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Chaos and Indeterminism

Published online by Cambridge University Press:  01 January 2020

Jesse Hobbs
Jesse Hobbs*
Affiliation:
Lehigh University, Bethlehem, PA18015, USA
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Extract

Laplacean determinism remains a popular theory among philosophers and scientists alike, in spite of the fact that the Copenhagen Interpretation of quantum mechanics, with which it is inconsistent, has been around for more than fifty years. There are a number of reasons for its continuing popularity. One, recently articulated by Honderich, is that there are too many possible interpretations of quantum mechanics, and the subject is too controversial even among physicists to be an adequate basis for overturning determinism. Nevertheless, quantum mechanics is an enormously successful theory, considering the quantity and variety of its predictions which have been verified under conditions never dreamt of by its originators; and the Copenhagen Interpretation is the only widely accepted interpretation of it. Although a hidden variable theory consistent with the results of quantum mechanics is not impossible, one of its major advocates admits that it is highly speculative, and far from adequately developed. Yet such a theory would be needed to reconcile Laplacean determinism with quantum mechanics; most of the controversies alluded to by Honderich are irrelevant.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 21 , Issue 2 , June 1991 , pp. 141 - 164
Copyright
Copyright © The Authors 1991

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References

1 I am indebted to Yong W. Kim,Professor of Physics at Lehigh University, for discussions which helped my understanding of the physics discussed herein. I am also indebted to an anonymous reviewer for the Canadian Journal of Philosophy whose comments on an earlier version helped make this a better paper.

2 Honderich, Ted A Theory of Determinism (New York: Oxford University Press 1988), 307, 315ffGoogle Scholar.

3 Bohm, David Wholeness and the Implicate Order (London: Routledge & Kegan Paul 1980)Google Scholar. He originally floated this theory in ‘A Suggested Interpretation of the Quantum Theory in terms of “Hidden” Variables,’ Physical Review 85 (1952) 166-93.

4 For example, the ‘many-worlds’ interpretation articulated by Everett, (‘Relative State Formulation of Quantum Mechanics,’ Reviews of Modern Physics 29 [1957] 454-62)CrossRefGoogle Scholar is wholly deterministic, but not in a way that supports Laplacean determinism. At each putatively indeterministic juncture, his proposal is that the world splits, with one ‘possible’ world following one path and the other following the other. Neither world has any contact with the other from thence forward. But which of these worlds will we call ‘real’? His interpretation offers neither a prediction nor any reason to believe that there is a fact of the matter. Thus, we find the real world still to be indeterministic.

5 As quoted by Schuster, Heinz Georg in Deterministic Chaos: An Introduction (Weinheim, Germany: VCH 1989), 222.Google Scholar

6 Schuster, 187

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9 As alleged by Casati, Giulio and Molinari, Luca ‘“Quantum Chaos” with Time-Periodic Hamiltonians,’ Progress of Theoretical Physics Supplement 98 (1989) 287-322, at 303CrossRefGoogle Scholar.

10 That is, as Earman has reminded me in conversation, although the total mass and momentum of the universe is not invariant in these examples, conservation of mass is observed in the more limited sense that there are no discontinuous particle trajectories.

11 The literature on the comparative features and merits of the syntactic and semantic views is rapidly growing. Perhaps the easiest route to an appreciation of the issues and positions involved, although cast in terms of biological theories rather than physics, is through the exchange between Peter Sloep and W. J. Vander Steen (who oppose the semantic view), and Beatty, John Lloyd, Lisa and Thompson, Paul (who defend it) in Biology and Philosophy 2 (1987) 1-41Google Scholar.

12 Others have noted that Earman devalues these questions; see, for example, Forge’s, John review in Australasian Journal of Philosophy 66 (1988) 263-6, at 265Google Scholar.

13 What about previous time-slices (i.e., historical determinism)? Many simple chaotic systems, such as the logistic equation

preclude recovering the past from the present because of their symmetry (around xn= 1/2, in this case). Thus, most of ‘deterministic chaos’ is historically indeterministic, even apart from quantum considerations. Earman points out (168) that the Baker’s transformation is historically indeterministic in each dimension considered separately, but is deterministic when all of the dimensions are taken together. Since making simple chaotic systems more realistic generally requires adding more dimensions, this raises the question whether the logistic equation and other chaotic formalisms can be embedded in larger functions that are single-valued, and so historically deterministic.

