Letters to the Editor

On One Article by K. V. Nikolsky and on His Response to Criticism of This Article

V. A. Fock, Leningrad

In his article “Principles of Quantum Mechanics I”¹), which is devoted to my critique of his note²), K. V. Nikolsky not only does not subject quantum mechanics as a whole to doubt, but he himself stands entirely on the generally accepted Bohr point of view, nowhere even hinting at his disagreement with it. The object of my criticism therefore was not, and could not have been, Nikolsky’s objections to quantum mechanics or to Bohr’s point of view: there were no such objections. My criticism concerned exclusively the method proposed by Nikolsky for deriving the mathematical apparatus of quantum mechanics, and not at all its interpretation, for Nikolsky’s interpretation coincided with the generally accepted one.

In Nikolsky’s reply note³), however, it is said that quantum mechanics is “nothing more than a very artificial detour for solving certain problems of atomic physics” (p. 558); the principle of complementarity arising from Heisenberg’s relations is there called completely unacceptable (p. 557); finally, the generally accepted conception of quantum mechanics, to which Nikolsky himself adhered in his first article, is called by him idealistic and Machist (p. 555).

Such an unexpected substitution of the subject of dispute, combined with the alteration of one’s views to the opposite ones, can hardly be recognized as a response to criticism. Since Nikolsky contradicts himself, he makes polemics with him on this question impossible: any reasonable polemic is possible only between opponents who acknowledge the ordinary rules of logic. As for the question itself of the conception of quantum mechanics, I consider its discussion deeply deserved, and I devote a separate article to it in the journal Under the Banner of Marxism. In that article my main thesis is that quantum mechanics is a materialist theory for the simple reason that it is a true theory of matter.

Let us now return to the original subject of the dispute: the question of the method of deriving the mathematical apparatus of quantum mechanics.

In his article Nikolsky, after purely mathematical remarks on expansions in series, first introduces wave functions on p. 545, where he says: “… let us pass from \(w(k,t)\) to auxiliary functions — we shall call them statistical — determined by the equations … \(w(k_n,t^*) = c(k_n,t)c^*(k_n,t)\).” (italics mine). The word “determined” is used here inaccurately: all of Nikolsky’s further reasoning is constructed as though the functions \(c(k_n,t^*)\) were indeed determined by these equations. In his reply to my criticism Nikolsky says: “I do not at all assert that

¹) Uspekhi fizicheskikh nauk, 16, 537, 1936.
²) Uspekhi fizicheskikh nauk, 17, 552, 1937.
³) Uspekhi fizicheskikh nauk, 17, 554, 1937.

the formula \(w = |c|^2\) defines the wave functions,” i.e., he simply denies the assertion he himself made earlier.

Further, in my critique I say that Nikolsky wants to avoid the necessity of postulating Hilbert space and the entire apparatus of quantum mechanics. Nikolsky, however, says in his reply that I attribute to him the tendency “to avoid obtaining the apparatus of quantum mechanics.”

In my critique I analyzed in detail only § 3 of Nikolsky’s article, as containing its basic ideas. Nikolsky objects to this (p. 559), saying that “what is new and most essential in the entire article is not at all § 3, which contains what is known, but the introduction of canonically conjugate variables given on pp. 553–554.” I am ready to agree that § 3 contains nothing new (except for the unsuccessful attempt to obtain wave functions from probabilities), but what is indicated on pp. 553–554 contains only a consideration of the connection between permutation relations and uncertainty relations, accompanied by the usual explanations of the latter in the spirit of Heisenberg and Bohr. What is new here is perhaps only that Planck’s constant divided by \(2\pi\) is called “the parameter of statistical correlation.”

In general, every formula of Nikolsky’s has its own correct formula of quantum mechanics corresponding to it. Only it is not derived in the way Nikolsky tries to do it.

Since the whole dispute concerned only methods of derivation, and since now Nikolsky himself has admitted that his article “contains very many defects that are quite substantial from the mathematical point of view” (p. 560), I may regard this dispute as exhausted.