INTRODUCTION In his essay ‘Quantum Mechanics Without “the Observer”’ (in [20], 7–44), Popper criticizes the Copenhagen Interpretation and suggests construing the quantum theory as a ‘generalization of classical statistical mechanics’ ([20], 16). The uncertainty relations, he says, set ‘limits to the statistical dispersion … of the results of sequences of experiments’ ([20], 20) and not to what can be said about individual systems. Some strange features of orthodox microphysics are due either to a misinterpretation of probability, involving some ‘very simple mistakes’ ([20], 42); or else they are a straightforward consequence of the fact that the quantum theory is a statistical theory. For example, ‘the reduction of the wave packet … has nothing to do with quantum theory: it is a trivial feature of probability theory’ ([20], 37). The idea of probability that is presupposed in all these arguments, however, is Popper's propensity interpretation. Adopting this interpretation suffices for making clear what the quantum theory really is: a ‘generalization of classical statistical mechanics’ ([20], 16). This is Popper's position as I understand it. This position, it seems to me, is attractive enough as long as one does not carry the analysis too far. But it breaks down when confronted with all the facts which Bohr wanted to take into account. Altogether Popper's criticism and his alternative proposals once more reveal the strong points of the Copenhagen philosophy, and especially of the ideas of Niels Bohr. Today it is very difficult to find a satisfactory account of these ideas.
INTRODUCTION In his essay ‘Quantum Mechanics Without “the Observer”’ (in [20], 7–44), Popper criticizes the Copenhagen Interpretation and suggests construing the quantum theory as a ‘generalization of classical statistical mechanics’ ([20], 16). The uncertainty relations, he says, set ‘limits to the statistical dispersion … of the results of sequences of experiments’ ([20], 20) and not to what can be said about individual systems. Some strange features of orthodox microphysics are due either to a misinterpretation of probability, involving some ‘very simple mistakes’ ([20], 42); or else they are a straightforward consequence of the fact that the quantum theory is a statistical theory. For example, ‘the reduction of the wave packet … has nothing to do with quantum theory: it is a trivial feature of probability theory’ ([20], 37). The idea of probability that is presupposed in all these arguments, however, is Popper's propensity interpretation. Adopting this interpretation suffices for making clear what the quantum theory really is: a ‘generalization of classical statistical mechanics’ ([20], 16). This is Popper's position as I understand it. This position, it seems to me, is attractive enough as long as one does not carry the analysis too far. But it breaks down when confronted with all the facts which Bohr wanted to take into account. Altogether Popper's criticism and his alternative proposals once more reveal the strong points of the Copenhagen philosophy, and especially of the ideas of Niels Bohr. Today it is very difficult to find a satisfactory account of these ideas.
Popper's program in the foundations of quantum mechanics defending objectivity and realism developed out of a profound dissatisfaction with the point of view associated with Bohr, which is usually designated the Copenhagen interpretation. Here I will argue that while Popper's aim is a noble one, his program does not succeed on two counts: he does not succeed in showing that Bohr's philosophy must be rejected as a variety of subjectivism, and his alternative interpretation of indeterminacy rests on a highly questionable assumption according to which simultaneously precise conjugate parameters are possible. Nevertheless I like Popper's propensity interpretation of probability and think that the propensity idea deserves further research. Quanta 2012; 1: 33–57.
Introduction Although the mathematical structure of quantum mechanics was understood within a few years after it was invented, numerous quantum paradoxes still disturb ‘simple-minded’ physicists. Most of them, as ‘naïve realists’, would probably never take Bohr's own over-philosophical and over-complicated treatment of these paradoxes seriously if they realized the philosophical consequences of the Copenhagen interpretation. To make my meaning clearer, let me quote Bohr's answer to Professor Hoffding's question regarding the double-slit experiment [1]. Bohr was asked: ‘What can the electron be said to be in its travel from the point of entry to the point of detection?’ And he replied: ‘ To be ? To be ? What does it mean to be ?’ However, if one questions the existence of microscopic constituents of macroscopic bodies, then the next logical step would be to question the existence of the macroscopic bodies and even ourselves. Needless to say, very few (if any) of us, when making experiments or analyzing their results, address the question of what it means ‘to be’ every time. Even in the context of elementary particles, probably nobody doubts that the particles exist and somehow travel from the point of entry to the point of detection. Moreover, within the accuracy allowed by the uncertainty relation, these particles can be localized and described just as well as macroscopic ‘classical’ objects.
One of the various interpretations of quantum mechanics occupies a privileged position in the opinion of the majority of physicists. This is the Copenhagen view, which owes its fame and popularity not only to historical reasons but also to its simplicity and practical efficiency. As is well known, the Copenhagen outlook was elaborated collectively. Nevertheless, Niels Bohr's and W. Heisenberg's contributions should be singled out as particularly outstanding. This chapter describes two principles, which are in fact the two pillars on which Bohr's doctrine is built. These are: The working of measuring instruments must be accounted for in purely classical terms . Another one is quantum systems that should not even be thought of as possessing individual properties independently of the experimental arrangement. In the particular case of the pair of observables "position" and "momentum," the Heisenberg uncertainty relations can be considered as a generalization of the complementarity principle.
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.
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.
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.