In the last chapter, we considered the possibility that an object such as the pointer of an apparatus designed to measure H/V polarisation (see Figure 7.1) might in principle be forbidden from being in a quantum superposition if it was large enough. A microscopic system, such as a photon polarised at 45° to the horizontal, would then collapse into an h or a ν state as a consequence of such a measurement. To test this idea, we considered how we might detect a macroscopic object in such a superposition and we found that this was very difficult to do. The oscillating pointer of Figure 7.1 is very sensitive to random thermal disturbances and as a result is almost certainly going to swing in one direction or the other, rather than being in a superposition of both. Macroscopic superpositions have indeed been observed in SQUIDs (see the last section in Chapter 7), but only after great care has been taken to eliminate similar thermal effects.

In the context of the last chapter, the randomness associated with thermal motion was considered as a nuisance to be eliminated, but might it instead be just what we are looking for? Perhaps it is not that thermal effects prevent us observing quantum superpositions, but rather that such states are impossible in principle when thermal disturbances are present. This could provide another way out of the measurement problem.

Irreversibility, strengthened by the idea of strong mixing, has been discussed in the last two chapters. We reached the conclusion that, once such processes have been involved in a quantum measurement, it is in practice impossible to perform an interference experiment that would demonstrate the continued existence of a superposition. It is then ‘safe’ to assume that the system has ‘really’ collapsed into a state corresponding to one of the possible measurement outcomes. Does this mean that the measurement problem has been solved? Clearly it has for all practical purposes, as has been pointed out several times in earlier chapters. But it may still not be sufficient to provide a completely satisfactory solution in principle: in particular, we note that we have still not properly addressed the question of actualisation outlined at the end of the first section of Chapter 8.

In the present chapter we discuss an interpretation of quantum physics that was developed during the last 15 or so years of the twentieth century and is based on the idea of describing quantum processes in terms of ‘consistent histories’. As we shall see, the resulting theory has much in common with the Copenhagen interpretation discussed in Chapter 4 and when applied to measurement it connects with the viewpoint, discussed in the last chapter, in which irreversible processes are to be taken as the primary reality.

We begin with a short discussion of the meaning and purpose of a scientific theory.

Quantum physics is the theory that underlies nearly all our current understanding of the physical universe. Since its invention some sixty years ago the scope of quantum theory has expanded to the point where the behaviour of subatomic particles, the properties of the atomic nucleus and the structure and properties of molecules and solids are all successfully described in quantum terms. Yet, ever since its beginning, quantum theory has been haunted by conceptual and philosophical problems which have made it hard to understand and difficult to accept.

As a student of physics some twenty-five years ago, one of the prime fascinations of the subject to me was the great conceptual leap quantum physics required us to make from our conventional ways of thinking about the physical world. As students we puzzled over this, encouraged to some extent by our teachers who were nevertheless more concerned to train us how to apply quantum ideas to the understanding of physical phenomena. At that time it was difficult to find books on the conceptual aspects of the subject – or at least any that discussed the problems in a reasonably accessible way. Some twenty years later when I had the opportunity of teaching quantum mechanics to undergraduate students, I tried to include some references to the conceptual aspects of the subject and, although there was by then a quite extensive literature, much of this was still rather technical and difficult for the non-specialist.

‘God’, said Albert Einstein, ‘does not play dice’. This famous remark by the author of the theory of relativity was not intended as an analysis of the recreational habits of a supreme being but expressed his reaction to the new scientific ideas, developed in the first quarter of the twentieth century, which are now known as quantum physics. Before we can fully appreciate why one of the greatest scientists of modern times should have been led to make such a comment, we must first try to understand the context of scientific and philosophical thought that had become established by the end of the nineteenth century and what it was about the ‘new physics’ that presented such a radical challenge to this consensus.

What is often thought of as the modern scientific age began in the sixteenth century, when Nicholas Copernicus proposed that the motion of the stars and planets should be described on the assumption that it is the sun, rather than the earth, which is the centre of the solar system. The opposition, not to say persecution, that this idea encountered from the establishment of that time is well known, but this was unable to prevent a revolution in thinking whose influence has continued to the present day. From that time on, the accepted test of scientific truth has increasingly been observation and experiment rather than religious or philosophical dogma.

