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Law and Prediction in the Light of Chaos Research pp 47–88Cite as

Under what transformations are laws invariant?

  • Part I Laws of Nature in the Light of Chaos
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References

  • Alpher, R.A., Herman, R.C. (1949): Remarks on the Evolution of the Expanding Universe. Physical Review 75, 1089–1095

    Article  ADS  MATH  Google Scholar 

  • Aristotle (Met): Metaphysics. In The Complete Works of Aristotle, The revised Oxoford Translation, Vol. 2, Barnes J. (ed.), Princeton Univerity Press, Princeton 1985, 1552–1728

    Google Scholar 

  • Aristotle (Phys): Physics. In The Complete Works of Aristotle. The revised Oxford Translation, Vol. 1, Barnes J. (ed.), Princeton University Press, Princeton 1985, 315–446

    Google Scholar 

  • Aristotle (Heav): On the Heavens. In The Complete Works of Aristotle, The revised Oxford Translation, Vol. 1, Barnes J. (ed.), Princeton University Press, Princeton 1985, 447–511

    Google Scholar 

  • Benedicks, M., Carleson, L. (1991): The Dynamics of the Hénon Map. Annals of Mathematics 133, 73–169

    Article  MathSciNet  Google Scholar 

  • Berry, M. (1978): Regular and Irregular Motion. In: Jorna, S. (ed.) Topics in Nonlinear Dynamics, Amer. Inst. of Physics, (New York), 16–120

    Google Scholar 

  • Berry, M. V., Percival, I. C.-Weiss, N.O. (eds.) (1987): Dynamical Chaos, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 413, 1844

    Google Scholar 

  • Boltzmann, L. (1896): Entgegnung auf die wärmetheoretischen Betrachtungen des Herrn E. Zermelo. In: Boltmann, L. Wissenschaftliche Abhandlungen, Vol. III, §119

    Google Scholar 

  • Boltzmann, L. (1897a): Zu Herrn Zermelos Abhandlung ‘Über die mechanische Erklärung irreversibler Vorgänge'. In: Boltzmann, L. Wissenschaftliche Abhandlunggen, Vol. III, §120

    Google Scholar 

  • Boltzmann, L. (1897b): Über einen mechanischen Satz Poincaré's. In: Boltzmann, L. Wissenschaftliche Abhandlungen, Vol. III, §121

    Google Scholar 

  • Boltzmann, L. (18–1905): Wissenschaftliche Abhandlungen, Vols. I–III, F. Hasenöhrl (ed.), Leipzig 1909, Reprinted by Chelsea Publ. Comp., New York 1968

    Google Scholar 

  • Brudno, A.A. (1983): Entropy and the Complexity of the Trajectories of a Dynamical System. Transactions of the Moscow Mathematical Society 2, 127–151

    Google Scholar 

  • Casati, G., Chirikov, B. V. (1994): The Legacy of Chaos in Quantum Mechanics. In: Casati, G., Chirikov, B. V. (eds.) Quantum Chaos Between Order and Disorder (Cambridge University Press)

    Google Scholar 

  • Chirikov, B.V. (1979): A Universal Instability of Many-Dimensional Oszillator Systems. Phys. Rep. 52, 463

    Article  MathSciNet  Google Scholar 

  • Chirikov, B.V. (1991a): Time-Dependent Quantum Systems In: Giannoni, M. J., Voros, A., Zinn-Justin, J. (eds.) Chaos and Quantum Physics (Les Houches 1989), Elsevier, Amsterdam, 443–545

    Google Scholar 

  • Chirikov, B.V. (1991b): Patterns in Chaos. Chaos Solitons and Fractals 1(1), 79–103

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Chirikov, B. V. (1992): Linear Chaos. In: Springer Proceedings in Physics 67, 3–13

    Google Scholar 

  • Chirikov, B. V. (these proceedings): Natural Laws and Human Prediction.

