The quantum revolution began in 1900 with a novel solution to what might seem to be one of the minor puzzles of theoretical physics, the problem of black-body radiation: the problem of the interaction of those two sorts of entity which figure in the dualist ontology of late classical physics.

The trouble for classical physics was that the facts about a black body's capacity to absorb and emit radiation defied thermodynamic explanation. The best that classical physics could do was to get the facts wrong and to generate paradox. So what was the problem of black-body radiation and why was it considered to be so puzzling?

First, what is a black body? Some bodies absorb and emit radiation more readily than others. A mirror is a poor absorber of radiation in the form of light, a piece of coal is a good one. A good absorber of radiation in the form of light is ‘blacker’ than one that is not.

One can extend the metaphor to radiation outside the visible range. Clearly, a body that is ‘blacker’ than another for one range of radiation frequencies need not be ‘blacker’ for all frequencies. A body's ‘blackness’ will, in general, depend on its chemical structure. But we can imagine a body whose blackness is maximal for all wavelengths. Such a body, if it exists, has a blackness which is independent of its chemical structure. We call it a black body. Two interesting questions are: first, are there bodies in Nature which are uniformly and maximally black for all wavelengths? and second, how does such a black body distribute the energy that it radiates as a function of the wavelength of the radiation it emits?

What do we expect of a quantum logical interpretation of quantum mechanics worthy of the name? In what sense should it resolve the paradoxes? What scope should it have? Should quantum logic, if it is successful in the micro world, replace classical logic in the macro world and in mathematics?

We distinguish between two kinds of quantum logical interpretations of quantum mechanics.

An example of the first kind, the activist kind, will do much more than simply rewrite the assertions that quantum mechanics makes about the quantum world in an unfamiliar notation - in the elementary language of quantum mechanics. It will offer a solution to the major puzzles of quantum mechanics. It will show that the paradoxes of quantum mechanics can be resolved if we do away with classical logic and replace it with quantum logic, at least in our descriptions of quantum phenomena. It may defend a form of quantum-mechanical realism, a sort of quantum logical particle view of quantum systems, protecting it from the paradoxes that classical logic would impose on it.

The second kind of quantum logical interpretation, the passive or quietist kind, is less ambitious. A quietist interpretation offers a solution to the paradoxes only in the following sense. It will assert that quantum mechanics, when it describes quantum phenomena in the elementary language, need not generate paradox, that the so-called paradoxes are not even formulable in quantum logic.

The concept of measurement plays both a central and a problematic role in quantum mechanics.

First of all, and unusually, the word ‘measurement’ figures in the fundamental axioms of quantum mechanics - in principle (3) of Chapter 2 for example - and in this quantum physics is quite unlike classical physics as a whole. For though a measurement made on a classical system naturally involves an interaction between the system and a measuring apparatus, there is nothing special according to classical physics about measurement interactions. Describing the measuring process is a straightforward problem of applied classical physics. The classical laws of motion do not break down during the measuring process.

For example, suppose you observe a classical particle using light bounced off it. In the classical account you can make the disturbance on the observed system as small as you like and, ‘in principle', you can observe the system with arbitrary accuracy. ‘In principle’ - a favorite expression of the philosopher of physics - means what it always means in physics. The contrast is with ‘in practice'. Of course, in practice there are all sorts of limitations on measurement. There are also some theoretical limitations, like those due to thermodynamics. But these are not the limitations imposed by the theory we are considering, namely classical mechanics. Such limitations as there are are imposed by some other theory. (The expression ‘in principle’ tends to be used when we are discussing the principles of a particular theory and, theoretically but not in practice, physics is a collection of disjoint theories.)

The simplest but deepest questions of the philosophy of quantum mechanics are these: Are quantum systems waves, or are they particles? Are they both or are they neither?

When light bounces an electron out of the surface of an alkali metal it behaves like a particle. Light carries momentum but also a punch. Just as there is no such thing as half a punch, so there is no such thing as half a quantum of light.

On the other hand, the shadow formed on a screen by an object has soft edges, edges which get softer as the object is moved away from the screen. Light exhibits the phenomena of diffraction and interference and so is wavelike.

This dual behaviour of light, and indeed of matter itself, is called wave-particle duality. The wave nature of a quantum system is reflected in wave mechanics which assigns a wave-function to the system. But the dual nature of light was noticed before Schrodinger developed the wave-mechanical formalism in 1926. In fact, it goes back at least as far as Einsteins explanation of the photoelectric effect in 1905.

Wave-particle duality is not something that arises within the quantum mechanical formalism. It is something which is expressed within it, and is something which is best discussed in terms of the paradoxes that quantum experiments force upon physics.

In fact, the simplest and most immediately disturbing of the quantummechanical paradoxes arise out of wave-particle duality. We take the two-slit experiment and the delayed-choice experiment as examples.

Metaphysics in the grand style, the product of a philosopher of genius working out from scratch and from his armchair a new conception of ultimate reality, has been out of fashion for a hundred years or so. This is not only because the results of this activity have so often been absurd. It is partly because other disciplines, such as physics, have developed remarkable and puzzling pictures of bits of the world, pictures that are at least as interesting as, at least as ‘deep’ as, and much more reliable than those of the armchair metaphysician.

Unlike armchair metaphysics, the theories of physics are the results of the efforts of many minds. They are also tested against the world in experiment and are continuously applied in technological devices and in weaponry. We take them seriously. Just why, and in precisely what respects, we should take them seriously is a problem for the philosophy of science. But we do, and if we were asked what is our best account of the way the world is, most of us would cite the fundamental theories of physics.

