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.
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.
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.
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.
‘Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One’. These views were contained in a letter written by Albert Einstein to Max Born in December 1926. Though the following year would see the completion of work on the theoretical foundation of the modern physics of atoms and particles, Einstein was never to change his judgement and remained firmly convinced that ‘this business […] contains some unreasonableness’. He was unwilling to sacrifice his own ideas as to the cognitive scope of science even in the face of the important results being achieved by the new theory. To the undeterministic findings of quantum mechanics he opposed his belief in the ‘possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability of their occurrence’. For this reason he chose to live with the isolation of his scepticism and dissent, ironically accepting the reputation as a obstinate heretic that he had won over the years among his colleagues, and worked to the end on his own research programme to develop a unified field theory of rigorously causal nature. As is generally known, Einstein carried on a strong scientific and philosophical dispute with the defenders of the so-called official interpretation of quantum mechanics.
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.
Forty years ago, twenty years after the discovery of the laser, physicists were developing laser cooling methods for ions trapped in electromagnetic fields.From the 1980s onwards, these techniques were refined and extended to atoms, thanks to the audacity and inventiveness of a generation of pioneering researchers.Actually, it was necessary to succeed simultaneously in trapping and cooling samples of atomic gases in a vacuum at a distance from any wall.Spectacular results followed and extraordinarily low temperatures were quickly reached, very close to absolute zero.The field of "cold atoms" was born, rewarded by successive Nobel prizes, first of which was awarded in 1997 to William D. Phillips, Steven Chu and Claude Cohen-Tannoudji, last in 2022 to Alain Aspect.Gaseous samples of a few thousand to a few billion atoms can be prepared at a few millionths of a degree above absolute zero, which means that the particles move at extremely low speed, of the order of centimetres per second.At these extreme temperatures, the behaviour of matter changes and its properties can only be described using quantum mechanics and the wave properties of particles.New physical phenomena have been discovered and innovations have followed the theoretical and experimental progress of the research.Initially imagined as a wonderful method for perfecting atomic physics, cold atoms have gradually proved to be powerful tools for research in cross-cutting fields of physics, such as condensed matter and even high-energy physics.These atoms are now referred to as 'quantum gases' at such low temperatures that their collective behaviour is modified by the laws of quantum mechanics.
Quantum Mechanics is an essential topic in today's physics curriculum at both the undergraduate and graduate levels. Quantum mechanics can explain the microscopic world with fantastic accuracy; the fruits from its insights have created technologies that have revolutionized the world. Computers, lasers, mobile telephones, optical communications are but a few examples. The language of quantum mechanics is now an accepted part of the language of physics and day-to-day usage of this language provides physicists with the intuition that is essential for achieving meaningful results. Nevertheless, most physicists acknowledge that, at least once in their scientific career, they have had difficulties understanding the foundations of quantum theory, perhaps even the impression that a really satisfactory and convincing formulation of the theory is still lacking. Numerous quantum mechanics textbooks are available for explaining quantum formalism and applying it to understand problems such as the properties of atoms, molecules, liquids, and solids; the interactions between matter and radiation; and more generally to understand the physical world that surrounds us. Other texts are available for elucidating the historical development of this discipline and describing the steps through which it went before quantum mechanics reached its modern formulation. In contrast, books are rare that review the conceptual difficulties of the theory and then provide a comprehensive overview of the various attempts to reformulate quantum mechanics in order to solve these difficulties. The present text by Franck Laloë does precisely this.