Can we prove the existence of completely random events?

Main Article Content

Marek Kuś


I show how classical and quantum physics approach the problem of randomness and probability. Contrary to popular opinions, neither we can prove that classical mechanics is a deterministic theory, nor that quantum mechanics is a nondeterministic one. In other words it is not possible to show that  randomness in classical mechanics has a purely epistemic character and that of quantum mechanics  an ontic one.  Nevertheless, recent developments of quantum theory and increasing experimental possibilities to check its predictions call for returning to the problem of comparing possibilities given by classical and quantum physics to accommodate and prove the existence of a `genuine randomness'.  Recent results  concerning `amplification of randomness' show that, in certain sense,  quantum physics is in fact  ‘more random’ that classical and outperforms it in producing a `truly random process'.

Article Details

Proceedings of the PAU Commission on the Philosophy of Science


Arnold, V.I., 1975. Równania różniczkowe zwyczajne. Warszawa: Państwowe Wydawnictwo Naukowe.

Arnold, V.I., 1981. Metody matematyczne mechaniki klasycznej. tłum. P. Kucharczyk. Warszawa: Państwowe Wydawnictwo Naukowe.

Aspect, A., Grangier, P. i Roger, G., 1982. Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell’s inequalities. Physical Review Letters, 49(2), s. 91–94.

Bell, J.S., 1964. On the Einstein-Podolsky-Rosen paradox. Physics, 1, s. 195–200.

Birkhoff, G. i von Neumann, J., 1936. The logic of quantum mechanics. Annals of Mathematics, s. 823–843.

Bohm, D., 1952. A suggested interpretation of the quantum theory in terms of „hidden” variables. I,II. Physical Review, 85(2), s. 166–193.

Boussinesq, J., 1878. Conciliation du véritable déterminisme mécanique avec l’existence de la vie et de la liberté morale. Paris: Gauthier-Villars.

Brans, C.H., 1988. Bell’s theorem does not eliminate fully causal hidden variables. International Journal of Theoretical Physics, 27(2), s. 219–226.

Cicero, M.T., 1873. De finibus bonorum et malorum libri V. Leipzig: Teubner.

Cicero, M.T., 1933. De natura deorum. Leipzig: Teubner.

Clauser, J.F., Horne, M.A., Shimony, A. i Holt, R.A., 1969. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23(15), s. 880–884.

Colbeck, R. i Renner, R., 2012. Free randomness can be amplified. Nature Physics, [online] 8(6), s. 450–453. Dostępne na: [dostęp 22.09.2018].

Diels, H., 1906. Die Fragmente der Vorsokratiker. Berlin: Weidmannsche Buchhandlung.

Diogenes Laertius, 1982. Żywoty i poglądy słynnych filozofów. tłum. I. Krońska, K. Leśniak i W. Olszewski. Warszawa: Państwowe Wydawnictwo Naukowe.

Diogenes Laertius, 2008. Diogenis Laertii Vitae philosophorum. Berlin: Walter de Gruyter.

Earman, J., 1986. A primer on determinism. Dordrecht: Reidel.

Earman, J., 2008. How determinism can fail in classical physics and how quantum physics can (sometimes) provide a cure. Philosophy of Science, 75(5), s. 817–829.

Earman, J., 2009. Essential self-adjointness: implications for determinism and the classical–quantum correspondence. Synthese, 169(1), s. 27–50.

Earman, J. i Friedman, M., 1973. The meaning and status of Newton’s law of inertia and the nature of gravitational forces. Philosophy of Science, 40(3), s. 329–359.

Everett III, H., 1957. „ Relative state” formulation of quantum mechanics. Reviews of Modern Physics, 29(3), s. 454.

Fletcher, S.C., 2012. What counts as a Newtonian system? The view from Norton’s dome. European Journal for Philosophy of Science, 2(3), s. 275–297.

Freeman, K., 1948. Ancilla to the pre-Socratic philosophers: a complete translation of the fragment in Diels, Fragmente der Vorsokratiker. [online] Cambridge: Harvard University Press. Dostępne na: [dostęp 21.09.2018].

Gallicchio, J., Friedman, A.S. i Kaiser, D.I., 2014. Testing Bell’s inequality with cosmic photons: Closing the setting-independence loophole. Physical Review Letters, 112(11), s. 110405.

Giustina, M., Versteegh, M.A., Wengerowsky, S., Handsteiner, J., Hochrainer, A., Phelan, K., Steinlechner, F., Kofler, J., Larsson, J.-Å. i Abellán, C., 2015. Significant-loophole-free test of Bell’s theorem with entangled photons. Physical Review Letters, 115(25), s. 250401.

Gleason, A.M., 1957. Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics, 6, s. 885–893.

Haake, F., 2013. Quantum signatures of chaos. wyd. 3. Berlin: Springer Science & Business Media.

Haake, F., Gnutzmann, S. i Kuś, M., 2018. Quantum signatures of chaos. wyd. 3. Springer Series in Synergetics. Berlin: Springer.

Hall, M.J., 2010. Local deterministic model of singlet state correlations based on relaxing measurement independence. Physical Review Letters, 105(25), s. 250404.

Hensen, B., Bernien, H., Dréau, A.E., Reiserer, A., Kalb, N., Blok, M.S., Ruitenberg, J., Vermeulen, R.F., Schouten, R.N. i Abellán, C., 2015. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526(7575), s. 682–686.