The 1935 paper by Einstein, Podolski and Rosen represented the culmination of a long debate that had begun soon after quantum theory was developed in the 1920s. One of the main protagonists in this discussion was Niels Bohr, a Danish physicist who worked in Copenhagen until, like so many other European scientists of his time, he became a refugee in the face of the German invasion during the Second World War. As we shall see, Bohr's views differed strongly from those of Einstein and his co-workers on a number of fundamental issues, but it was his approach to the fundamental problems of quantum physics that eventually gained general, though not universal, acceptance. Because much of Bohr's work was done in that city, his ideas and those developed from them have become known as the ‘Copenhagen interpretation’. In this chapter we shall discuss the main ideas of this approach. We shall try to appreciate its strengths as well as attempting to understand why some believe that there are important questions left unanswered.

When Einstein said that ‘God does not play dice’, Bohr is said to have replied ‘Don't tell God what to do!’ The historical accuracy of this exchange may be in doubt, but it encapsulates the differences in approach of the two men. Whereas Einstein approached quantum physics with doubts, and sought to reveal its incompleteness by demonstrating its lack of consistency with our everyday ways of thinking about the physical universe, Bohr's approach was to accept the quantum ideas and to explore their consequences for our everyday ways of thinking.

My aims in preparing this second edition have been to simplify and clarify the discussion, wherever this could be done without diluting the content, and to update the text in the light of developments during the last 17 years. The discussion of non-locality and particularly the Bell inequalities in Chapter 3 is an example of both of these. The proof of Bell's theorem has been considerably simplified, without, I believe, damaging its validity, and reference is made to a number of important experiments performed during the last decade of the twentieth century. I am grateful to Lev Vaidman for drawing my attention to the unfairness of some of my criticisms of the ‘many worlds’ interpretation, and to him and Simon Saunders for their attempts to lead me to an understanding of how the problem of probabilities is addressed in this context. Chapter 6 has been largely rewritten in the light of these, but I am sure that neither of the above will wholeheartedly agree with my conclusions.

Chapter 7 has been revised to include an account of the influential spontaneous-collapse model developed by G. C. Ghiradi, A. Rimini and T. Weber. Significant recent experimental work in this area is also reviewed. There has been considerable progress on the understanding of irreversibility, which is discussed in Chapters 8, 9 and 10. Chapter 9, which emphasised ideas current in the 1980s, has been left largely alone, but the new Chapter 10 deals with developments since then.

The last two chapters have described two extreme views of the quantum measurement problem. On the one hand it was suggested that the laws of quantum physics are valid for all physical systems, but break down in the assumed non-physical conscious mind. On the other hand the many-worlds approach assumes that the laws of physics apply universally and that a branching of the universe occurs at every measurement or measurement-like event. However, although in one sense these represent opposite extremes, what both approaches have in common is a desire to preserve quantum theory as the one fundamental universal theory of the physical universe, able to explain equally well the properties of atoms and subatomic particles on the one hand and detectors, counters and cats on the other. In this chapter we explore an alternative possibility, that quantum theory may have to be modified before it can explain the behaviour of large-scale macroscopic objects as well as microscopic systems. We will require that any such modification preserves the principle of weak reductionism discussed towards the end of Chapter 5.

The first point to be made is that the problems we have been discussing seem to make very little difference in practice. As we emphasised in Chapter 1, quantum physics has been probably the most successful theory of modern science. Wherever it can be tested, be it in the exotic behaviour of fundamental particles or the operation of the silicon chip, quantum predictions have always been in complete agreement with experimental results.

