At least three authors have proposed the concept of light as a traveling series of ‘matter waves.’ Such a concept does not require an ‘aether’ medium as does the more prevalent concept of light, if behaving as a wave, doing so analogous to other types of ‘disturbance waves,” such as sound or water. One author’s concept is examined mathematically for plausibility and, when found to be so, extended qualitatively to incorporate that of the other authors’ to at least what is hoped may be viewed as a reasonable extent.
At least three authors have proposed the concept of light as a traveling series of ‘matter waves.’ Such a concept does not require an ‘aether’ medium as does the more prevalent concept of light, if behaving as a wave, doing so analogous to other types of ‘disturbance waves,” such as sound or water. One author’s concept is examined mathematically for plausibility and, when found to be so, extended qualitatively to incorporate that of the other authors’ to at least what is hoped may be viewed as a reasonable extent.
For all practical purposes the wave theory of light is a certainty. This is the story of a radical change in humans' concept of light. In 1896 most physicists were convinced that light consisted of wave disturbances in a medium, the electromagnetic aether. The energy transported in radiation was thought to propagate spherically outward from its source and to spread out over successively larger volumes in space. Thirty years later, a remarkably different concept of light prevailed. Physicists then took seriously the evidence collected over the preceding two decades showing that the energy of radiation does not spread in space. Under certain conditions, light behaves like a stream of particles. Our subject is more than the story of a shift from one theoretical explanation of radiation to another. This reconsideration of the nature of light was a significant event in our scientific understanding of the world. To resolve the paradox that faced them, physicists rejected the venerable Platonic dictum that the microscopic realm recapitulates the macroscopic; that laws generalized from the behavior of objects in the perceivable world may be applied to the imperceivable one. By 1927 physicists had assigned to all forms of radiation a curious amalgam of wave and particle behavior. Waves spread energy over larger and larger volumes of space; particles do not. Reconciliation of these conflicting properties was possible only through appeal to an ontology that transcended mechanical incompatibility. Nature was declared to be only imperfectly rationalizable in terms of human experience with macroscopic interactions. The programmatic goal formulated in the seventeenth century to reduce all physical phenomena to consistent mechanical representations was here recognized to be unattainable.
Waves of light Light behaves like a wave. In the laboratory, we can measure the vibrations that are set up in matter when a light wave comes by. We can also observe the peculiar light-and-dark patterns that occur when two light rays are made to act simultaneously, an unmistakable sign of wave behaviour. Let us make a small excursion into wave motion. Throughout this exposition, you are encouraged to experiment as much as possible with waves (preferably real ones, or at least those in the diagrams), to become familiar with their fascinating behaviour. Water waves in the bathtub, or those seen on open water from a high tower or an airplane, are especially instructive. Waves are periodic; if you pick a point in space (e.g. the surface of a pond at the point where a reed pokes through) and you watch the motion of the wave carrier (the water that bobs up and down), then you will see that the state of motion of the carrier repeats itself at regular intervals of time. This interval is the period of the wave. A free wave has a velocity, i.e. a direction and a speed. At a given point, a wave alternates periodically between a certain maximum and a minimum.
Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by these aether waves. Times have changed. Light corpuscles are now known as photons, and the majority of physicists have dispensed with the notion of aether. Nevertheless, certain features of Newton's metaphor live on in one particular version of quantum mechanics. According to pilot wave theory, first proposed by de Broglie (2) and later developed by Bohm (3) with Einstein's encouragement, microscopic elements such as photons and electrons consist of both particle and wave, the former being guided by the latter. Although this physical picture has not been widely accepted, it has had some notable proponents, including Bell (4). Its principal appeal is that it restores realism and determinism to quantum mechanics, its weakness that the physical nature of the guiding wave field remains unclear. At the time that pilot wave theory was developed and then overtaken by the Copenhagen interpretation as the standard view of quantum mechanics, there was no macroscopic pilot wave analog to draw upon. Now there is.
This paper further explores intuitions we highlighted in previous papers already: 1. The concept of the matter-wave traveling through the vacuum, an atomic lattice or any medium can be equated to the concept of an electric or electromagnetic signal traveling through the same medium. 2. There is no need to model the matter-wave as a wave packet: a single wave – with a precise frequency and a precise wavelength – will do. 3. If we do want to model the matter-wave as a wave packet rather than a single wave with a precisely defined frequency and wavelength, then the uncertainty in such wave packet reflects our own limited knowledge about the momentum and/or the velocity of the particle that we think we are representing. The uncertainty is, therefore, not inherent to Nature, but to our limited knowledge about the initial conditions. 4. The fact that such wave packets usually dissipate very rapidly, reflects that even our limited knowledge about initial conditions tends to become equally rapidly irrelevant. Indeed, as Feynman puts it, “the tiniest irregularities” tend to get magnified very quickly at the micro-scale. In short, as Hendrik Antoon Lorentz noted a few months before his demise, there is no reason whatsoever “to elevate indeterminism to a philosophical principle.”
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.
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.