The Copenhagen Interpretation of quantum mechanics has become the standard way of explaining the physical philosophical meaning of the mathematics of microscopic behavior. It developed from the thought of people who attended the Institute for Theoretical Physics of the University of Copenhagen during the 40 years that Niels Bohr directed it, from 1920 to 1962. Bohr took a large part in developing the Copenhagen Interpretation, he didn't escape all controversy over it (although the quote above is a bit of an exaggeration). Bohr did die before the experimental theoretical developments that have transposed the debate over the appropriateness adequacy of the Copenhagen Interpretation into a new key, he may well have been lucky to have escaped when he did. There is no authoritative codification of CI [the Copenhagen Interpretation], write T Gornitz C. E von Weizsacker of the Max Planck Institute in Starnberg, West Germany in' their formal presentation to the recent Loyola Conference on Mathematical Interpretational Problems in Relativistic Quantum Theory, and under the conditions of its origin there probably could not be one.... All prominent authors of the time who wrote on these questions, like Bohr, [Werner] Heisenberg, [Wolfgang] Pauli, J[ohn] v[on] Neumann on one side, [Albert] Einstein [Erwin] Schrodinger on the other, fell, so we feel, into some stammering when they tried to express their own positions. Nevertheless there is what might be called a Copenhagen attitude. It concentrates on observable phenomena, makes statistics probability central to its understanding, considers quantum mechanics primarily a theory of knowledge or information becomes a kind of physica negativa (analogous to a theologia negativa) in trying not to say too much about things that can't be seen or felt. For example, it doesn't much care whether the orbits of electrons in atoms are real or not and, in fact, tends to regard them as unreal. It appears in most textbooks as the standard way of looking at things.
The Copenhagen Interpretation of quantum mechanics has become the standard way of explaining the physical philosophical meaning of the mathematics of microscopic behavior. It developed from the thought of people who attended the Institute for Theoretical Physics of the University of Copenhagen during the 40 years that Niels Bohr directed it, from 1920 to 1962. Bohr took a large part in developing the Copenhagen Interpretation, he didn't escape all controversy over it (although the quote above is a bit of an exaggeration). Bohr did die before the experimental theoretical developments that have transposed the debate over the appropriateness adequacy of the Copenhagen Interpretation into a new key, he may well have been lucky to have escaped when he did. There is no authoritative codification of CI [the Copenhagen Interpretation], write T Gornitz C. E von Weizsacker of the Max Planck Institute in Starnberg, West Germany in' their formal presentation to the recent Loyola Conference on Mathematical Interpretational Problems in Relativistic Quantum Theory, and under the conditions of its origin there probably could not be one.... All prominent authors of the time who wrote on these questions, like Bohr, [Werner] Heisenberg, [Wolfgang] Pauli, J[ohn] v[on] Neumann on one side, [Albert] Einstein [Erwin] Schrodinger on the other, fell, so we feel, into some stammering when they tried to express their own positions. Nevertheless there is what might be called a Copenhagen attitude. It concentrates on observable phenomena, makes statistics probability central to its understanding, considers quantum mechanics primarily a theory of knowledge or information becomes a kind of physica negativa (analogous to a theologia negativa) in trying not to say too much about things that can't be seen or felt. For example, it doesn't much care whether the orbits of electrons in atoms are real or not and, in fact, tends to regard them as unreal. It appears in most textbooks as the standard way of looking at things.
