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Albert Einstein. Myth Buster Again: Quantum Mechanics

Helge Kastrup, Jeffry V. Mallow A

Published Sep 27, 2022• 0 citations
Publisher

Abstract

This chapter comprises Einstein's explanation of the photoelectric effect, his analysis of the transition of electrons in atoms, his study of the behavior of bosons (named after their discoverer, Satyendra Bose), and his opposition to the standard interpretation of quantum mechanics. For the photoelectric effect, Einstein showed that light could behave as a particle, not only as a wave. Using this “photon” model, he explained how atoms absorbed and emitted light. He also predicted that a photon could stimulate the emission of many more, through (decades later) light amplification by stimulated emission of radiation. He studied bosons, particles that, unlike fermions (named after Enrico Fermi), such as electrons in atoms, had no “Exclusion Principle”: any number of them could “condense” into a single state. Finally, he opposed Bohr's “Copenhagen interpretation,” that a system such as an electron has a range of values for its properties such as spin, until a measurement is made, forcing it to choose one. Einstein argued for a “hidden variable theory” in which there was something deeper than quantum mechanics: that a system was in a specific state before a measurement. (He was wrong.)

DOI
10.1063/9780735421721_009

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This chapter comprises Einstein's explanation of the photoelectric effect, his analysis of the transition of electrons in atoms, his study of the behavior of bosons (named after their discoverer, Satyendra Bose), and his opposition to the standard interpretation of quantum mechanics. For the photoelectric effect, Einstein showed that light could behave as a particle, not only as a wave. Using this “photon” model, he explained how atoms absorbed and emitted light. He also predicted that a photon could stimulate the emission of many more, through (decades later) light amplification by stimulated emission of radiation. He studied bosons, particles that, unlike fermions (named after Enrico Fermi), such as electrons in atoms, had no “Exclusion Principle”: any number of them could “condense” into a single state. Finally, he opposed Bohr's “Copenhagen interpretation,” that a system such as an electron has a range of values for its properties such as spin, until a measurement is made, forcing it to choose one. Einstein argued for a “hidden variable theory” in which there was something deeper than quantum mechanics: that a system was in a specific state before a measurement. (He was wrong.)
We review here the main contributions of Einstein to the quantum theory. To put them in perspective we first give an account of Physics as it was before him. It is followed by a brief account of the problem of black body radiation which provided the context for Planck to introduce the idea of quantum. Einstein's revolutionary paper of 1905 on light-quantum hypothesis is then described as well as an application of this idea to the photoelectric effect. We next take up a discussion of Einstein's other contributions to old quantum theory. These include (i) his theory of specific heat of solids, which was the first application of quantum theory to matter, (ii) his discovery of wave-particle duality for light and (iii) Einstein's A and B coefficients relating to the probabilities of emission and absorption of light by atomic systems and his discovery of radiation stimulated emission of light which provides the basis for laser action. We then describe Einstein's contribution to quantum statistics viz Bose-Einstein Statistics and his prediction of Bose-Einstein condensation of a boson gas. Einstein played a pivotal role in the discovery of Quantum mechanics and this is briefly mentioned. After 1925 Einstein's contributed mainly to the foundations of Quantum Mechanics. We choose to discuss here (i) his Ensemble (or Statistical) Interpretation of Quantum Mechanics and (ii) the discovery of Einstein-Podolsky-Rosen (EPR) correlations and the EPR theorem on the conflict between Einstein-Locality and the completeness of the formalism of Quantum Mechanics. We end with some comments on later developments.
Einstein extended the quantization to light itself with the photon hypothesis with the explanation of the photoelectric effect. Bohr used Planck's ideas to explain the line emission of hydrogen atoms which gave an indication that the newborn quantum mechanics was giving a better description of experiments. In this chapter, the authors not follow a rigorous mathematical description. The postulates come in classes: the description of states, the description of physical quantities, the description of the act of measurement, the effect of the measurements on the state and the time evolution of a quantum system. Sommerfeld modifications of Bohr's theory was seen favorably because it gave a solutions to a few anomalous effects like the Zeeman effect and the Stark effects. As in the classical case of a two body problem, positive values of the total energy E correspond to free particles while negative values of E correspond to bound states. In quantum mechanics, electrons are indistinguishable.
Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.
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Einstein is best known for relativity and his other 1905 breakthroughs – explaining the photoelectric effect and his work on Brownian motion – but his ideas also underpinned the development of the laser and the creation of a new state of matter called the Bose-Einstein condensate. These discoveries, which were made in 1916 and 1924, respectively, were based on Einstein's investigations into bosonic particles such as photons. Moreover, Bose – Einstein condensation was predicted to occur in one of the simplest physical systems: the ideal gas.
In this chapter, three problems whose resolution laid the foundation of quantum mechanics are discussed. First the pioneering work of Max Planck is described who explained the spectrum of light emitted from a so-called blackbody by making a bold ansatz that the energy associated with the oscillations of electrons comes in packets or quanta of energy. Second it is shown how Einstein invoked Planck’s hypothesis to explain the photoelectric effect by arguing that light should come in packets or quanta of energy and this energy should be proportional to the frequency. Electrons are emitted if the energy of the quantum of light, which has come to be known as a photon, is higher than a critical value. The third problem relates to the atomic structure of hydrogen. A full description is given of how Bohr applied a quantization condition to explain the emission of light at certain specific frequencies.