Abstract
We investigate and develop further two models, the GRW model and the K model, in which the Schrödinger evolution of the wave function is spontaneously and repeatedly interrupted by random, approximate localizations, also called “self-reductions” below. In these models the center of mass of a macroscopic solid body is well localized even if one disregards the interactions with the environment. The motion of the body shows a small departure from the classical motion. We discuss the prospects and the difficulties of observing this anomaly. As far a the influence of the surroundings on submacroscopic objects (like dust particles) is concerned, we show that the estimates obtained recently in the theory of continuous measurements and in the K model are compatible. Also, we elaborate upon the relationship between the models. Firstly, borrowing a line of thought from the K model, we find the transition region between macroscopic and microscopic behaviors in the GRW model. Secondly, we refine the propagation rule of the wave function in the K model with the help of the time-evolution equation proposed in the GRW model.
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References
G. C. Ghirardi, A. Rimini, and T. Weber, “Unified Dynamics for Microscopic and Macroscopic Systems,”Phys. Rev. D 34, 470 (1986); see alsoPhys. Rev. D 36, 3287 (1987) andFound. Phys. 18, 1 (1988).
F. Károlyházy, “Gravitation and Quantum Mechanics of Macroscopic Bodies,”Magy. Fiz. Foly. 22, 23 (1974) (in Hungarian). The basic ideas of the model have been outlined by Károlyházy inNuovo Cimento 42, 390 (1966). For an (incomplete) presentation of the model see Ref. 5 and A. Frenkel, inQuantum Mechanics—a Half Century Later, J. Leite Lopes and M. Paty. eds., (Reidel, Dordrecht, 1977).
E. Joos and H. D. Zeh,Z. Phys. B 59, 223 (1985).
W. H. Zurek, inProceedings of the International Symposium Foundations of Quantum Mechanics, S. Kamefuchiet al., eds. (Physical Society of Japan, Tokyo, 1984), p. 181, and references therein.
F. Károlyházy, A. Frenkel, and B. Lukács, inPhysics as Natural Philosophy, A. Shimony and H. Feschbach, eds. (MIT Press, Cambridge, Massachusetts, 1982), p. 204, and inQuantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon Press, Oxford, 1986), p. 109.
D. M. Greenberger,Rev. Mod. Phys. 55, 875 (1983).
C. M. Caves and G. J. Milburn,Phys. Rev. A 36, 5543 (1987).
K. Kraus,States, Effects and Operations (Lecture Notes in Physics, Vol. 190) (Springer, New York, 1983).
V. Gorini, A. Frigero, M. Verri, A. Kossakowski, and E. C. G. Sudarshan,Rep. Math. Phys. 13, 149 (1978).
E. P. Wigner, inQuantum Optics, Experimental Gravitation and Measurement Theory, P. Meystre and M. O. Scully, eds. (Plenum, New York, 1983), p. 43.
T. Banks, M. Peskin, and L. Susskind,Nucl. Phys. B 244, 125 (1984).
E. Joos,Phys. Rev. D 36, 3285 (1987).
P. W. Wooden, Jr., and C. W. F. Everitt, inExperimental Gravitation, B. Bertotti, ed. (Academic Press, New York, 1974), p. 381.
“Technology innovations from the relativity gyroscope experiment development program,” NASA report, U.S. Government Printing Office 1981-640-066/289; C. W. F. Everitt, inProceedings of the First Marcel Grossmann Meeting on General Relativity, R. Ruffini, ed. (North-Holland, Amsterdam, 1977), p. 570.
A. Frenkel, “The Reduction of the Schrödinger Wave Function and the Emergence of Classical Behavior,” Preprint, KFKI-1988-17/A, unpublished.
A. Shimony, “Search for a world view which can accommodate our knowledge of microphysics,” Departments of Philosophy and Physics, Boston University preprint, 1988, to be published inPhilosophical Consequences of Quantum Theory, J. Cushing and E. McMullin, eds. (Notre Dame Press, Notre Dame, Indiana, 1989).
A. Aspect, P. Grangier, and G. Roger,Phys. Rev. Lett. 47, 460 (1981) and49, 91 (1982).
J. S. Bell,Physics 1, 195 (1964).
B. d'Espagnat,Found, Phys. 17, 507 (1987).
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Frenkel, A. Spontaneous localizations of the wave function and classical behavior. Found Phys 20, 159–188 (1990). https://doi.org/10.1007/BF00731645
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DOI: https://doi.org/10.1007/BF00731645