Abstract
About 35 years ago Wheeler introduced the motto “law without law” to highlight the possibility that (at least a part of) Physics may be understood only following regularity principles and few relevant facts, rather than relying on a treatment in terms of fundamental theories. Such a proposal can be seen as part of a more general attempt (including the maximum entropy approach) summarized by the slogan “it from bit”, which privileges the information as the basic ingredient. Apparently it seems that it is possible to obtain, without the use of physical laws, some important results in an easy way, for instance, the probability distribution of the canonical ensemble. In this paper we will present a general discussion on those ideas of Wheeler’s that originated the motto “law without law”. In particular we will show how the claimed simplicity is only apparent and it is rather easy to produce wrong results. We will show that it is possible to obtain some of the results treated by Wheeler in the realm of the statistical mechanics, using precise assumptions and nontrivial results of probability theory, mainly concerning ergodicity and limit theorems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wheeler, J.A.: On recognizing “law without law”, oersted medal response at the Joint APS-AAPT meeting, New York, 25 January 1983. Am. J. Phys. 51, 398 (1983)
Wheeler, J.A.: Recent thinking about the nature of the physical world—it from bit. Ann. N. Y. Acad. Sci. 655, 349 (1992)
Deutsch, D.: On Wheeler notion of law without law in physics. Found. Phys. 16, 565 (1986)
Emch, G., Liu, C.: The Logic of Thermostatistical Physics. Springer, New York (2002)
Chibbaro, S., Rondoni, L., Vulpiani, A.: Reductionism, Emergence and Levels of Reality. Springer, New York (2014)
Castiglione, P., Falcioni, M., Lesne, A., Vulpiani, A.: Chaos and Coarse Graining in Statistical Mechanics. Cambridge University Press, Cambridge (2008)
Cercignani, C.: Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford Univ Press, Oxford (1998)
Blackwell, D., Mauldin, R.D.: Ulam’s redistribution of energy problem. Lett. Math. Phys. 60, 149 (1985)
Bertrand, J.: Calcul des probabilités. Gauthier-Villars, Paris (1889)
Puglisi, A., Loreto, V., Marconi, U.M.B., Petri, A., Vulpiani, A.: Clustering and non-gaussian behavior in granular matter. Phys. Rev. Lett. 81, 3848 (1998)
Nagel, E.: The Structure of Science. Hackett Publ. Comp, Indianapolis (1979)
Cerino, L., Puglisi, A., Vulpiani, A.: A consistent description of fluctuations requires negative temperatures. J. Stat. Mech. 2015, P12002 (2015)
Dumas, H.S.: The KAM Story. World Scientific, Hackensack (2014)
Ciccotti, G., Hoover, W.G. (eds.): Molecular Dynamics Simulations of Statistical Mechanical Systems. North-Holland, Amsterdam (1986)
Khinchin, A.I.: Mathematical Foundations of Statistical Mechanics. Dover Publ, New York (1949)
Mazur, P., van der Linden, J.: Asymptotic form of the structure function for real systems. J. Math. Phys. 4, 271 (1963)
Koralov, L.B., Sinai, Y.G.: Theory of Probability and Random Processes. Springer, New York (2007)
Gallavotti, G. (ed.): The Fermi-Pasta-Ulam Problem: A Status Report. Springer, New York (2007)
Jona-Lasinio, G.: Renormalization group and probability theory. Phys. Rep. 352, 439 (2001)
Di Castro, C., Raimondi, R.: Statistical Mechanics and Applications in Condensed Matter. Cambridge University Press, Cambridge (2015)
Bleher, P.M., Sinai, J.G.: Investigation of the critical point in models of the type of Dyson’s hierarchical models. Commun. Math. Phys. 33, 23 (1973)
Jaynes, E.T.: Foundations of probability theory and statistical mechanics. In: Bunge, M. (ed.) Delaware Seminar in the Foundations of Physics, p. 77. Springer, Berlin (1967)
Auletta, G., Rondoni, L., Vulpiani, A.: On the relevance of the maximum entropy principle in non-equilibrium statistical mechanics. Eur. Phys. J. Spec. Top. 226, 2327 (2017)
Kuzemskij, A.L.: Probability, information and statistical mechanics. Int. J. Mod. Phys. 55, 1378 (2015)
von Plato, J.: Creating Modern Probability. Cambridge University Press, Cambridge (1994)
Popper, K.R.: The Logic of Scientific Discovery. Routledge, London (2002)
Goldstein, S.: Typicality and notions of probability in physics. In: Ben-Menahem, Y., Hemmo, M. (eds.) Probability in Physics, pp. 59–71. Springer, New York (2012)
Cerino, L., Cecconi, F., Cencini, M., Vulpiani, A.: The role of the number of degrees of freedom and chaos in macroscopic irreversibility. Physica A 442, 486–497 (2016)
Zanghì, N.: I fondamenti concettuali dell’approccio statistico in fisica. In: Allori, V., Dorato, M., Laudisa, F., Zanghì, N. (eds.) La natura delle cose: Introduzione ai fondamenti e alla filosofia della fisica, Carocci, pp. 202–247 (2005)
Kac, M.: On the notion of recurrence in discrete stochastic processes. Bull. Am. Math. Soc. 53, 1002 (1947)
Ma, S.K.: Statistical Mechanics. World Scientific, Philadelphia (1985)
Acknowledgements
We wish to thank M. Falcioni and A. Puglisi for many useful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Caprara, S., Vulpiani, A. Law Without Law or “Just” Limit Theorems?. Found Phys 48, 1112–1127 (2018). https://doi.org/10.1007/s10701-018-0210-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-018-0210-z