Although my Logik der Forschung may have looked to some like a criticism of the Vienna Circle, its main aims were positive. I tried to propound a theory of human knowledge. But I looked upon human knowledge in a way quite different from the way of the classical philosophers. Down to Hume and Mill and Mach, most philosophers took human knowledge as something settled. Even Hume, who thought of himself as a sceptic, and who wrote the Treatise in the hope of revolutionizing the social sciences, almost identified human knowledge with human habits. Human knowledge was what almost everybody knew: that the cat was on the mat; that Julius Caesar had been assassinated; that grass was green. All this seemed to me incredibly uninteresting. What was interesting was problematic knowledge, growth of knowledge—discovery.
If we are to look upon the theory of knowledge as a theory of discovery, then it will be best to look at scientific discovery. A theory of the growth of knowledge should have something to say especially about the growth of physics, and about the clash of opinions in physics.
At the time (1930) when, encouraged by Herbert Feigl, I began writing my book, modern physics was in turmoil. Quantum mechanics had been created by Werner Heisenberg in 1925;121 but it was several years before outsiders—including professional physicists—realized that a major breakthrough had been achieved. And from the very beginning there was dissension and confusion. The two greatest physicists, Einstein and Bohr, perhaps the two greatest thinkers of the twentieth century, disagreed with one another. And their disagreement was as complete at the time of Einstein’s death in 1955 as it had been at the Solvay meeting in 1927. There is a widely accepted myth that Bohr won a victory in his debate with Einstein;122 and the majority of creative physicists supported Bohr and subscribed to this myth. But two of the greatest physicists, de Broglie and Schrödinger, were far from happy with Bohr’s views (later called “the Copenhagen interpretation of quantum mechanics”) and proceeded on independent lines. And after the Second World War, there were several important dissenters from the Copenhagen School, in particular Bohm, Bunge, Landé, Margenau, and Vigier.
The opponents of the Copenhagen interpretation are still in a small minority, and they may well remain so. They do not agree among themselves. But quite a lot of disagreement is also discernible within the Copenhagen orthodoxy. The members of this orthodoxy do not seem to notice these disagreements or at any rate to worry about them, just as they do not seem to notice the difficulties inherent in their views. But both are very noticeable to outsiders.
These all too superficial remarks will perhaps explain why I felt at a loss when I first tried to get to grips with quantum mechanics, then often called “the new quantum theory”. I was working on my own, from books and from articles; the only physicist with whom I sometimes talked about my difficulties was my friend Franz Urbach. I tried to understand the theory, and he had doubts whether it was understandable—at least by ordinary mortals.
I began to see light when I realized the significance of Born’s statistical interpretation of the theory. At first I had not liked Born’s interpretation: Schrödinger’s original interpretation appealed to me, aesthetically, and as an explanation of matter; but once I had accepted the fact that it was not tenable, and that Born’s interpretation was highly successful, I stuck to the latter, and was thus puzzled to know how one could uphold Heisenberg’s interpretation of his indeterminacy formulae if Born’s interpretation was accepted. It seemed obvious that if quantum mechanics was to be interpreted statistically, then so must be Heisenberg’s formulae: they had to be interpreted as scatter relations, that is, as stating the lower bounds of the statistical scatter, or the upper bounds of the homogeneity, of any sequence of quantum-mechanical experiments. This view has now been widely accepted.123 (I should make clear, however, that originally I did not always clearly distinguish between the scatter of the results of a set of experiments and the scatter of a set of particles in one experiment; although I had found in “formally singular” probability statements the means for solving this problem, it was only completely cleared up with the help of the idea of propensities.)124
A second problem of quantum mechanics was the famous problem of the “reduction of the wave packet”. Few perhaps will agree that this problem was solved in 1934 in my Logik der Forschung; yet some very competent physicists have accepted the correctness of this solution. The proposed solution consists in pointing out that the probabilities occurring in quantum mechanics were relative probabilities (or conditional probabilities).125
The second problem is connected with what was perhaps the central point of my considerations—a conjecture, which grew into a conviction, that the problems of the interpretation of quantum mechanics can all be traced to problems of the interpretation of the calculus of probability.
A third problem solved was the distinction between a preparation of a state and a measurement. Although my discussion of this was quite correct and, I think, very important, I made a serious mistake over a certain thought experiment (in section 77 of Logik der Forschung). I took this mistake very much to heart; I did not know at that time that even Einstein had made some similar mistakes, and I thought that my blunder proved my incompetence. It was in Copenhagen in 1936, after the Copenhagen “Congress for Scientific Philosophy”, that I heard of Einstein’s mistakes. On the initiative of Victor Weisskopf, the theoretical physicist, I had been invited by Niels Bohr to stay a few days for discussion at his Institute. I had previously defended my thought experiment against von Weizsäcker and Heisenberg, whose arguments did not quite convince me, and against Einstein, whose arguments did convince me. I had also discussed the matter with Thirring and (in Oxford) with Schrödinger, who told me that he was deeply unhappy about quantum mechanics and thought that nobody really understood it. Thus I was in a defeatist mood when Bohr told me of his discussions with Einstein—the same discussions he described later in Schilpp’s Einstein volume.126 It did not occur to me to derive comfort from the fact that, according to Bohr, Einstein had been as mistaken as I; I felt defeated, and I was unable to resist the tremendous impact of Bohr’s personality. (In those days Bohr was irresistible anyway.) I more or less caved in, though I still defended my explanation of the “reduction of the wave packet”. Weisskopf seemed willing to accept it, but Bohr was much too eager to expound his theory of complementarity to take any notice of my feeble efforts to sell my explanation, and I did not press the point, content to learn rather than to teach. I left with an overwhelming impression of Bohr’s kindness, brilliance, and enthusiasm; I also felt little doubt that he was right and I wrong. Yet I could not persuade myself that I understood Bohr’s “complementarity”, and I began to doubt whether anybody else understood it, though clearly some were persuaded that they did. This doubt was shared by Einstein, as he later told me, and also by Schrödinger.
