Abstract
It is claimed that for all apparatus capable of performing macroscopic measurements of microscopic systems there exist special internal states for which deterministic quantum evolution alone yields a particular macroscopic outcome rather than a superposition of macroscopically distinct outcomes. We maintain that these special states are distributed uniformly (in a certain sense) among the set of all states. It is hypothesized that for all actually performed experiments the initial conditions lie among the special states. We postulate that in the absence of precise information on apparatus initial conditions one should give equal weight to those microstates that are consistent with the macroscopic stateand are special in the sense used above. Evidence is presented for this postulate's recovering the usual quantum probabilities. This theory is fully deterministic, has no collapsing wave functions, and offers a resolution of the quantum measurement problem through a revision of the usual statistical mechanical handling of initial conditions. It requires a single wave function for the entire universe and an all encompassing conspiracy to arrange the right sort of special wave function for each experiment. In other words, an apparatus is in an appropriate microstate for the experiment that will actually happen even if an ostensibly random process is used to determine that experiment from among apparent alternatives. Although we do not provide physical or philosophical justification for our central hypothesis, some perspective is given by examining the notions implicit in the usual principles of thermodynamics.
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References
J. A. Wheeler and W. H. Zurek, eds.,Quantum Theory and Measurement (Princeton University Press, Princeton, New Jersey, 1983).
K. Gottfried,Quantum Mechanics (Benjamin, New York, 1966); especially Section 20.3.
L. E. Ballentine,Rev. Mod. Phys. 42:358 (1970).
P. Edwards and A. Pap,A Modern Introduction to Philosophy (Macmillan, New York, 1973).
D. J. O'Connor,Free Will (Anchor Doubleday, Garden City, New York, 1971).
D. C. Dennett,Elbow Room (MIT Press, Cambridge, Massachusetts, 1984).
A. Komar,Phys. Rev. 126:365 (1962).
L. S. Schulman,Phys. Lett. 102A:396 (1984).
H. Everett III,Rev. Mod. Phys. 29:454 (1957); reprinted in Ref. 1.
P. K. Kabir,The CP Puzzle: Strange Decays of the Neutral Kaon (Academic Press, New York, 1968) Appendix A.
L. S. Schulman, R. G. Newton, and R. Shtokhamer,Philos. Sci. 42:503 (1975).
M. Kac,Probability and Related Topics in Physical Sciences (Interscience, New York, 1959) Sections 14 and 15.
L. S. Schulman,J. Stat. Phys. 16:217 (1977).
V. I. Arnold and A. Avez,Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
L. S. Schulman and R. Shtokhamer,Int. J. Theor. Phys. 16:287 (1977); see also the Appendix to Ref. 13.
L. S. Schulman,Techniques and Applications of Path Integration (Wiley, New York, 1981).
H. Goldstein,Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Massachusetts, 1980).
M. V. Berry, Semiclassical mechanics of regular and irregular motion, inChaotic Behavior of Deterministic Systems, G. Iooss, R. Helleman and R. Stora, editors (North-Holland, Amsterdam, 1983).
M. V. Berry and M. Tabor,Proc. Soc. A356:375 (1977).
A. S. Wightman, inPerspectives in Statistical Physics, H. J. Reveche, ed. (North-Holland, Amsterdam, 1981).
A. O. Caldeira and A. J. Leggett,Phys. Rev. Lett. 46:211 (1981).
S. Chakravarty, Macroscopic Quantum Coherence in Superconducting Interference Devices, presented at conference on “Fundamental Questions in Quantum Mechanics,” SUNY at Albany, 1984.
A. J. Leggett, in Proc. Int. Symp. Foundations of Quantum Mechanics, Tokyo, 1983.
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Schulman, L.S. Deterministic quantum evolution through modification of the hypotheses of statistical mechanics. J Stat Phys 42, 689–719 (1986). https://doi.org/10.1007/BF01127734
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DOI: https://doi.org/10.1007/BF01127734