Knuth, D.E., 1969. The art of computer programming. Seminumerical algorithms 2. Reading, Mass.: Addison-Wesley.

Kochen, S. i Specker, E.P., 1967. The Problem of Hidden Variables in Quantum Mechanics. Journal of Mathematics and Mechanics, 17, s. 59–87.

Koh, D.E., Hall, M.J., Pope, J.E., Marletto, C., Kay, A., Scarani, V. i Ekert, A., 2012. Effects of reduced measurement independence on Bell-based randomness expansion. Physical Review Letters, 109(16), s. 160404.

Koleżyński, A., 2007. Determinizm Laplace’a w świetle teorii fizycznych mechaniki klasycznej. Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce), [online] (40), s. 59–75. Dostępne na: [dostęp 22.09.2018].

Landau, L.D. i Lifszic, E.M., 1961. Mechanika. ser. Fizyka teoretyczna. tłum. S.L. Bażański. Warszawa: Państwowe Wydawnictwo Naukowe.

Laplace, P.S. de, 1814. Essai philosophique sur les probabilités. Paris: Mme. Ve. Courcier.

Laraudogoitia, J.P., 1997. Classical particle dynamics, indeterminism and a supertask. The British Journal for the Philosophy of Science, 48(1), s. 49–54.

Mather, J.N. i McGehee, R., 1975. Solutions of the collinear four body problem which become unbounded in finite time. W: Dynamical systems, theory and applications. New York: Springer, s. 573–597.

Nagel, E., 1961. The structure of science; problems in the logic of scientific explanation. New York: Harcourt, Brace & World.

Newton, I., 1687. Philosophiae naturalis principia mathematica. Londini; [London]: J. Societatis Regiae ac Typis J. Streater.

Newton, I., 2011. Matematyczne zasady filozofii przyrody. tłum. J. Wawrzycki. Kraków; Rzeszów: Copernicus Center Press ; Konsorcjum Akademickie.

Norton, J.D., 2007. Causation as folk science. W: Causation, physics, and the constitution of reality: Russells republic revisited. Oxford: Oxford University Press, s. 11–44.

Norton, J.D., 2008. The dome: An unexpectedly simple failure of determinism. Philosophy of Science, 75(5), s. 786–798.

Poincaré, H., 1912. Calcul des probabilitiés. wyd. 2 éd., revue et augmentée par l'auteur. Paris: Gauthier-Villars.

Popescu, S. i Rohrlich, D., 1994. Quantum nonlocality as an axiom. Foundations of Physics, 24(3), s. 379–385.

Popper, K.R., 1988. The Open Universe: An Argument for Indeterminism. Psychology Press.

Santha, M. i Vazirani, U.V., 1984. Generating quasi-random sequences from slightly-random sources. Foundations of Computer Science 1984, 25th Annual Symposium on IEEE, s. 434–440.

Saunders, S., Barrett, J., Kent, A. i Wallace, D. red., 2010. Many worlds?: Everett, quantum theory, & reality. Oxford: Oxford University Press.

Shalm, L.K., Meyer-Scott, E., Christensen, B.G., Bierhorst, P., Wayne, M.A., Stevens, M.J., Gerrits, T., Glancy, S., Hamel, D.R. i Allman, M.S., 2015. Strong loophole-free test of local realism. Physical Review Letters, 115(25), s. 250402.

Smoluchowski, M., 1918. Über den Begriff des Zufalls und den Ursprung der Wahrscheinlichkeitsgesetze in der Physik. Die Naturwissenschaften, 17, s. 253–263.

Smoluchowski, M., 1923. O pojęciu przypadku i pochodzeniu praw Fizyki opartych na prawdopodobieństwie. Wiadomości Matematyczne, XXVII, z. 2, s. 27–52.

Smoluchowski, M., 2017. Uwagi o roli przypadku we fizyce. Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce), [online] (62), s. 277–302. Dostępne na: .

Solèr, M.P., 1995. Characterization of Hilbert spaces by orthomodular spaces. Communications in Algebra, 23(1), s. 219–243.

Stone, M.H., 1936. The theory of representation for Boolean algebras. Transactions of the American Mathematical Society, 40(1), s. 37–111.

Tylec, T.I. i Kuś, M., 2015. Non-signaling boxes and quantum logics. Journal of Physics A: Mathematical and Theoretical, [online] 48(50), s. 505303. Dostępne na: [dostęp 22.09.2018].

Tylec, T.I. i Kuś, M., 2018. Ignorance is a bliss: Mathematical structure of many-box models. Journal of Mathematical Physics, [online] 59(3), s. 032202. Dostępne na: [dostęp 22.09.2018].

Weinan, E. i Vanden-Eijnden, E., 2003. A note on generalized flows. Physica D: Nonlinear Phenomena, 183(3–4), s. 159–174.

Wüthrich, C., 2010. Can the World Be Shown to Be Indeterministic After All? W: C. Beisbart i S. Hartmann, red., Probabilities in Physics. Oxford: Oxford University Press, s. 365–389.

Zimba, J., 2008. Inertia and determinism. The British Journal for the Philosophy of Science, 59(3), s. 417–428.

Zinkernagel, H., 2010. Causal fundamentalism in physics. W: M. Suárez, M. Dorato i M. Rédei, red., EPSA philosophical issues in the sciences. Dordrecht: Springer, s. 311–322.