If armchair metaphysics is out of date, a new kind of metaphysics, scientific metaphysics, has come into fashion. The new metaphysician asks: what is there in the physical world, and what is true of what there is in the physical world? The answers are provided by the philosophy of physics, a subject whose metaphysical part sets out to tell us the way the world is, if physics is true.

Quantum logic is the logic of the high-level language in which we describe what is true and false of quantum systems. I use the term ‘highlevel’ in its computational sense. The language whose logic quantum logic is, is inexpressive. It has no machinery for describing probabilities, only truths and falsehoods and perhaps whatever is in between. Quantum logic conceals from its user the underlying details of the formalism of quantum mechanics, and the details (whatever they may be) of the underlying ‘machine’, the physical world. Quantum logic encourages a top-down view of the quantum world. Quantum mechanics, as done by the practising physicist, is bottom-up.

The program of feeding back quantum logic into our metalevel discussion of realism fails. Quantum logic does not licence quantummechanical realism. It cannot override or rewrite the bottom-up view. The program itself is odd in that quantum logic is most naturally thought of as expressing quantum-mechanical antirealism, just as quantum mechanics itself is most naturally interpreted antirealistically. Thus quantum logic is consonant with nonlocality, in the sense that it does not allow one to derive the Bell inequalities. The conditional in quantum logic nicely expresses the effect of ideal measurements on quantum systems.

My association with Erwin Schrödinger was not a close one, although I spent the summer of 1927 in Zürich, with the stated purpose (stated in my letters to the John Simon Guggenheim Memorial Foundation) of working under his supervision. In fact, I spent most of my time in my room, trying to solve the Schrödinger equation for a system consisting of two helium atoms. I did not have very much success, except that, as was mentioned later by John C. Slater, I formulated a determinant of the several spin-orbital functions of the individual electrons as a way of ensuring that the wave function is antisymmetric. This was a device that Slater made much use of in discussing the electronic structure of atoms and also of molecules in 1929 and 1931.

Walter Heitler and Fritz London were also in Zürich that summer, also with the plan of working with Schrödinger. They told me that they had talked with Schrödinger several times about their work, while walking through the woods. I did not have even that much contact with him, because he was working so hard on his own problems.

It might be possible to put theoretical physicists on a scale ranging from one extreme, those who deal with ideas, to the other, those who deal with mathematics. Wolfgang Pauli is an example of a theoretical physicist near the mathematics end.

The prehistory to Schrödinger's activity in unifed field theory

Unification is one of those long-standing quests of science. A superior point of view allows one to recognize connections and to uncover common roots. In the theory of general relativity Einstein succeeded in achieving a superior point of view in an especially impressive manner. By extension of the theory of special relativity he was able to comprehend gravitation in the geometrization of the space-time-continuum. After the success of this process of geometrization, the inclusion and unification of the electromagnetic field and possibly other fields could be considered to be a particularly important goal.

A few years after the discovery of general relativity, Weyl (1918) had already tried a fundamental extension of the framework of the theory in order to include electromagnetism as well. His attempt was based on the idea of gauge in variance–a concept which was to emerge 30 years later as a cornerstone of the modern theories of unification. Nevertheless, no agreement with observed facts could be reached by his concept of the path-dependence of a displaced length.

Whereas Weyl's generalization consisted in placing a connection of lengths beside the connection of directions given by the metric, Eddington (1923) followed a different course in considering the connection of directions as an a priori property of the manifold. In this case the metric becomes a deduced quantity.

Introduction

Erwin Schrödinger and those in his scientific generation – men like Werner Heisenberg and P. A. M. Dirac – were interested in physics because it provides us with the basic understanding of the laws of nature. Thus, even though their work has provided us with the basis of most of modern high technology, particularly through the emergence of the quantum theory of the solid state, their pursuit of physics was not motivated by this. In this sense we, in our generation, look upon Erwin Schrödinger's situation and that of his colleagues with a degree of envy.

In keeping with the tradition of Erwin Schrödinger, I have pleasure in presenting this overview of particle physics as in early 1986. I am sure this overview will be outdated by the time it sees print – but that is the fate of anything one may write in so fast moving a subject.

Physics is an incredibly rich discipline: it not only provides us with the basic understnading of the laws of nature, it is also the basis of most of modern high technology. This remark is relevant to our developing countries. A fine example of this synthesis of a basic understanding of nature with high technology is provided by liquid-crystal physics which was worked out at Bangalore by Prof. S. Chandrasekhar and his group. In this context, one may note that, because of this connection with high technology and materials’ exploitation, physics is the ‘science of wealth creation’ par excellence.

Introduction

Having the privilege of writing this paper as a grandson of Boltzmann I apologize for not being a historian of science. A manifestation of Boltzmann's influence on Schrödinger is Schrödinger's enthusiastic quotation of Boltzmann's line of thought: ‘His line of thought may be called my first love in science. No other has ever thus enraptured me or will ever do so again.’ (Schrödinger, 1929; reprinted in Schrödinger, 1957, p. XII.) Even though Schrödinger had no personal contact with Boltzmann, his scientific education at the University of Vienna was in the tradition of Boltzmann. His thesis advisor and director of the second Institute for Experimental Physics at the University of Vienna, Franz Serafin Exner, was an ardent admirer of Boltzmann and so was Boltzmann's successor on the chair for theoretical physics, Friedrich Hasenöhrl. Schrödinger paid the most impressive tribute to his teacher Hasenöhrl when he received the Nobel Prize in 1933. He avowed that Hasenöhrl might have stood in his place had he not been killed in the first world war (Schrödinger, 1935, p. 87).

Later one of Schrödinger's main fields of interest was the application of Boltzmann's statistical methods which he called ‘natural statistics’ to various problems. And it was not an accident that a paper in this field ‘On Einstein's Gas Theory’ triggered the idea of wave mechanics (Schrödinger, 1926, 1984).