As expected when I started out on this project, this has proved to be a complex and, at times, difficult story. After all, what was involved was tearing up the foundations of classical physics, which had been extraordinarily successful in explaining the macroscopic world about us, and replacing it by something radically different and non-intuitive in terms of our everyday experience. But the effort involved has been more than repaid by the very much deeper appreciation I have gained of the extraordinary works of the pioneers of quantum mechanics, both the theorists and the experimenters. If the brilliant theoretical researches of Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Schrödinger, Pauli, Dirac and many others form the central core of this story, it should be remembered that their researches were inspired by the equally brilliant achievements of experimental physics. Another huge bonus has been a deepened understanding of quantum mechanics itself – if only I had these insights more than 50 years ago when I first encountered the subject. There is a great deal more that could be said. I must reiterate that I have presented a somewhat streamlined version of the story in order to ensure that there is some continuous pathway, however tortuous, to the way in which the new understandings came about. For a full appreciation of the complexity of the story and the numerous blind alleys and diversions which took place, there is no substitute for in-depth absorption in Mehra and Rechenberg's magisterial exposition of the history of quantum theory.
As expected when I started out on this project, this has proved to be a complex and, at times, difficult story. After all, what was involved was tearing up the foundations of classical physics, which had been extraordinarily successful in explaining the macroscopic world about us, and replacing it by something radically different and non-intuitive in terms of our everyday experience. But the effort involved has been more than repaid by the very much deeper appreciation I have gained of the extraordinary works of the pioneers of quantum mechanics, both the theorists and the experimenters. If the brilliant theoretical researches of Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Schrödinger, Pauli, Dirac and many others form the central core of this story, it should be remembered that their researches were inspired by the equally brilliant achievements of experimental physics. Another huge bonus has been a deepened understanding of quantum mechanics itself – if only I had these insights more than 50 years ago when I first encountered the subject. There is a great deal more that could be said. I must reiterate that I have presented a somewhat streamlined version of the story in order to ensure that there is some continuous pathway, however tortuous, to the way in which the new understandings came about. For a full appreciation of the complexity of the story and the numerous blind alleys and diversions which took place, there is no substitute for in-depth absorption in Mehra and Rechenberg's magisterial exposition of the history of quantum theory.
Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at this level.
Now that we have reached the end of our brief tour through the early history of quantum theory, we need to stop and consider some important themes. From a historical point of view, a distinction can be drawn between ‘old quantum theory’ and the full quantum theory that we now use. Old quantum theory was in essence a patchwork cobbled together from classical physics with a few quantum ideas thrown in. e works of Planck, Einstein, Bohr, and Sommerfeld can be classed as old quantum theory. is is not meant to undermine the tremendous achievements that old quantum theory represents, but simply to underline its standing as a stage on the way to a fully formed quantum theory, which slowly emerged from the works of Heisenberg, Schrödinger, Born, and Dirac.
We have reached the goal I set myself when this journey began. From about 1927 onwards, the quantum theory in its modern guise for non-relativistic quantum mechanics was essentially complete, although there remained problems of interpretation which took a number of years to unravel – some of them are still hotly debated. But much of the apparatus was already in place and the subsequent developments changed completely the face of physics. Jammer (1989) summarises the achievement as follows: ‘Since 1927, the development of quantum mechanics and its applications to molecular physics, to the solid state of matter, to liquids and gases, to statistical mechanics, as well as to nuclear physics, demonstrated the overwhelming generality of its methods and results. In fact, never has a physical theory given a key to the explanation and calculation of such a heterogeneous group of phenomena and reached such a perfect agreement with experience as has quantum mechanics.’ As noted by Mehra and Rechenberg (2001), the 1930s also saw the beginning of the compartmentalisation of physics into separate quantum disciplines. Thus, during the 1930s,with the general acceptance and success of quantum mechanics, the quantum physicists began to specialise in disciplines such as atomic physics, molecular physics, solid state physics, including metal and semiconductor physics, condensed matter physics and low temperature physics, while at high energies, nuclear, particle and cosmic ray physics developed as disciplines in their own right. Whereas the pioneers of quantum mechanics regarded the whole province of quantum physics as their domain, the various branches of quantum physics became fragmented into these specialisms, not so different from those encountered in any physics department today.
In completing the story of spin, we have run far ahead of the continued development of the understanding of the matrix, operator and wave mechanical approaches to quantum mechanics. The reconciliation of these approaches was described in Chap. 15, but there remained the issue of the interpretation of the wavefunction and the deeper implications of the theory. The understanding came gradually with Born's interpretation of the wavefunction, Ehrenfest's demonstration of the equivalence of the classical and quantum pictures and Heisenberg's enunciation of the uncertainty principle. These led to what became known as the Copenhagen interpretation of quantum mechanics. At the same time, the formal mathematical foundations of the different approaches to quantum phenomena were set on a secure foundation thanks to the efforts of Hilbert and many others. These developments resulted in what may be referred to as the completion of quantum mechanics, in the sense that it laid the foundations for all the future development of physics at the atomic and subatomic level – some of these achievements are summarised in Chap. 18. Schrödinger's interpretation (1926) Schrödinger regarded wave mechanics as superior to the matrix mechanical approach to quantum physics, not only because it was based upon the well-known eigenfunction techniques of classical physics, but also because it was much more visualisable. His first attempt at interpreting the wavefunction appeared in the final Sect. 7 of the fourth part of his great series of papers (Schrödinger, 1926f) and was entitled On the physical significance of the field scalar.
One way of reading this book is as an epilogue-or (more precisely) as a denouement-to a book I wrote more than thirty years ago, which was called Quantum Mechanics and Experience.That earlier book was meant to do two things:1) To introduce its readers to the elementary nuts and bolts of the foundations of quantum mechanics-the idea of superposition, the basics of the standard mathematical formalism of quantum mechanics, the argument of Einstein and Podolsky and Rosen to the effect that that formalism, considered as a description of the fundamental real ity of the world, must be somehow incomplete, Bell's extension of that argument into a general and power ful theorem about locality, the elaboration (by figures like Erwin Schrödinger, and John von Neumann, and Eugene Wigner) of the quantum-mechanical mea surement prob lem, and vari ous proposals (theories of the spontaneous collapse of the wave-function, Bohmian mechanics, the so-called many-worlds interpretations of quantum mechanics, and so on) for solving it.2) To show how the above-mentioned proposals for solving the mea sure ment prob lem, taken together, amount to a
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.