Of all the many rival interpretations of quantum mechanics, none is more important or influential than the Copenhagen interpretation. Unfortunately, there is no one Copenhagen interpretation of quantum mechanics. If one uses the expression, and everyone does, one should not think of the Copenhagen interpretation as a single consistent interpretation of the theory. Philosophers of physics tend to use the expression ‘the Copenhagen interpretation of quantum mechanics’ as a label covering a variety of different interpretations all of which either originate with Niels Bohr or were invented by him, his colleagues and guests at the Institute for Theoretical Physics in Copenhagen beginning in the middle 1920s. Perhaps one should say that the Copenhagen interpretation in this diffuse sense goes back farther than this, back even before the rise of the new quantum mechanics. Heisenberg tells the story of a boat trip he, Bohr, and some friends took from Copenhagen to the island of Fyn around the time when the then new quantum mechanics was being developed. Bohr, ‘full of the new interpretation of quantum theory’, talked of ‘the difficulties of language, of the limitations of all our means of expressing ourselves’ and of how these limitations had been expressed ‘in the foundation of atomic theory in a mathematically lucid way’. ‘Finally,’ Heisenberg ends the story, ‘one of the friends remarked drily, “But, Niels, this is not really new, you said exactly the same ten years ago”
The dominance of the Copenhagen interpretation is the result of a historical accident (Cushing, 1994). At the Solvay conference in 1927, Louis de Broglie put forward the deterministic pilot wave theory, described later. Never slow to criticize, Pauli jumped up and demolished de Broglie’s proposal, and de Broglie was so discouraged by this that he did not develop his interpretation any further. The Copenhagen interpretation was then developed by Bohr, Heisenberg, Pauli and many others, as described in the previous chapter. It was strongly supported by von Neumann’s proof of the impossibility of hidden variables. Years later, in 1952, Bohm published a deterministic hidden variable theory, showing that there must be something wrong with von Neumann’s proof. The error was found by John Bell in 1966, as described in the last chapter, and he also showed how Pauli’s objections to de Broglie’s original idea can be answered. If this had been done at the conference in 1927, quantum mechanics could have been interpreted deterministically from the beginning. The essential mistake in the Copenhagen interpretation is to treat it as a complete account of the behaviour of each individual system. It is frequently claimed that it enables us to calculate, at least in principle, everything that can be measured. Thus Hooft (1997, p. 11) said that ‘The laws of quantum mechanics have been formulated very accurately. We know exactly how to compute anything we would like to know.’ Also Peierls (1997, p. 25) has said that quantum mechanics ‘had become a complete and consistent scheme capable of giving a unique answer to any questions relating to actual or possible observations’. Even if this were true, it would not imply that it is the final complete theory, for it is always possible that some new phenomenon might be found that cannot be calculated quantum-mechanically. However, it is not true: there are many phenomena such as the time of decay of a radioactive nucleus, or the direction a particle is scattered by a nucleus, that cannot be calculated, even in principle. Quantum mechanics is therefore an incomplete theory. We can only calculate the statistical properties of these systems, such as the half-life of a radioactive decay or the differential scattering cross-section that gives the probabilities that a particle is scattered through various angles. All measurements of quantum systems are of this statistical character. It might be thought that the possibility of making measurements on a single electron provides an exception to this. However, even in such cases the electron is continually bathed in a fluctuating background radiation from nearby atoms. Since this is variable, that electron is a member of an ensemble of electrons subject to different fluctuations. All these examples clearly demonstrate the statistical character of quantum mechanics. ‘I am rather firmly convinced’, Einstein (in Schilpp, 1949, pp. 666, 671) remarked, ‘that the essentially statistical character of contemporary quantum theory is solely to be ascribed to fact that this theory operates with an incomplete description of physical systems’. As a result, ‘the c-function is to be understood as the description not of a single system but of an ensemble of systems’. So, ‘if the statistical quantum theory does not pretend to describe the individual system completely, it appears unavoidable to look elsewhere for a complete description of the individual systems’. Thus ‘the difficulties of theoretical interpretation disappear, if one views the quantum-mechanical description as a description of an ensemble of systems’. If this is achieved, ‘the statistical theory would, within the framework of future physics, take an approximately analogous position to statistical mechanics within the framework of classical mechanics’. ‘Thus, essentially, nothing has changed since Galileo or Newton or Faraday concerning the status of the ‘‘observer’’ or our ‘‘consciousness’’ or of our ‘‘information’’ in physics’ (Popper, 1982, p. 46). Once this is accepted, the quantum paradoxes that plagued the Copenhagen interpretation are easily resolved, as described below. In any textbook of quantum mechanics problems such as the calculation of the energy levels of the hydrogen atom are solved as if that hydrogen atom is alone in the universe. As Feynman (1972) remarked, ‘when we solve a quantum-mechanical problem, what we really do is to divide the universe into two parts – the system in which we are interested and the rest of the universe. We then usually act as if the system in which we are interested comprised the whole universe.’ In fact, however, every hydrogen atom on which measurements are made is surrounded by other atoms and exposed to their radiations. Quantum mechanics somehow takes this into account and gives the average behaviour of an ensemble of hydrogen atoms. A more detailed theory takes these influences into account. One attempt to do this is stochastic electrodynamics, described in a later section.
