A group of electrons that traverses a sufficiently small aperture will exhibit diffraction effects. It is not entirely surprising that the earliest reaffirmation of the dualism inherent in radiation came neither from Britain nor Germany. There the issues had been recognized, discussed, and dismissed over the preceding twenty years. And American research traditions were largely derivative of German and British models; Duane and Millikan had both studied under Planck, and Richardson did research with Thomson in Cambridge. It took an outsider to these traditions to raise the issues in a way that began to convince others. That process began in France. Maurice and Louis de Broglie were, by any standards, unusual physicists. Amateurs in an age of professionals, possessing a confidence born of noble status, working on experiments that had only the meagerest precedent in their homeland, they were not as firmly bound by the predispositions that prevented physicists of other nations from directly assessing the spatially localized lightquantum. Their conversion was real. Maurice had once been convinced that x-rays and γ-rays fit neatly into the electromagnetic spectrum. In his discussion, La nature des rayons de Röntgen in 1915, there was no thought that x-rays might be anything other than periodic waves. As late as May 1920, he spoke freely of x-ray “wavelengths” and discussed the optical fluorescence that results from degradation of x-ray “frequency.” But late in 1920 he reviewed the new evidence accumulated at high x-ray frequencies. There he hinted at unspecified difficulties in the orthodox wave interpretation of x-rays.
A group of electrons that traverses a sufficiently small aperture will exhibit diffraction effects. It is not entirely surprising that the earliest reaffirmation of the dualism inherent in radiation came neither from Britain nor Germany. There the issues had been recognized, discussed, and dismissed over the preceding twenty years. And American research traditions were largely derivative of German and British models; Duane and Millikan had both studied under Planck, and Richardson did research with Thomson in Cambridge. It took an outsider to these traditions to raise the issues in a way that began to convince others. That process began in France. Maurice and Louis de Broglie were, by any standards, unusual physicists. Amateurs in an age of professionals, possessing a confidence born of noble status, working on experiments that had only the meagerest precedent in their homeland, they were not as firmly bound by the predispositions that prevented physicists of other nations from directly assessing the spatially localized lightquantum. Their conversion was real. Maurice had once been convinced that x-rays and γ-rays fit neatly into the electromagnetic spectrum. In his discussion, La nature des rayons de Röntgen in 1915, there was no thought that x-rays might be anything other than periodic waves. As late as May 1920, he spoke freely of x-ray “wavelengths” and discussed the optical fluorescence that results from degradation of x-ray “frequency.” But late in 1920 he reviewed the new evidence accumulated at high x-ray frequencies. There he hinted at unspecified difficulties in the orthodox wave interpretation of x-rays.
Abstract We have seen that it took about two decades to fully realize that light or, generally, electromagnetic radiation has both wave and particle properties. The final proof came with the discovery of the Compton effect (Episode 31). Even Compton himself needed years before he saw that the particle picture of radiation was unavoidable in view of the experimental evidence. Still in the year of Compton’s publications, Louis de Broglie [1] on purely theoretical grounds proposed that the particle–wave duality not only holds for radiation but also for material particles, i.e., for particles with a rest mass such as the electron.
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.
To members of the British Institute of Radiology the cathode ray is probably most familiar as the necessary antecedent of X rays. You are interested in them chiefly as a means to an end, but the cathode rays had a very real intrinsic interest in the nineties of last century. It was the study of the beam of light in a low-pressure discharge tube which led to the recognition of the existence of a universal constituent of matter—the electron—and I hope to show that the importance of cathode rays for the study of fundamental problems in physics is not yet exhausted. The cathode rays still form in many respects the most convenient way of studying the properties if electrons. Of recent years our views on the nature of these electrons have undergone a striking change, as a result of the brilliant inspiration of Prince Louis de Broglie, who has been rewarded with a Nobel Prize. He founded the theory which is now dominant in physics under the name of wave mechanics, and which is a general theory of the behaviour of any form of particle. According to this view all particles are associated with some form of wave, the properties of which determine much of the behaviour of the particle. This theory was originally devised by de Broglie from considerations based upon relativity.
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.
Where did we get that [equation] from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger. Richard Feynman De Broglie's matter waves The early struggles of physicists towards a quantum theory were mostly concerned with attempts to understand the nature of light. The traditional picture of light as a wave motion had been challenged by Planck and Einstein. They had shown that certain experimental results that were impossible to understand in terms of a wave picture could be easily explained if light was thought of as a stream of particles, now called photons. William Bragg, who, with his son, won the 1915 Nobel Prize for studies of crystal structure using X-rays, summarized this dilemma for physics by exclaiming in despair that he was teaching the corpuscular theory of light on Mondays, Wednesdays and Fridays, and the undulatory theory on Tuesdays, Thursdays and Saturdays! Physicists were still wrestling with these apparently contradictory properties of light when, in 1924, Prince Louis de Broglie (pronounced ‘de Broy’) suggested that all matter, even objects that we usually think of as particles – such as electrons – should also display wavelike behaviour! This revolutionary idea was completely unexpected and, what is more, was included by de Broglie in his Ph. D. thesis. Like most people, physicists are generally reluctant to accept any wild new idea, especially if there is not a shred of evidence to support it.
The author has worked with high-resolution transmission electron microscope for many years, which provides the most direct evidence of wave-particle duality. This relates to Crookes and J. J. Thomson's cathode rays tubes to determine that electron beams are of particle nature. This also relates to Röntgen's discovery that when an electron beam in the cathode rays tube strikes the glass wall, it produces X-rays with extremely high penetrating power. This behavior is consistent with Maxwell-Lorentz’s electrodynamics that electromagnetic waves must be produced whenever electricity carriers alter their velocity. The wave-particle duality proposed by de Broglie refers to accelerated electron beam, rather than single electron. De Broglie emphasized that the crystallographic diffraction pattern produced by his electron beam was completely consistent with the crystallographic diffraction pattern of von Laue by X-rays, therefore, he proposed that electrons possess wave-particle duality. This is actually the selected area electron diffraction pattern in transmission microscope. It is X-rays, not the waves of the electrons themselves to produce diffraction pattern. He extended this to the wave-particle duality of all matter and light. Schrödinger directly introduced de Broglie's electron beam behavior into electron wave in atoms. It was just at this stage that illogical reasoning occurred, making the quantum theory increasingly difficult to understand.