14 Wilson discusses a number of them.

15 Aspect, A. Grangier, P. and Roger, G. ‘Experimental Realization of Einstein-Podolsky- Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities,’ Physical Review Letters 49 (1982) 91-4CrossRefGoogle Scholar

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18 Bell, 97, 127

19 Bell, 192

20 Bell, 124, 166

21 Bell, 135-6

22 Bell, 36

23 Earman, 38

24 Earman, 226

25 Many introductions to the chaos literature exist, but the amount that is accessible to non-specialists is small. Most of the older papers cited herein appear in Cvitanovic, Predrag ed., Universality in Chaos (Bristol: Adam Hilger 1984)Google Scholar, which contains a useful introduction by the editor. A very accessible introduction, oriented toward applications in the life sciences, appears in chs. 2 and 3 of Glass, Leon and Mackey, Michael From Clacks to Chaos: The Rhythms of Life (Princeton, NJ: Princeton University Press 1988)Google Scholar. For a mathematically oriented introduction, see Barnsley, Michael and Demko, Stephen eds., Chaos, Dynamics and Fractals (Orlando, FL: Academic Press 1986)Google Scholar. Textbook treatments aimed at physics graduate students include Schuster, as well as McCauley, Joseph An Introduction to Nonlinear Dynamics and Chaos Theory (Stockholm: Royal Swedish Academy of Sciences 1988)CrossRefGoogle Scholar, also known as Physica Scripta T20. For a wholly popularized introduction to chaos, see Gleick, James Chaos: Making a New Science (New York: Penguin 1988)Google Scholar; or Stewart, Ian Does God Play Dice? The Mathematics of Chaos (Oxford: Basil Blackwell 1989)Google Scholar.

26 Ruelle, David ‘Strange Attractors,’ The Mathematical Intelligencer 2 (1980) 126-37CrossRefGoogle Scholar; May, Robert ‘Simple Mathematical Models with Very Complicated Dynamics,’ Nature 261 (1976) 459-67CrossRefGoogle ScholarPubMed

27 Feigenbaum, Mitchell ‘Universal Behavior in Nonlinear Systems,’ Los Alamos Science 1 (1980) 4-27Google Scholar

28 Schuster, 3

29 Takahashi, Kin’ya ‘Distribution Functions in Classical Quantum Mechanics,’ Progress of Theoretical Physics Supplement 98 (1989) 109-56, at 11 Of.CrossRefGoogle Scholar

30 Perhaps the most readable introduction to the field is A Voros, ‘Selected Topics on “Quantum Chaos,”’ Helvetica Physim Acta 62 (1989) 595-612. See also Schuster, ch. 8.

31 Berry, Michael ‘Quantum Chaology, not Quantum Chaos,’ Physica Scripta 40 (1989) 335-6CrossRefGoogle Scholar. The theory of scars has been pioneered by Heller, Eric ‘Qualitative Properties of Eigenfunctions of Classically Chaotic Hamiltonian Systems,’ in Seligman, T.H. and Nishioka, H. eds., Quantum Chaos and Statistical Nuclear Physics (Berlin: Springer-Verlag 1986), 162-81CrossRefGoogle Scholar.

32 See Casati and Molinari.

33 See Casati, G. Guarneri, I. and Shepelyansky, D.L. ‘Classical Chaos, Quantum Localization and Fluctuations: A Unified View,’ Physica A 163 (1990) 205-14CrossRefGoogle Scholar; also Bliimel, R. and Smilansky, U. ‘Ionization of Excited Hydrogen Atoms by Microwave Fields: A Test Case for Quantum Chaos,’ Physica Scripta 40 (1989) 386-93CrossRefGoogle Scholar. The experiments were originally reported by Bayfield, J.E. and Koch, P.M. ‘Multiple Ionization of Highly Excited Hydrogen Atoms,’ Physical Review Letters 33 (1974) 258-61CrossRefGoogle Scholar. There is also some discussion of this in Casati and Molinari, 288,309-15.

34 Cartwright, Nancy How the wws of Physics Lie (Oxford: Clarendon Press 1983), 14-19, 79-81CrossRefGoogle Scholar.

35 See especially Berry; and Casati, Guarneri, and Shepelyansky, 205-6.

36 Schuster, 15

37 Grössing, G. ‘Quantum Systems as “Order Out of Chaos” Phenomena,’ II Nuovo Cimento B 103, 5 (1989) 497-509CrossRefGoogle Scholar

38 McCauley, 24-5

39 Wilson, 515-21; indeterminism and cracks are mentioned at 521.

40 Glass, 164-5; this hypothesis must be considered speculative. 41 May attributes this to Lorenz, but it is not mentioned in his landmark paper, ‘Dderministic Nonperiodic Flow,’ journal of Atmospheric Science 20 (1963) 130-41.

41 May attributes this to Lorenz, but it is not mentioned in his landmark paper, Deterministic Nonperiodic Flow, journal of Atmospheric Science 20 (1963) 130-41.