This set me thinking about “understanding”. Bohr, in a way, was asserting that quantum mechanics was not understandable; that only classical physics was understandable and that we had to resign ourselves to the fact that quantum mechanics could be only partially understood, and then only through the medium of classical physics. Part of this understanding was achieved through the classical “particle picture”, part through the classical “wave picture”; these two pictures were incompatible, and they were what Bohr called “complementary”. There was no hope for a fuller or more direct understanding of the theory; and what was required was a “renunciation” of any attempt to reach a fuller understanding.
I suspected that Bohr’s theory was based on a very narrow view of what understanding could achieve. Bohr, it appeared, thought of understanding in terms of pictures and models—in terms of a kind of visualization. This was too narrow, I felt; and in time I developed an entirely different view. According to this view what matters is the understanding not of pictures but of the logical force of a theory: its explanatory power, its relation to the relevant problems and to other theories. I developed this view over many years in lectures, first I think in Alpbach (1948) and in Princeton (1950), in Cambridge in a lecture on quantum mechanics (1953 or 1954), in Minneapolis (1962), and later again in Princeton (1963), and other places (London too, of course). It will be found, though only sketchily, in some of my later papers.127
Concerning quantum physics I remained for years greatly discouraged. I could not get over my mistaken thought experiment, and although it is, I think, quite right to grieve over any of one’s mistakes, I think now that I attributed too much weight to it. Only after some discussions, in 1948 or 1949, with Arthur March, a quantum physicist whose book on the foundations of quantum mechanics128 I had quoted in my Logik der Forschung, did I return to the problem with something like renewed courage.
I went again into the old arguments, and I arrived at the following:129
(A) The problem of determinism and indeterminism.
(1) There is no such thing as a specifically quantum-mechanical argument against determinism. Of course, quantum mechanics is a statistical theory and not a prima facie deterministic one, but this does not mean that it is incompatible with a prima facie deterministic theory. (More especially, von Neumann’s famous proof of this alleged incompatibility—of the nonexistence of so-called “hidden variables”—is invalid, as was shown by David Bohm and more recently, by more direct means, by John S. Bell.)130 The position at which I had arrived in 1934 was that nothing in quantum mechanics justifies the thesis that determinism is refuted because of its incompatibility with quantum mechanics. Since then I have changed my mind on this issue more than once.
A model showing that the existence of a prima facie deterministic theory was indeed formally compatible with the results of quantum mechanics was given by David Bohm in 1951. (The basic ideas underlying this proof had been anticipated by de Broglie.)
(2) There is, on the other hand, no valid reason whatever for the assertion that determinism has a basis in physical science; in fact there are strong reasons against it, as pointed out by C. S. Peirce,131 Franz Exner, Schrödinger,132 and von Neumann:133 all these drew attention to the fact that the deterministic character of Newtonian mechanics was compatible with indeterminism.134 Moreover, while it is possible to explain the existence of prima facie deterministic theories as macrotheories on the basis of indeterministic and probabilistic microtheories, the opposite is not possible: nontrivial probabilistic conclusions can only be derived (and thus explained) with the help of probabilistic premises.135 (In this connection some very interesting arguments of Landé’s should be consulted.)136
(B) Probability.
In quantum mechanics we need an interpretation of the probability calculus which
(1) is physical and objective (or “realistic”);
(2) yields probability hypotheses which can be statistically tested.
Moreover,
(3) these hypotheses are applicable to single cases; and
(4) they are relative to the experimental setup.
In Logik der Forschung I developed a “formalistic” interpretation of the probability calculus which satisfied all these demands. I have since improved upon this, replacing it by the “propensity interpretation”.137
(C) Quantum Theory.
(1) Realism. Although I had no objections of principle to “wavicles” (wave-cum-particles) or similar nonclassical entities, I did not see (and I still do not see) any reason to deviate from the classical, naive, and realistic view that electrons and so on are just particles; that is to say, that they are localized, and possess momentum. (Of course, further developments of the theory may show that those who do not agree with this view are right.)138
(2) Heisenberg’s so-called “indeterminacy principle” is a misinterpretation of certain formulae, which assert statistical scatter.
(3) The Heisenberg formulae do not refer to measurements; which implies that the whole of the current “quantum theory of measurement” is packed with misinterpretations. Measurements which according to the usual interpretation of the Heisenberg formulae are “forbidden” are according to my results not only allowed, but actually required for testing these very formulae.139 However, the scatter relations refer to the preparation of the states of quantum mechanical systems. In preparing a state we always introduce a (conjugate) scatter.139a
(4) What is indeed peculiar to quantum theory is the (phase-dependent) interference of probabilities. It is conceivable that we may have to accept this as something ultimate. However, this does not seem to be the case: while still opposing Compton’s crucial tests of Einstein’s photon theory Duane produced, in 1923, long before wave mechanics, a new quantum rule,140 which may be regarded as the analogue with reference to momentum of Planck’s rule which refers to energy. Duane’s rule for the quantization of momentum can be applied not only to photons but (as stressed by Landé)141 to particles, and it then gives a rational (though only qualitative) explanation of particle interference. Landé has further argued that quantitative interference rules of wave mechanics can be derived from simple additional assumptions.
(5) Thus a host of philosophical spectres can now be exorcised, and all those many staggering philosophical assertions about the intrusion of the subject or the mind into the world of the atom can now be dismissed. This intrusion can be largely explained as due to the traditional subjectivist misinterpretation of the probability calculus.142