    Google Scholar 

  • Damour, T. et al. (1988): Limits on the variability of G using binary-pulsar data. Phys. Rev. Lett. 61, 1151ff

    Article  ADS  Google Scholar 

  • Dirac, P. A. M. (1937): Cosmological Constants. Nature 139, 323ff

    Article  ADS  MATH  Google Scholar 

  • Dirac, P. A. M. (1972): The Fundamental Constants and Their Time Variation. In Salam and Wigner (1972), 213–236

    Google Scholar 

  • Dirac, P.A.M. (1973): Fundamental Constants and Their Development in Time. In: Mehra, J. (ed.). The Physicist's Conception of Nature, Reidel, Dordrecht, 45–54

    Google Scholar 

  • Dyson, F. J. (1972): The Fundamental Constants and Their Time Variation In Salam and Wigner (1972), 213–236

    Google Scholar 

  • Einstein, A., Podolski, B., Rosen, N. (1935): Can Quantum-mechanical Description of Physical Reality be Considered Complete. Physical Review 47 777–780. Reprinted in: Wheeler, J. A.—Zurek, W. H. (eds.) Quantum Theory and Measurement, Princeton University Press (1983)

    Article  ADS  MATH  Google Scholar 

  • Farmer, J. D. (1982): Information Dimension and the Probabilistic Structure of Chaos. Zeitschrift fúr Naturforschung 37a, p. 1304

    MathSciNet  ADS  Google Scholar 

  • Feynman, R. P. (1967): The Character of Physical Law (MIT Press)

    Google Scholar 

  • Galileo Galilei (DNS): Dialogues Concerning Two New Sciences, transl by H. Crew and A. de Salvio (Dover, New York)

    Google Scholar 

  • Galileo Galilei (DWS): Dialogue Concerning the Two Chief World Systems-Ptolematic & Copernican, transl. St. Drake (University of California Press, Berkeley)

    Google Scholar 

  • Galton, F. (1889): Natural Inheritance (London)

    Google Scholar 

  • Gell-Mann, M., Hartle, J.B. (1994): Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology. In: Halliwell, J.J. (et al.), 311–345

    Google Scholar 

  • Genz, H., Decker, R. (1991): Symmetrie und Symmetriebrechung in der Physik (Vieweg, Braunschweig)

    Google Scholar 

  • Großmann, S. (1989): Selbstähnlichkeit. Das Strukturgesetz im und vor dem Chaos. In: Gerok, W. (ed.), Ordnung und Chaos (Hirzel, Stuttgart), 101–122

    Google Scholar 

  • Haken, H. (1982): Synergetics. An Introduction (Springer, Berlin)

    Google Scholar 

  • Haken, H. (1984): Advanced Synergetics (Springer, Berlin)

    Google Scholar 

  • Halliwell, J.J., Perez-Mercader, J., Zurek, W.H. (eds.) (1994): Origins of Time Asymmetry (Cambridge University Press)

    Google Scholar 

  • Halliwell, J.J. (1994): Quantum Cosmology and Time Asymmetry. In Halliwell et al. (1994), 369–389

    Google Scholar 

  • Hawking, St. (1985): The Arrow of Time in Cosmology. Physical Review D 32, 2489

    Article  ADS  MathSciNet  Google Scholar 

  • Hawking, St. (1988): A Brief History of Time (London, Bantam)

    Google Scholar 

  • Hawking, St. (1994): The No Boundary Condition and the Arrow of Time. In Halliwell et al. (1994), 346–357

    Google Scholar 

  • Hénon, M. (1976): A Two Dimensional Map with a Strange Attractor. Commun. Math. Phys. 50, 69–77

    Article  ADS  MATH  Google Scholar 

  • Holt, D.L., Holt, R. G. (1993): Regularity in Nonlinear Dynamical Systems. British Journal for the Philosophy of Science 44, 711–727

    Article  MathSciNet  Google Scholar 

  • Irvine, J.M. (1983): The Constancy of the Laws of Physics in the Light of Prehistoric Nuclear Reactors. Contemporary Physics 24(5), 427–437

    Article  ADS  Google Scholar 

  • Kuhn, T. (1978): Black-Body Theroy and the Quantum Theory 1894–1912 (Oxford)

    Google Scholar 

  • Laflamme, R. (1994): The Arrow of Time and the No Boundary Proposal. In Halliwell et al. (1994), 358–368

    Google Scholar 

  • Laplace, P.S. (1814): Essai philosophique sur les probabilités (Paris, Courcier)

