Inst. Steklov (LOMI), Vol. 142 (1985), pp. 174–194 (in Russian).Google Scholar - 236.Boris Tsirelson, “On a formal description of quantum systems that are similar to systems of stochastic automata,” in
*Proceedings 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.W. G. Unruh, “Quantum coherence, wormholes, and the cosmological constant,”
*Phys. Rev. D***40**, 1053–1063 (1989).Google Scholar - 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.Leon Van Hove, “Quantum-mechanical perturbations giving rise to a statistical transport equation,”
*Physica***21**, 517–540 (1955).Google Scholar - 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.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.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.Milan Vujičic and Fedor Herbut, “Distant correlations in quantum mechanics,” Ref. 157, pp. 677–689.Google Scholar
- 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.D. Walls and G. Milburn, “Effect of dissipation on quantum coherence,”
*Phys. Rev. A***31**, 2403–2408 (1985).Google Scholar - 246.W. H. Weber (ed.), “Squeezed States of the Electromagnetic Field,”
*J. Opt. Soc. Am. B***4**(10) (1987).Google Scholar - 247.Carl Weizsacker, “Heisenberg's philosophy,” Ref. 156, pp. 277–293.Google Scholar
- 248.Carl Weizsacker, “Quantum theory and space-time,” Ref. 157, pp. 223–237.Google Scholar
- 249.John Archibald Wheeler, “Assessment of Everett's ‘relative state’ formulation of quantum theory,”
*Rev. Mod. Phys.***29**, 463–465 (1957).Google Scholar - 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.Eugene Wigner, “Remarks on the mind-body question,” in
*The Scientist Speculates*, I. J. Good, ed. (Heinemann, London 1962).Google Scholar - 252.C. H. Woo, “Why the classical-quantal dualism is still with us,”
*Am. J. Phys.***54**, 923–928 (1986).Google Scholar - 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.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.H. Zeh, “Measurement in Bohm's versus Everetts's quantum theory,”
*Found. Phys.***18**, 723–730 (1988).Google Scholar - 256.H. Zeh, “Emergence of classical time from a universal wavefunction,”
*Phys. Lett. A***116**, 9–12 (1986).Google Scholar - 257.
- 258.
- 259.H. Zeh, “On the irreversibility of time and observation in quantum theory,” Ref. 59, pp. 263–273.Google Scholar
- 260.H. Zeh, “On the interpretation of measurement in quantum theory,”
*Found. Phys.***1**, 69–76 (1970).Google Scholar - 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.Wojciech Zurek, “Quantum measurements and the environment induced transition from quantum to classical,” Preprint LA-UR-89-25, Los Alamos (1988).Google Scholar
- 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.Wojciech Zurek, “Reduction of the wave packet and environment-induced superselection,” Ref. 92, pp. 89–97.Google Scholar
- 265.Wojciech Zurek, “Environment-induced superselection rules,”
*Phys. Rev. D***26**, 1862–1880 (1982).Google Scholar - 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