It is an often repeated claim in the literature that quantum mechanics is indeter-ministic and that it has put an end to the classical notion of causality. From the impossibility of determining the exact spatio-temporal trajectory of an atomic system, for instance, Heisenberg infers ‘the invalidity of the causal law’ in quantum mechanics [1]. What is tacitly assumed in such views is a chain of reasoning, which leads from determinism to causality. One form of determinism — predictive determinism — is the view that a sufficient knowledge of the laws of nature and appropriate boundary conditions will enable a superior intelligence to predict the future states of the physical world and to retrodict its past states with infinite precision. Laplace attributes this capacity to his famous demon: for the demon the physical world stretches out like the frames of a filmstrip. Each frame is caused by an earlier frame and in its turn causes a later frame. From the present frame the Laplacean demon is capable of predicting and retrodicting all other frames. Hence the demon identifies determinism and causality. ‘We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow’ [9]. Laplace assumes that these states are unique and can be determined with mathematical precision such that prediction and retrodiction become possible. The laws of physics are typically expressed in differential equations which describe the evolution of some physical parameter, P, as a function of time, t. As one state of a system, S1, evolves to another state, S2, where this temporal evolution is made precise by the employment of differential equations, it becomes easy to think of differential equations as precise mathematical representations of causal laws [10]. This is indeed how Einstein presented the matter: ‘The differential law is the only form which completely satisfies the modern physicist's demand for causality’ [2]. Although Russell [11] had argued that the ‘law of causality (…) is the product of a bygone age’ he nevertheless admitted causal laws in the form of functional relations and differential equations into physics.
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Primary Literature
W. Heisenberg: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43, (1927), 174–79, 197; W. Heisenberg: Kausalgesetz und Quantenmechanik. Annalen der Philosophie 2, (1931), 179–81; reprinted in W. Heisenberg: Gesammelte Werke/Collected Works Abteilung C, Band I: Physik und Erkenntnis 1927–1955; eds. W. Blum, H.P. Dürr/H. Rechenberg, München/Zürich: Piper (1984–5), 29–39
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E. Cassirer: Determinismus und Indeterminismus in der Modern Physik (1936), in: E. Cassirer, Gesammelte Werke 19. Ed. by B. Recki (Felix Meiner Verlag, Hamburg 2008); English translation: Determinism and Indeterminism in Modern Physics (Yale University Press, New Haven 1956)
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Secondary Literature
P. Laplace: Théorie analytique des probabilities (Couvier, Paris 1820, Introduction VI–VII). Translation quoted from E. Nagel: The Structure of Science (Routledge & Kegal Paul, London 1961, 281–2)
Ph. Frank: Das Kausalgesetz und seine Grenzen (Springer, Wien 1932, 142–46). Note that the functional view was already held by Mach and Boltzmann, see M. Stöltzner, Vienna Indeter-minism: Mach, Boltzmann, Exner, Synthese 119, (1999), 85–111
B. Russell: On the notion of cause. Proceedings of the Aristotelian Society XIII, (1912–13), 1–26; reprinted in B. Russell: On the Philosophy of Science, edited, with an Introduction, by Charles A. Fritz (The Bobbs—Merrill Company, Indianapolis 1965, 163–186)
D. Bohm: Causality and Chance in Modern Physics (Routledge and Kegan Paul, London 1957) J.L. Mackie: The Cement of the Universe (Clarendon Press, Oxford 1980); F. Weinert: The Scientist as Philosopher (Springer, Berlin 2004, Chap. 5)
A. Einstein, B. Podolsky, N. Rosen: Can quantum-mechanical description of physical reality be considered complete? Physical Review 47, (1935), 777–80
B. Falkenburg: Particle Metaphysics. A Critical Account of Subatomic Reality (Springer, Heidelberg 2007)
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Falkenburg, B., Weinert, F. (2009). Indeterminism and Determinism in Quantum Mechanics. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_96
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