    Google Scholar 

  • Laskar, J. (1994): Large-Scale Chaos in the Solar System. Astron. Astrophys. 287 L9

    ADS  Google Scholar 

  • Lee, T.D. (1988): Symmetries, Asymmetries and the world of Particles (Univ. of Washington Press, Seattle)

    Google Scholar 

  • Lighthill, J. (1986): The Recently Recongnized Failure of Predictability in Newtonian Dynamics. Proceedings of the Royal Society London A 407, 35–50

    Article  ADS  MATH  Google Scholar 

  • Linde, A. (1990): Inflation and Quantum Cosmology (Academic Press)

    Google Scholar 

  • Lorenz, E.N. (1963): Deterministic Nonperiodic Flow. J. Atmos., Sci. 20, 130ff

    Article  ADS  Google Scholar 

  • Mandelbrot, B.B. (1982): The Fractual Geometry of Nature (Freeman, San Francisco)

    Google Scholar 

  • Maxwell, J.C. (MaM): Matter and Motion (Dover, New York 1992)

    Google Scholar 

  • Meessen, A. (1989): Is It Logical Possible to Generalize Physics through Space-Time Quantization? In: Weingartner, P., Schurz, G. (eds.) Philosophy of the Natural Sciences. Proceedings of the 13th Int. Wittgenstein Symposium Vienna, Hölder-Pichler-Tempsky, 19–47.

    Google Scholar 

  • Miles, J. (1984): Resonant Motion of a Spherical Pendulum. Physica 11D, 309–323

    ADS  MathSciNet  Google Scholar 

  • Moser, J. (1978): Is the Solar System Stable? Mathematical Intelligencer 1, 65–71.

    Article  MathSciNet  Google Scholar 

  • Norman, E.B. (1986): Are Fundamental Constants Really Constant? Amer. J. of Physics 54, 317ff

    Article  ADS  Google Scholar 

  • Particle Data Group (1990): Review of Particle Properties. Physics Letters B, 204, 1ff

    Google Scholar 

  • Peitgen, H.-O., Richter, P.H. (1986): The Beauty of Fractals (Springer, Berlin)

    MATH  Google Scholar 

  • Peirce, Ch.S. (1935, 1960): Collected Papers of Ch.S. Peirce ed. by Ch. Hartshorne and P. Weiss (Harvard U.P., Cambridge—Mass)

    Google Scholar 

  • Penzias, A.A. Wilson, R.W. (1965): A Measurement of Excess Antenna Temperature at 4080 Mc/s. Astrophysical Journal 142, 419–421

    Article  ADS  Google Scholar 

  • Pesin, Ya.B. (1977): Characteristic Lyapunov Exponents and Smooth Ergodic Theory. Russian Math. Surveys 32(4), 55–114

    Article  MathSciNet  ADS  Google Scholar 

  • Poincaré, H. (1892): Les Méthodes Nouvelles de la Méchanique Céleste Vol. 1 (Paris)

    Google Scholar 

  • Popper, K.R. (1956): The Arrow of Time. Nature 177, 538

    Article  ADS  Google Scholar 

  • Popper, K.R. (1959): The Logic of Scientific Discovery (London, Hutchinson)

    MATH  Google Scholar 

  • Popper, K.R. (1965): Of Clouds and Clocks. In Popper (1972), 206–255. Originally published as the second A.H. Compton Memorial lecture (Washington)

    Google Scholar 

  • Popper, K.R. (1972): Objective Knowledge (Oxford)

    Google Scholar 

  • Prigogine, I. (1993): Time, Dynamics and Chaos: Integrating Poincaré's'Non-Integrable Systems. In: Holte, J. (ed.) Nobel Conference XXVI. Chaos: The New Science (London, Univ. Press of America)

    Google Scholar 

  • Prigogine, I., Stengers, I. (1993): Das Paradox der Zeit, Zeit. Chaos und Quanten (Munich, Piper)

    Google Scholar 

  • Ruelle, D. (1980): Strange Attractors. Mathematical Intelligencer 2, 126–137

    Article  MathSciNet  MATH  Google Scholar 

  • Ruelle, D. (1990): Deterministic Chaos: The Science and the Fiction. Proceedings of the Royal Society London A 427, 241–248

