Abstract By the beginning of the twentieth century most scientists were satisfied that their basic problems were solved, all that remained being to fill in a few details. The principles of mechanics had been well worked out, heat was understood to be a mode of motion, and light to have wave properties. Some difficulties did, of course, remain, and were referred to in a lecture given by Lord Kelvin at the Royal Institution on 27 April 1900:The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. I. The first ... involves the question, How could the earth move through an elastic solid, such as essentially is the aluminiferous ether? II. The second is the Maxwell– Boltzmann doctrine of partition of energy.In referring to the partition of energy Kelvin had in mind the problem of interpreting the specific heats of gases and of solids. Here the belief in the equipartition of energy, which Maxwell and Boltzmann seemed to have estab¬lished beyond any doubt, was leading to the wrong answers (Section 5.3). Another difficulty, not mentioned here by Kelvin, was the interpretation of the spectra of atoms and molecules. The fact that spectral lines appear only at particular wavelengths had never been given an adequate explanation; some of the ideas put forward were mentioned in Section 6.5, and they were obviously inadequate.
Abstract By the beginning of the twentieth century most scientists were satisfied that their basic problems were solved, all that remained being to fill in a few details. The principles of mechanics had been well worked out, heat was understood to be a mode of motion, and light to have wave properties. Some difficulties did, of course, remain, and were referred to in a lecture given by Lord Kelvin at the Royal Institution on 27 April 1900:The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. I. The first ... involves the question, How could the earth move through an elastic solid, such as essentially is the aluminiferous ether? II. The second is the Maxwell– Boltzmann doctrine of partition of energy.In referring to the partition of energy Kelvin had in mind the problem of interpreting the specific heats of gases and of solids. Here the belief in the equipartition of energy, which Maxwell and Boltzmann seemed to have estab¬lished beyond any doubt, was leading to the wrong answers (Section 5.3). Another difficulty, not mentioned here by Kelvin, was the interpretation of the spectra of atoms and molecules. The fact that spectral lines appear only at particular wavelengths had never been given an adequate explanation; some of the ideas put forward were mentioned in Section 6.5, and they were obviously inadequate.
The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. This chapter sees how quantum mechanics kicks in when matter and forces are described at small distances. How perspective is changed by introducing quantisation of energy. How quanta move through space-time in the form of granular waves. What the difficulties were and still are in interpreting quantum mechanics. In a classical ideal gas with massive particles, the energy of the particles is distributed according to a Maxwell-Boltzmann distribution. Equilibrium is established by the particles themselves: they collide with each other, exchanging energy and momentum in the process. Spectroscopic separation of wavelengths was achieved with specialised prisms and lenses made of halite, fluorite and sylvine, which transmit light efficiently up to far infrared wavelengths.
Abstract Toward the end of the nineteenth century Lord Kelvin, one of the best known and most respected physicists at that time, commented that “only two small clouds” remained on the horizon of knowledge in physics. In other words, there were, in Kelvin’s view, only two sources of confusion in our otherwise complete understanding of material reality. The two clouds were the results of the Michelson-Morley experiment, which failed to detect the existence of a hypothetical substance called the ether, and the inability of electromagnetic theory to predict the distribution of radiant energy at different frequencies emitted by an idealized “radiator” called the black body. These problems seemed so small that some established physicists were encouraging those contemplating graduate study in physics to select other fields of scientific study where there was more opportunity to make original contributions to knowledge. What Lord Kelvin could not have anticipated was that efforts to resolve these two anomalies would lead to relativity theory and quantum theory, or to what came to be called the new physics.
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.
Despite its intuitive appeal, classical mechanics is just as fraught with conceptual difficulties and problems of interpretation as its quantum replacement. The problems just happen to be rather less obvious, and so more easily overlooked or ignored. Quantum mechanics was born not only from the failure wrought by trying to extend classical physical principles into the microscopic world of atoms and molecules, but also from the failure of some of its most familiar and cherished concepts. To set the scene and prepare for what follows, this Prologue highlights some of the worst offenders, including: space and time; force and energy; the troublesome concept of mass; light waves and the ether; and atoms and the second law of thermodynamics.
The behavior of light and its interaction with matter is certainly one of the most interesting phenomena of physics. It has puzzled thinkers and scientists in ancient Greece (Archimedes) and through the Middle Ages, at least since the times of Robert Grosseteste (1168–1235), right up to the theories of Galileo Galilei and Isaac Newton. The classical electromagnetic theory of light (see Tab. 13.1) was beautifully established in the second half of the nineteenth century with the Maxwell equations. Quantum optics is nothing other than the quantum theory of light. It finds its roots in Planck's discovery (1900) that the assumption of energy quantization for a harmonic oscillator allowed us to solve the black-body problem (see Subsec. 1.5.1). The successive early steps that led to the quantization of the electromagnetic field include Einstein's explanation of the photoelectric effect with the introduction of the quantum of light (see Subsec. 1.2.1) and the interpretation of atomic spectra (see Subsec. 1.5.4). Quantum optics is usually not covered by conventional textbooks on quantum mechanics. We include its discussion here for two main reasons: first, because it is a fundamental and advanced application of the basic framework of quantum mechanics, and, second, because in the last 30 years quantum optics has played (and is still playing) a major role in the advancement and understanding of quantum mechanics.
The description of the physical and chemical properties of matter is a central issue that has occupied the minds of scientists since the age of the ancient Greeks. In their route to dissect matter down to what cannot be divided any further, they coined the term atom , the indivisible . Matter became then a collection of atoms. More than twenty centuries had to pass until the development of a more precise concept of atom, thanks, amongst others, to the systematic studies of Mendeleyev and the establishment in 1869 of the periodic table of the elements (Mendeleyev, 1869). The discovery of the electron in 1897 and the first modern model of the atomic structure by Sir Joseph Thomson were soon refined by his student, Sir Ernest Rutherford, who in 1910 showed that an atom was made of a positively charged small nucleus and a number of negatively charged electrons that neutralize the nuclear charge. Much in the spirit of planetary systems, and drawing from the analogy between gravitational and electrostatic interactions, scientists in the beginning of the twentieth century built an image of the atom that consisted of a number Z of electrons – of elementary charge – e – orbiting around the nucleus of charge Ze . A number of experimental observations, though, were incompatible with this idea of orbiting electrons. In particular, according to the successful electromagnetic theory, charged electrons in orbital (radially accelerated) motion should radiate energy, thus decelerating and eventually collapsing onto the nucleus. Clearly, such a picture would imply that matter is essentially unstable, in flagrant contradiction with our everyday experience of the very existence of matter.