Albert Einstein's comment that ‘God does not play dice’ sums up the way many people react when they first encounter the ideas discussed in the previous chapters. How can it be that some future events are not completely determined by the way things are at present? How can a cause have two or more possible effects? If the choice of future events is not determined by natural laws does it mean that some supernatural force (God?) is involved wherever a quantum event occurs? Questions of this kind trouble many students of physics, though most get used to the conceptual problems, say ‘Nature is just like that’ and apply the ideas of quantum physics to their study or research without worrying about their fundamental truth or falsity. Some, however, never get used to the, at least apparent, contradictions. Others believe that the fundamental processes underlying the basic physics of the universe must be describable in deterministic, or at least realistic, terms and are therefore attracted by hidden-variable theories. Einstein was one of those. He stood out obstinately against the growing consensus of opinion in the 1920s and 30s that was prepared to accept indeterminism and the lack of objective realism as a price to be paid for a theory that was proving so successful in a wide variety of practical situations. Ironically, however, Einstein's greatest contribution to the field was not some subtle explanation of the underlying structure of quantum physics but the exposure of yet another surprising consequence of quantum theory.

A completely different interpretation of the measurement problem, one which many professional scientists have found attractive if only because of its mathematical elegance, was first suggested by Hugh Everett III in 1957 and is known variously as the ‘relative state’, ‘many-worlds’ or ‘branching-universe’ interpretation. This viewpoint gives no special role to the conscious mind and to this extent the theory is completely objective, but we shall see that many of its other consequences are in their own way just as revolutionary as those discussed in the previous chapter.

The essence of the many-worlds interpretation can be illustrated by again considering the example of the 45° polarised photon approaching the H/V detector. Remember what we demonstrated in Chapters 2 and 4: from the wave point of view a 45° polarised light wave is equivalent to a superposition of a horizontally polarised wave and a vertically polarised wave. If we were able to think purely in terms of waves, the effect of the H/V polariser on the 45° polarised wave would be simply to split the wave into these two components. These would then travel through the H and V channels respectively, half the original intensity being detected in each. Photons, however, cannot be split but can be considered to be in a superposition state until a measurement ‘collapses’ the system into one or other of its possible outcomes. Up to now, we have argued that collapse must inevitably happen somewhere in the measurement chain – even if only when the information reaches a conscious mind.

In this chapter we ask if there is some aspect of the nature of the thermodynamic changes that occur in measuring processes that could clearly distinguish them from the kind of process for which reversibility is a possibility and to which pure quantum theory can be applied. This idea has been suggested on a number of occasions, and was developed in the 1980s by Ilya Prigogine, who won a Nobel prize in 1977 for his theoretical work in the field of irreversible chemical thermodynamics. The starting point of the approach by Prigogine and his co-workers is a re-examination of the validity of the ergodic principle, which leads to the idea of the Poincaré recurrence. We made the point in the last chapter that, in the simple case of a single particle confined to a rectangle, unless the starting angle has a special value the particle trajectory will fill the whole rectangle and the particle will sooner or later revisit a state that is arbitrarily close to its initial state. By this we meant that, although the initial and final states cannot in general be precisely identical, we can make the difference between the initial and final positions and velocities as small as we like by waiting long enough. The implicit assumption is that the future behaviour of the system will not be significantly affected by this arbitrarily small change in state; its behaviour after the recurrence will then be practically the same as its behaviour was in the first place.

The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation. In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.

Now that we have completed our survey of the conceptual problems of quantum physics, what are we to make of it all? One thing that should be clear is that there is considerable scope for us all to have opinions and there is a disappointing lack of practicable experimental tests to confirm or falsify our ideas. Because of this, I intend to drop the use of the conventional scientific ‘we’ in this chapter and to use the first person singular pronoun wherever I am stating an opinion rather than describing an objective fact or a widely accepted scientific idea. This is not to say that everything in the earlier chapters has been free of personal bias, but I have tried to maintain a greater basis of objectivity there than will be appropriate from now on.

I first want to refer briefly to a way of thinking about philosophical problems known as ‘positivism’. Encapsulated in Wittgenstein's phrase ‘of what we cannot speak thereof should we be silent’, positivism asserts that questions that are incapable of verification are ‘non-questions’, which it is meaningless to try to answer. Thus the famous, if apocryphal, debate between mediaeval scholars about how many angels can dance on the point of a pin has no content because angels can never be observed or measured so no direct test of any conclusion we might reach about them is ever possible. Opinions about such unobservable phenomena are therefore a matter of choice rather than logical necessity.

Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels.

However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.