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Salam, A., Wigner, E.P., Eds., (1972): Aspects of Quantum Theory (Cambridge University Press, Cambridge)

    Google Scholar 

  • Schuster, H.G. (1989): Deterministic Chaos (VCH, Weinheim)

    MATH  Google Scholar 

  • Schurz, G., Weingartner, P. (1987): Verisimilitude Defined by Relevant Consequence Elements. In: Kuipers, Th. (ed.) What is Closer-to-the-Truth? (Amsterdam, Rodopi), 47–77

    Google Scholar 

  • Shannon, C.E., Weaver, W. (1949): The Mathematical Theory of Information (Univ. of Illinois Press, Urbana)

    Google Scholar 

  • Thomas Aquinas (STh): Summa Theologica, transl. by Fathers of the English Dominican Province, (Christian Classics, Westminster, Maryland 1981)

    Google Scholar 

  • Van Fraassen, B. (1991): Quantum Mechanics. An Empricist View (Oxford)

    Google Scholar 

  • Weierstrass, K. (1993): Briefwechsel zwischen Karl Weierstrass und Sofja Kowalewskaya, ed. R. Bölling, (Akademie Verlag. Berlin)

    Google Scholar 

  • Weinberg, St. (1977): The First Three Minutes (London, Deutsch)

    Google Scholar 

  • Weinberg, St. (1987): Towards the Final Laws of Physics. In: Elementary Particles and the Laws of Physics. The 1986 Dirac Memorial Lectures (Cambridge), 61–110

    Google Scholar 

  • Weingartner, P. (1993) A Logic for QM Based on Classical Logic. In: de la Luiz Garcia Alonso, M., Moutsopoulos, E., Seel, G., (eds.) L'art, la science et la métaphysique. Essays in honour of A. Mercier (Bern, P. Lang), 439–458

    Google Scholar 

  • Weingartner, P. (1994): Can there be Reasons for Putting Limitations on Classical Logic?, In: Humphreys, P. (ed.) Patrick Suppes: Scientific Philosopher Vol. 3 (Dordrecht, Kluwer), 89–124

    Google Scholar 

  • Weingartner, P. (1995): Are Statistical Laws Genuine Laws? A concern of Poincaré and Boltzmann. Grazer Philosophische Studien (to appear)

    Google Scholar 

  • Weingartner, P. (1996): Can the Laws of Nature (of Physics) be Complete? in: Dalla Chiara, M.L. et al. (eds.) Proceedings of the 10th International Congress of Logic, Methodology and Philosophy of Science, North Holland Publ. Comp., Amsterdam.

    Google Scholar 

  • Wess, J. (1989): The CPT-Theorem and its Significance for Fundamental Physics. Nuclear Physics B (Proc. Suppl.) 8, 461ff

    Article  ADS  Google Scholar 

  • Wigner, E. P. (1967): Symmetries and Reflections. Scientific Essays of Eugene P. Wigner ed. by Moore, W.J. and Scriven, M. (Indiana Univ. Press, Bloomington)

    Google Scholar 

  • Winger, E. P. (1972): On the Time-Energy Uncertainty Relation. —. In: Salam, A., Wigner, E. P., Eds., 237–247.

    Google Scholar 

  • Wunderlin, A. (these proceedings): On the Foundations of Synergetics

    Google Scholar 

  • Zermelo, E. (1896a): Über eine Satz der Dynamik und die mechanische Wäretheorie. Wied. Annalen 57, 485ff

    Article  Google Scholar 

  • Zermelo, E. (1896b): Über die mechanische Erklärung irreversibler Vorgänge. Wied. Annalen 59, 793ff

    Article  Google Scholar 

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  1. Universität Salzburg, Austria

    P. Weingartner

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Paul Weingartner Gerhard Schurz

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Weingartner, P. (1996). Under what transformations are laws invariant?. In: Weingartner, P., Schurz, G. (eds) Law and Prediction in the Light of Chaos Research. Lecture Notes in Physics, vol 473. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101869

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  • DOI: https://doi.org/10.1007/BFb0101869

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