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Published online by Cambridge University Press: 14 March 2022
In the following, limiting ourselves to two objects—the processes X and Y—we will compare three kinds of regularities in their specific manifestation in physics: (1) interaction; (2) causality; and (3) functional dependence. In considering as objective all the regularities which are inherent in things and material processes themselves, and in considering causality and functional dependence merely as one-sided abstractions of interaction, which in its turn is an abstraction from the universal interconnection of things, we avoid such an arbitrary definition of causality as, for instance, the possibility of exact prognosis which leads to the negation of causality. We also avoid placing functional dependence above causality.
1 Cf., for instance, Max Planck “Die Kausalitat im Naturgeschehen,” “Scientia” of March 1, 1933, where he says: “Ein Eregnis ist dann kausal bedingt wenn es mit Sicherheit vorausgesagt werden kann,” and where, proceeding from mechanistic materialism, Planck arrives with logical consistency at the recognition of an omniscient absolute spirit.
2 This identity takes place only for symmetrical functions, for instance, if
then
3 Cf. also G. Windred, “The History of Mathematical Time,” in “Isis,” Nos. 55, 58 (1933).
4 Extremely characteristic are the arguments of E. Zilsel in an article “Ueber die Symmetrie der Kausalität und die Einsinnigkeit der Zeit.” “Naturwissenschaften,” No. 12, 1927, where the proposition of “unidirectial time being included in the second principle of thermodynamics” is coordinated with arguments springing from it against the materialistic conception of history. Cf. also H. Reichenbach, “Axiomatik des relativistischen Raum und Zeitlehre,” 1924; R. Carnap, “Die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit,” 1925; Zilsel is, however, compelled to admit the existence of a connection between the unidirectionality of time and the difference between mass (which is his terminology for “matter”) and field and consequently, the impossibility of reducing the unidirectionality of time to the second law; nevertheless he is reluctant to carry out this argument to the end.
5 Cf., for instance, A. Eddington, in “The Decline of Determinism,” “Nature” of February 13, 1932, makes the following deduction: “So far as the physical universe is concerned, determinism appears to explain nothing.”
6 E. Schrödinger, “Spezielle Relativitätstheorie und Quantenphysik,” Sitzungsberichte der Preuss. Akademie der Wiss., no. 12, 1931, p. 328, where he says: “Durch diese Sonderstellung der Zeit erweist sich die Quantenmechanik in ihrer gegenwärtigen Gestalt und vor allem in ihrer gegenwärtigen Interpretation als durch und durch unrelativistisch. Das wird nicht behoben, wenn man blos durch Adaptierung des Formelapparates eine rein äusserliche Gleichstellung das heisst formale Invarianz gegen Lorentztransformation herbeiführt.”
7 Proc. of the Royal Soc. of Edinburgh, XLVI, p. 90.
8 “Naturwissenschaften,” No. 87, 1927.
9 Ztschr. f. Phys., 64, #7-8, 563 (1930).
10 Ztschr. f. Ph. 72, 9–10, 1931, S.621.
11 Ztschr. f. Ph. 69, 6–6, 1931.
12 Phys. Z. d. Sowjetunion, I, 3, 1932, S.397.
13 Discontinuity of time, as indeed any other theory, may be splendidly made use of by idealists and theologians. Cf. for instance the views of Mutakillimûn, the Arabian mediæval philosopher of orthodox-Islam tendency, who supposed that time is discontinuous and that God at each new instant, by a special act, creates the world anew.
14 Cf. for instance the work (Russian) of I. M. Sechenov “Reflexes of the Cerebrum” (1863) and N. E. Vvedensky “On the correlations between irritation and excitement” (1886) or Lapique's “L'excitabilité en fonction du temps” 1926.
15 J. A. Schouten and D. Van Dantzig “Zum Unifizierungsproblem der Physik, Skizze einer generellen Feldtheorie.” Koninklijke Akademie van Wettenschappen te Amsterdam, Proc., XXXV, 5, 1932.