FOR twenty years and more we have been hearing continually about the conflict between the corpuscular and the undulatory theories of light, and it is possible that for years to come we may be hearing about a similar contest between the wave-theory and the particle-theory of matter. Furthermore, there are intimations that if an adequate theory either of light or of matter ever is attained, it will involve conceptions of waves which in certain limiting cases approach to conceptions of particles. Already it is established that the appropriate way to attack the typical problems of the atom consists in setting up a wave-equation, and dealing with it in the same manner as one adopts to solve the typical problem of acoustics: how to determine the resonance-frequencies of a piece of elastic matter, such as a taut wire or a drumhead or a column of air in a tube. Therefore it seems opportune to restudy, with care and in detail, the great classical example of a wave-theory highly developed and widely successfulthe great theory of light dimly foreshadowed by Huygens, endowed with its essen tial attributes by Young and Fresnel and Kirchhoff and a host of their coevals, utilized in the design of a multitude of ingenious instruments, perfected by Maxwell and connected with the theory of electricity and magnetism, and serving to this day as the basis for the theory of quanta. So doing, we shall be reminded of many triumphs of the past century of physical research, discoveries which in their time were as exciting as new quantum phenomena in ours; we shall notice certain achievements themselves as recent as those of quanta, and perhaps not less impressive; we shall retrace the reasonings which led to certain conclusions which the quantum-theories, unable to do without them and yet incompetent to derive them, have taken bodily over from their forerunner; we shall reconsider the evidence which in the litigation of a century ago caused the verdict to be rendered in favour of the wave-theory over the particle-theory; and perhaps incidentally we shall be drilling ourselves to test the evidence lately submitted and still to be submitted in the appeal of that case, and in the hearing of that other which impends.
FOR twenty years and more we have been hearing continually about the conflict between the corpuscular and the undulatory theories of light, and it is possible that for years to come we may be hearing about a similar contest between the wave-theory and the particle-theory of matter. Furthermore, there are intimations that if an adequate theory either of light or of matter ever is attained, it will involve conceptions of waves which in certain limiting cases approach to conceptions of particles. Already it is established that the appropriate way to attack the typical problems of the atom consists in setting up a wave-equation, and dealing with it in the same manner as one adopts to solve the typical problem of acoustics: how to determine the resonance-frequencies of a piece of elastic matter, such as a taut wire or a drumhead or a column of air in a tube. Therefore it seems opportune to restudy, with care and in detail, the great classical example of a wave-theory highly developed and widely successfulthe great theory of light dimly foreshadowed by Huygens, endowed with its essen tial attributes by Young and Fresnel and Kirchhoff and a host of their coevals, utilized in the design of a multitude of ingenious instruments, perfected by Maxwell and connected with the theory of electricity and magnetism, and serving to this day as the basis for the theory of quanta. So doing, we shall be reminded of many triumphs of the past century of physical research, discoveries which in their time were as exciting as new quantum phenomena in ours; we shall notice certain achievements themselves as recent as those of quanta, and perhaps not less impressive; we shall retrace the reasonings which led to certain conclusions which the quantum-theories, unable to do without them and yet incompetent to derive them, have taken bodily over from their forerunner; we shall reconsider the evidence which in the litigation of a century ago caused the verdict to be rendered in favour of the wave-theory over the particle-theory; and perhaps incidentally we shall be drilling ourselves to test the evidence lately submitted and still to be submitted in the appeal of that case, and in the hearing of that other which impends.
In a period when a limited domain of physical phenomena is exciting wide fervent interest and commanding intensive study, and continues for years to monopolize the attention of many brilliant theorists, sometimes it is the fortune of an ingenious mind to express or interpret or picture the already-discovered laws in a new way which makes so greatly favourable an impression, that in a moment it sweeps its rivals from the field. The new theory may not lead to more or better agreements with experience than did its predecessors; it need not make predictions which they were incapable of making; its mathematical processes may be identical with theirs, the old symbols reappearing with new names in the old equations. Contrariwise it may be born well endowed with these advantages which normally decide the contest between old theories and new, yet owe its victory not to them at all. It triumphs because it seems natural or sensible or reasonable or elegant or beautiful-words said of a theory which fulfils some deep-seated demand or evades some deep-rooted prejudice in the minds of its judges. Later its vogue may pass, not through the disclosure of any intrinsic defect, but because the physicists of the rising generation do not share the prejudices and the predilections of those who first applauded it. The kinetic theory of gases was welcomed by a generation which wished to believe in atoms; the electromagnetic theory by people prejudiced against the notion of action at a distance; the quantum-theory has always had to do battle against those who yearn for continuity in their images of Nature, and the theory to which these pages are devoted has captivated the world of physics in a few brief months because it seems to promise a fulfilment of that long-baffled and insuppressible desire.
