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Science

Recent Developments in Quantum Mechanics

E. U. Condon

Published Aug 31, 1928• 0 citations
Publisher

Abstract

The fundamental fact for quantum physics which has emerged from experimental investigations in the field is a double duality of wave and particle concepts. The wave theory of light, firmly grounded by the wave explanations of interference and diffraction and by Maxwell’s electromagnetic theory of light waves, is now recognized as giving but one aspect of the nature of radiation. The corpusclar aspect of radiation is revealed in the photoelectric effect and in the Compton effect. In these effects Planck’s constant appears as a universal constant which connects the wave and particle modes of description of the same radiation.

DOI
10.1126/science.68.1757.193

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The fundamental fact for quantum physics which has emerged from experimental investigations in the field is a double duality of wave and particle concepts. The wave theory of light, firmly grounded by the wave explanations of interference and diffraction and by Maxwell’s electromagnetic theory of light waves, is now recognized as giving but one aspect of the nature of radiation. The corpusclar aspect of radiation is revealed in the photoelectric effect and in the Compton effect. In these effects Planck’s constant appears as a universal constant which connects the wave and particle modes of description of the same radiation.
Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
The following Master’s thesis is concerned with several aspects of the wave-particle duality of light. It is loosely divided in three parts. In the first part we consider historical, theoretical and experimental aspects of the duality problem. We explain how the notion of duality has developed through the last 400 years. We discuss theoretical underpinnings of the duality emodied by Maxwell’s electromagnetic theory, quantization of electromagnetic modes, Fock’s states and coherent states. We critically review several experiments which serve to demonstrate the corpuscular or undulatory behaviour of light and matter; in particular we present how the photoelectric effect and the Compton effect can be explained using the undulatory model, and we critically review Grangier, Roger and Aspect correlation experiment.\n\nIn the second part we describe two illustrative experiments on the duality of light conducted at Quantum Optics Laboratory at University of Oslo. The results of the experiment allow us to discuss how coincidence measurements can be used to exhibit the corpuscular behaviour of light, and how Mach-Zender interferometry performed at very low intensity can be used to exhibit the undulatory behaviour at\nthe (assumed) single-photon level. In addition, in the second part we review elements of theories closely associated with the experiment and the experimental setup: optical coherence, photocount and photon\nstatistics, beam splitter models and Gaussian beams. A proposition for extending the semiclassical model is given, and shortcomings of the present beam splitter models are discussed.\n\nIn the third part of the thesis we consider first Afshar’s experiment and some of the critical response that it has been met with. Then we discuss how the wave-particle duality is to be understood in the\nstandard interpretation of quantum mechanics, and how it could possibly be explained using either an alternative model for light or an alternative interpretation of quantum mechanics, and what difficulties such explanations present.
A new foundational physics is emerging which radically changes our concepts of electromagnetic waves. The original quantum ideas of Max Planck and Albert Einstein from the turn of the twentieth century, are undergoing an impressive renaissance now at the turn of the twenty-first century. The result is a fundamental physics of electromagnetic waves that is both new and classical. Einstein’s insistence that quantum mechanics was incomplete that “hidden variables” were yet to be discovered was correct. The recent discovery of those variables is the driving force behind this rebirth of the foundations of quantum mechanics and the fundamental physics of electromagnetic (“EM”) waves. The new quantum variables have led to the discovery of new universal constants for EM waves. The new constants have revealed an elegant simplicity in quantum concepts, that requires no paradoxical explanations and imposes no uncertainties or limits. Instead, the new physics provides a more realistic understanding of physical concepts related to EM waves. The old paradigm is disappearing, and yielding to a new paradigm which is both more understandable and more powerful.
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.
Duality (Dual Nature) is a universal character of our life in this Universe. There is an analogy of dual nature of radiation and matter in the domain of Indian Philosophy and Sikh religion, where Ultimate Reality is revealed to exist in its dual nature as sarguna and nirguna Brahman. The concept of Dual Nature of radiation has been in existence since the historical times but it was Max Planck who introduced it on firm footing to explain black body radiation spectrum. Louis de Broglie proposed the concept of dual nature of matter in 1924 in his doctoral thesis. It was established during investigations of Photoelectric effect and Compton effect. The real break-through in interpreting dual nature of matter and radiation may be ascribed to the advent of Quantum Mechanics. It was observed that in the microscopic world of particles, classical concepts of wave and particle fail to justify the experimental investigations; hence there is a need to invoke quantum concepts.