Few great men have had an intellectual impact upon the twentieth century comparable to that of Ernst Mach. He influenced physics, physiology, psychology, the philosophy of science, and pure (or speculative) philosophy. He influenced Einstein, Bohr, Heisenberg, William James, Bertrand Russell—to mention just a few names. Mach was not a great physicist; but he was a great personality and a great historian and philosopher of science. As a physiologist, psychologist, and philosopher of science, he held many important and original views to which I subscribe. He was, for instance, an evolutionist in the theory of knowledge, and in the field of psychology and physiology, especially in the study of the senses. He was critical of metaphysics, but he was sufficiently tolerant to admit, and even to stress, the necessity of metaphysical ideas as guiding lights for the physicist, even the experimental physicist. Thus he wrote, in his Principles of the Theory of Heat, about Joule:244
When it comes to general (philosophical) questions [which Mach calls “metaphysical” on the previous page], Joule is almost silent. But where he speaks, his utterances closely resemble those of Mayer. And indeed, one cannot doubt that such comprehensive experimental investigations, all with the same aim, can be carried out only by a man who is inspired by a great and philosophically most profound view of the world.
A passage like this is the more remarkable as Mach had previously published a book, The Analysis of Sensations, in which he wrote that “my approach eliminates all metaphysical questions”, and that “all we can know of the world expresses itself necessarily in sensations” (or in sense data, “Sinnesempfindungen”).
Unfortunately, neither his biological approach nor his tolerance made much impact on the thought of our century; what was so influential—especially upon atomic physics—was his antimetaphysical intolerance, combined with his theory of sensations. That Mach’s influence on the new generation of atomic physicists became so persuasive is indeed one of the ironies of history. For he was a vehement opponent of atomism and the “corpuscular” theory of matter, which he, like Berkeley,245 regarded as metaphysical.
The philosophical impact of Mach’s positivism was largely transmitted by the young Einstein. But Einstein turned away from Machian positivism, partly because he realized with a shock some of its consequences; consequences which the next generation of brilliant physicists, among them Bohr, Pauli, and Heisenberg, not only discovered but enthusiastically embraced: they became subjectivists. But Einstein’s withdrawal came too late. Physics had become a stronghold of subjectivist philosophy, and it has remained so ever since.
Behind this development there were, however, two serious problems, connected with quantum mechanics and the theory of time; and one problem which is, I think, not so serious, the subjectivist theory of entropy.
With the rise of quantum mechanics, most of the younger physicists became convinced that quantum mechanics, unlike statistical mechanics, was not a theory of ensembles, but of the mechanics of single fundamental particles. (After some wavering I too accepted this view.) On the other hand, they were also convinced that quantum mechanics, like statistical mechanics, was a probabilistic theory. As a mechanical theory of fundamental particles, it had an objective aspect. As a probabilistic theory, it had (or so they thought) a subjective aspect. Thus it was an utterly new type of fundamental theory, combining objective and subjective aspects. Such was its revolutionary character.
Einstein’s view diverged somewhat from this. For him, probabilistic theories such as statistical mechanics were extremely interesting and important and beautiful. (In his early days he had made some crucial contributions to them.) But they were neither fundamental physical theories, nor objective: they were, rather, subjectivist theories, theories which we have to introduce because of the fragmentary character of our knowledge. From this it follows that quantum mechanics, in spite of its excellence, is not a fundamental theory, but incomplete (because its statistical character shows that it works with incomplete knowledge), and that the objective or complete theory we must search for would not be a probabilistic but a deterministic theory.
It will be seen that the two positions have an element in common: both assume that a probabilistic or statistical theory somehow makes use of our subjective knowledge, or lack of knowledge.
This can be well understood if we consider that the only objectivist interpretation of probability discussed at that time (the late 1920s) was the frequency interpretation. (This had been developed in various versions by Venn, von Mises, Reichenbach; and later by myself.) Now frequency theorists hold that there are objective questions concerning mass phenomena, and corresponding objective answers. But they have to admit that whenever we speak of the probability of a single event, qua element of a mass phenomenon, the objectivity becomes problematic; so that it may well be asserted that with respect to single events, such as the emission of one photon, probabilities merely evaluate our ignorance. For the objective probability tells us only what happens on the average if this sort of event is repeated many times: about the single event itself the objective statistical probability says nothing.
It was here that subjectivism entered quantum mechanics, according to both Einstein’s view and to that of his opponents. And it was here that I tried to fight subjectivism by introducing the propensity interpretation of probability. This was not an ad hoc introduction. It was, rather, the result of a careful revision of the arguments underlying the frequency interpretation of probability.
The main idea was that propensities could be regarded as physical realities. They were measures of dispositions. Measurable physical dispositions (“potentials”) had been introduced into physics by the theory of fields. Thus there was a precedent here for regarding dispositions as physically real; and so the suggestion that we should regard propensities as physically real was not so very strange. It also left room, of course, for indeterminism.
To show the kind of problem of interpretation which the introduction of propensities was intended to solve, I will discuss a letter which Einstein wrote to Schrödinger.246 In this letter, Einstein refers to a well-known thought experiment which Schrödinger had published in 1935.247 Schrödinger had pointed out the possibility of arranging some radioactive material so as to trigger a bomb, with the help of a Geiger counter. The arrangement can be made in such a way that either the bomb explodes within a certain time interval or else the fuse is disconnected. Let the probability of an explosion equal 1/2. Schrödinger argued that if a cat is placed next to the bomb, the probability that it will be killed will also be 1/2. The whole arrangement might be described in terms of quantum mechanics, and in this description, there will be a superposition of two states of the cat—a live and a dead state. Thus the quantum-mechanical description—the ψ-function—does not describe anything real: for the real cat will be either alive or dead.
Einstein argues in his letter to Schrödinger that this means that quantum mechanics is subjective and incomplete:
If one tries to interpret the ψ-function as a complete description [of the real physical process described by it]… then this would mean that at the moment in question, the cat is neither alive nor blown to bits. Yet one condition or the other would be realized by an observation.
If one rejects this view [of the completeness of the ψ-function] then one has to assume that the ψ-function does not describe a real state of affairs, but the totality of our knowledge with respect to the state of affairs. This is Born’s interpretation which, it seems, is today accepted by most theoretical physicists.248
Upon acceptance of my propensity interpretation, however, this dilemma disappears, and quantum mechanics, that is the ψfunction, does describe a real state of affairs—a real disposition—though not a deterministic state of affairs. And although the fact that the state of affairs is not deterministic may well be said to indicate an incompleteness, this incompleteness may be not a fault of the theory—of the description—but a reflection of the indeterminateness of reality, of the state of affairs itself.
Schrödinger had always felt that |ψ ψ*| must describe something physically real, such as a real density. And he also was aware of the possibility249 that reality itself may be indeterminate. According to the propensity interpretation these intuitions were quite correct.
I will not discuss here any further the propensity theory of probability and the role it can play in clarifying quantum mechanics, because I have dealt with these matters fairly extensively elsewhere.250 I remember that the theory was not well received to start with, which neither surprised nor depressed me. Things have changed very much since then, and some of the same critics (and defenders of Bohr) who at first dismissed my theory contemptuously as incompatible with quantum mechanics now say that it is all old hat, and in fact identical with Bohr’s view.
I regarded myself as more than rewarded for almost forty years of heartsearching when I received a letter from B. L. van der Waerden, the mathematician and historian of quantum mechanics, about my paper of 1967, “Quantum Mechanics without ‘The Observer’ ”, in which he said that he fully agreed with all the thirteen theses of my paper, and also with my propensity interpretation of probability.251