Abstract It will probably be agreed that among all the recent developments of the quantum theory, one of the least satisfactory is the theory of radiation. The present paper is intended as a preliminary to a new line of attack on the subject. It was begun some time ago, but owing to lack of success in carrying it to a conclusion, its publication has been much delayed. In the meantime other papers have appeared, which in some respects follow the same train of thought. The authors of these works have carried their methods further in some directions than I have attempted, but there is still perhaps room for the discussion of a number of questions from the rather different point of view adopted here. 1. The main principle of the present work is the idea that, since matter and light both possess the dual characters of particle and wave, a similar mathematical treatment ought to be applied to both, and that this has not yet bee done as fully as should be possible. Whereas we have a fairly complete calculus for dealing with the behaviour of any number of electrons or atoms, for photons the existing processes are much less satisfactory. The central difficulty, which makes it hard to apply the ordinary methods of wave mechanics to light, is the fact that (at least according to our present ideas) photons can be created and annihilated, and to represent this in a wave system we have to be able to think of a medium suddenly coming into existence and then going out again, when the light that it was carrying is absorbed. Such behaviour is a grave difficulty in the way of allowing us to think of the photon as a wave, and tends to make us think with more favour of its particle aspect, until we recall that after all it is quite unlike any known particle to come into existence and later to disappear without trace. The theories at present current, such as that of Heisenberg and Pauli, avoid these difficulties because they are mainly formal generalisations of the classical theory; this frees them from the above difficulties, but they pay for it in being highly abstract, and, as it has turned out, rather unsuccessful.
Modern attempts to understand light go back to Newton who considered light to be particles, the so called corpuscular theory, and the other school of Huygens, Young and others. Huygens and Young viewpoint emphasised the wave property. This difference of opinions persisted for close to two centuries till Maxwell theory solidly established light as a wave phenomenon associated with Electromagnetism. A serious schism so to speak was introduced into the theory of light with the understanding of "Light gas", the so called Black Body radiation. Einstein's photon hypothesis and Bose's successful derivation of the Planck spectrum put the corpuscular theory back in place, while classical description continues to be used as well. One may then wonder if this being a classical limit may have to be corrected when dealing with quantum phenomena. To most people's surprise, the classical description was in fact a subset of the full quantum description, and the classical states of light could be shown to be subsumed within the fully quantum description without having to take the limit of Planck's constant h going to zero. This was the resolution provided by E. C. G. Sudarshan's Diagonal representation as the most general formalism for dealing with light.
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.
Have you ever tried to define light? If so, your definition is probably related to vision, the ability to see things. The Merriam-Webster English dictionary defines light as “something that makes vision possible”. However, the definition of the “nature of light” is a complex term already discussed by philosophers of Ancient Greece. In the 17th century, the debate on the matter focused on whether light was a particle or a wave, based on the different properties of light that had been gradually discovered over time. Isaac Newton (1642−1727) was a defender of the corpuscular theory of light, which considered light to be formed by particles, i.e., small pieces of matter, like dust or grains of sand. He was the author of Opticks (1706), the front cover of which appears in Fig. 1.1. Christian Huygens (1629–1695), on the other hand, supported the theory that light is a wave. These are two completely different definitions of the same physical concept. A range of experiments were developed to attempt to clarify this dilemma, but it was only until 1900 when Max Planck (1858-1947) introduced the basis of a theory that would go on to revolutionize scientific thinking, marking the beginning of modern physics: quantum theory. Developed during the 20th century thanks to advances made by scientists such as Niels Bohr, Born, Heisenberg, Schrödinger, Pauli, Dirac, Einstein or de Broglie, quantum theory clarified that light is neither a particle nor a wave, but that it has a dual nature: it behaves like a wave as it spreads but like a particle in its interactions with matter. In this book, we will specify where necessary whether light behaves as a particle or as a wave, although in most cases we refer to rays of light, which always represent the direction of propagation of light.
THE conceptual problems raised by the discovery of quantum effects have not been fully resolved after half a century. Part of the reason for this is undoubtedly to be found in the mutual ignorance which prevails between physicists and philosophers. In his book Heisenberg brings together a philosophically inclined temperament with an unrivalled knowledge of physics. The result is a book of very great interest, however much one might disagree with his conclusions. The collection of essays of which the other book is made up is intended to bring crucial conceptual problems in physics especially to the notice of philosophers. The design and intention of the collection is admirable for this is the proper way to overcome the departmentalization of interest that has left the deep conceptual problems still unresolved. Men like Heisenberg who combine philosophical temperament with scientic knowledge of great distinction are rare, and yet the difficulties can only be cleared up by the application of philosophical techniques of analysis to problems which are an intimate and difficult part of physics. A great deal of the interest of Heisenberg's book lies in the very comprehensive account he gives of the origin and growth of the Copenhagen school, and the way the new phenomena forced a largely unwelcome picture of nature upon Bohr and his friends. The most important chapter from a philosophical point of view is that in which Heisenberg defends this interpretation against the attacks to which it has been subjected. The essence of his argument for the interpretation can be summed up in two propositions. (i) The Copenhagen interpretation of physical theory, which depends upon the acceptance of the so-called Principle of Complementarity, is an inevitable and final interpretation. The reason for this is that there are only two possible general models for understanding given physical phenomena; a particle model or a wave model. These are exhaustive and exclusive because the former depends upon discontinuous and the latter upon continuous (using substance here in the traditional philosophical sense). If we find, as we do, that the two fundamental constituents of the universe, matter and radiation, each exhibit two classes of phenomena, one explainable only on a particle model and one on a wave model, then we are compelled to adopt a complementarity hypothesis and give up the idea of finding a single and uniform model for the understanding of phenomena. There are only two kinds of models; they are mutually exclusive; both are required; hence we either despair before an insoluble problem or adopt the Copenhagen interpretation. (2) Any serious criticism of this interpretation must offer an alternative