Wonderful news from Copenhagen Heisenberg and Schrödinger invented mathematical formalisms that provided correct answers to all the various problems of (non-relativistic) quantum theory. It was Bohr who uncovered the underlying significance of the theory; in particular he showed how the profound conceptual difficulties encountered as the theory developed – the so-called wave–particle duality, the totally unclassical nature of the uncertainty principle – could be neutralised by a revision, or more accurately a generalisation, of our use of physical concepts. Such was the generally accepted view of things from soon after 1927, when Bohr first put forward his ideas on complementarity at an international meeting of physicists at Como, through the 1930s, when it was felt that Bohr destroyed Einstein's contrary opinions, and certainly up to the time of Bohr's death in 1962. Bohr's analysis is usually spoken of as the Copenhagen interpretation of quantum theory, though it is instructive to realise that such a term was frowned upon by those closest to Bohr, since it appears to suggest that the interpretation is just one among (conceivably) many. Let us examine, for example, the words of Léon Rosenfeld, Bohr's disciple and long-term collaborator, as expounded at a conference in 1957 [52]. Rosenfeld maintained that any idea of ‘interpreting a formalism’ was a ‘false problem’, that in a good theory, the ‘ordinary language (spiced with technical jargon for the sake of conciseness)’ in which it is described, is ‘ inseparably united … with whatever mathematical apparatus is necessary’, that ‘we are here not faced with a matter of choice between two possible languages or two possible interpretations, but with a rational language intimately connected with the formalism and adapted to it, on the one hand, and with rather wild, metaphysical speculations … on the other’.
In this paper, I try to explain the philosophical problems that Niels Bohr felt had been exposed by the discovery of the "quantum of action," and by the emergence of the quantum theory that arose in large part as a result of his efforts. I won't have space to make the case adequately here, but my own view is that we have not yet fully digested the message brought to us by Bohr's "Copenhagen Interpretation" of Quantum Mechanics, and I suspect that it will finally prove to be every bit as revolutionary as Bohr thought it was.
The founding fathers of quantum mechanics had already perceived the essence of the difficulties of quantum mechanics; today, after almost a century, the discussions are still lively and, if some very interesting new aspects have emerged, at a deeper level the questions have not changed so much. What is more recent, nevertheless, is a general change of attitude among physicists: until about 1970 or 1980, most physicists thought that the essential questions had been settled, and that “Bohr was right and proved his opponents to be wrong”. This was probably a consequence of the famous discussions between Bohr, Einstein, Schrödinger, Heisenberg, Pauli, de Broglie, and others (in particular at the Solvay meetings [1–3], where Bohr's point of view had successfully resisted Einstein's extremely clever attacks). The majority of physicists did not know the details of the arguments. They nevertheless thought that the standard “Copenhagen interpretation” had clearly emerged from the infancy of quantum mechanics as the only sensible attitude for good scientists. This interpretation includes the idea that modern physics must contain indeterminacy as an essential ingredient: it is fundamentally impossible to predict the outcome of single microscopical events; it is impossible to go beyond the formalism of the wave function (or its generalization, the state vector ∣ψ) and complete it.
At the close of the nineteenth century, we stood on the threshold of one of the greatest periods of science, in which the entire world and understanding of science would be shaken to the core and greatly modified. This explosion of knowledge led ultimately to that same information revolution that we live in today. Planck and Einstein showed that light was not continuous but made of small corpuscles that today we call photons. Einstein changed the understanding of mechanics with his theory of relativity: airplanes became conceivable; radio and television blossomed; and the microelectronics industry, which drives most of modern technology, came into being. New areas of science were greatly expanded and developed, and one of these was quantum mechanics, which is the story to be told here. Yet, the development of quantum mechanics and the leadership of Niels Bohr have distorted the understanding of quantum mechanics in a strange way. There are some who would say that Bohr set back the real understanding of quantum mechanics by half a century. I believe they underestimate his role, and it may be something more like a full century. Whether we call it the Copenhagen interpretation, or the Copenhagen orthodoxy, it is the how for the continuing mysticism provided by Mach that is still remaining in quantum mechanics. It is not the why. Why it perseveres and why it was forced on the field in the first place is an important perception to be studied. In this book, I want to trace the development of quantum mechanics and try to uncover the why.