Fifty years have passed since Louis de Broglie created the theory of matter waves and published his first papers on the subject—inaugurating the era of modern quantum mechanics. De Broglie's undertaking was a very bold one. Unlike Planck's work in the older quantum theory, which had its origin in the measurements of black-body radiation, and unlike the photon hypothesis of Einstein, where the early experiments on the photoelectric effect offered some corroboration, de Broglie's theory lacked the support of any direct experimental evidence. Had it not been for the intervention of such established figures as Langevin and Einstein, who recognized the importance of what he had accomplished, de Broglie's work probably would have had little immediate effect.
Fifty years have passed since Louis de Broglie created the theory of matter waves and published his first papers on the subject—inaugurating the era of modern quantum mechanics. De Broglie's undertaking was a very bold one. Unlike Planck's work in the older quantum theory, which had its origin in the measurements of black-body radiation, and unlike the photon hypothesis of Einstein, where the early experiments on the photoelectric effect offered some corroboration, de Broglie's theory lacked the support of any direct experimental evidence. Had it not been for the intervention of such established figures as Langevin and Einstein, who recognized the importance of what he had accomplished, de Broglie's work probably would have had little immediate effect.
This chapter examines the wave properties of matter. Early attempts to extend the quantum ideas to the theory of matter had some limited success, but did not progress very far. Another radical idea was required before a satisfactory theory could be developed. As light has both wave and particle properties, perhaps the same is true of 'ordinary' particles such as electrons. This bold suggestion was made by Louis de Broglie in 1923, and within a few years it had been confirmed experimentally. De Broglie's wave hypothesis formed the basis for Schrödinger's equation, which was found capable of predicting the allowed energy levels in atoms and molecules, and must be regarded as one of the most important mathematical equations of modern science. Before discussing these ideas, the chapter begins by considering the classical mechanics of particles, reviewing some simple concepts that form an essential background to the quantum theory of matter.
This chapter discusses the conceptual foundations of quantum mechanics in the context of matter. Classical physics identified matter with particles and radiation with "waves." Although this description accounted for a large number of very important facts, it became apparent around the turn of the century that other phenomena, such as blackbody radiation and photoelectric effect, are satisfactorily explained only if radiation is described in terms of particles. Sometime later the hypothesis that, conversely, matter has wave properties was proposed by Louis de Broglie and was confirmed by the Davisson-Germer experiment of electron diffraction. In this experiment and similar ones, an electron beam was passed through a regular lattice (crystal), and subsequently showed the well-known diffraction patterns that are characteristic of waves. These results confirmed the theoretical predictions that a monoenergetic electron beam should be described by a plane wave and that the wave vector k of the wave should be related to the momentum p of an individual electron.
Classical physics identified matter with particles and radiation with waves. Although these descriptions accounted for a large number of very important facts, it became apparent at the beginning of the twentieth century that other phenomena, such as blackbody radiation and photoelectric effect, are satisfactorily explained only if radiation is described in terms of particles. Louis de Broglie developed a theory according to which, conversely, matter has wave properties. As an outcome of this theory, he was able to write down a formula relating the corresponding wavelength with the momentum of the particle. Diffraction patterns characterize waves, and the basic fact that corroborated the validity of the notion of matter waves was that the Davisson and Germer experiment proved electrons can be diffracted. In classical optics the simplest experiment displaying this phenomenon is the well-known Young two-slit experiment, in which a beam of light is passed through a diaphragm with two slits.
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 wave-particle duality of photons, as hypothesized by Einstein, was well accepted by the early 1920's. De Broglie's bold hypothesis in 1924, that all matter likewise has a wave-particle duality added further fuel to the fire in the development of Quantum Mechanics. It seared into the minds of physicists the wave-particle duality of Nature. Needless to say, this counter intuitive and bold assertion mystified the World beyond any sensible comprehension by common sense. The question often asked by ordinary people is what is the matter with de Broglie waves? We provide just this answer and demystify this 'matter' in this short paper.
The fundamental question in this manuscript is: “Is it possible to build matter out of Light (confined electromagnetic waves)?” To answer this question we first have to answer the question how we have come to this world of Probability Waves and Elementary Particles and Quantum Physics. Louis de Broglie described in 1924 in his PhD thesis the wave properties of matter. Erwin Schrödinger published in 1926 the well-known Schrödinger wave equation with the characteristic spherical and elliptical wave solutions. To describe these material waves, the immediately and first explanation was: “There is only one possibility. These are “electromagnetic waves”. De Broglie waves are ” Light Waves”. Because these were the only waves, known in the world of Physics. But there was a fundamental problem. These material waves, discovered by Louis de Broglie and mathematically described by Erwin Schrödinger could never be solutions of the well-known 4 equations of James Clerk Maxwell. The material waves were spherical and elliptical solutions and that was impossible for the solutions of the Maxwell Equations. According to the Maxwell Equations, light always travels along a straight path. A second problem was that the model of the atom of Bohr could not hold. How could an electron be everywhere at the same time in a kind of a spherical shell surrounding the nucleus. And be a particle at the same time. And Bohr found a compromise to declare the “De Broglie” waves to be the probability waves. Two problems were solved. Bohr’s planetary model could hold. And there was a name for the unknown material waves, discovered by Louis de Broglie and mathematically described by Erwin Schrödinger. The theory of “Probability Waves, Elementary Particles and Quantum Physics” had been created. To find a possibility, to create matter out of light we have to go back to the Equations of James Clerk Maxwell. The only possibility to declare the probability waves, discovered by Louis de Broglie, to be electromagnetic waves, to be light, and to be the building element of our universe, is to find evidence that he Maxwell Equations are not complete and that it is possible to confine light (electromagnetic waves) in spherical and elliptical shapes. A new equation has to be found. In this article it has been claimed that this missing equation is equation (5). Because the Theory of General Relativity has been built on the Einstein-Maxwell Equation, a new equation has to be found that describes in a generalized way the interaction between light and matter. This missing equation is equation (5-a).