Introduction to Volume One

2019 ◽  
pp. 1-42
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Theory ◽  
Black Body ◽  
Black Body Radiation ◽  
Quantum Model ◽  
Light Quantum ◽  
Quantum Hypothesis ◽  
Specific Heats ◽  
Adiabatic Principle ◽  
Old Quantum Theory ◽  
Energy And Momentum

We provide an overview, as non‐technical as possible, of the contents of Vol. 1 of the book. Reflecting the structure of the volume, this overview consists of two parts. In the first part, we summarize the most important early contributions to quantum theory (covered in detail in Chs. 2–4). This part starts with Planck’s work on black‐body radiation culminating in the introduction of Planck’s constant in 1900. It then moves on to Einstein’s 1905 light‐quantum hypothesis, his theory of specific heats, and his formulas for energy and momentum fluctuations in black‐body radiation. After summarizing Bohr’s path to his quantum model of the atom, it concludes with Einstein’s 1916–17 radiation theory combining elements of Bohr’s model with his own light‐quantum hypothesis. In the second part we summarize our analysis of the old quantum theory (given in detail in Chs. 5–7). After a brief overview of the career of Sommerfeld, who together with Bohr took the lead in developing the old quantum theory, we review the three principles we have identified as the cornerstones of the theory (the quantization conditions, the adiabatic principle, and the correspondence principle). We then discuss three of the theory’s most notable successes (fine structure, Stark effect, X‐ray spectra) and, finally, three of its most notorious failures (multiplets, Zeeman effect, helium).

Einstein, Equipartition, Fluctuations, and Quanta

2019 ◽  
pp. 84-142
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Theory ◽  
Statistical Mechanics ◽  
Black Body ◽  
Black Body Radiation ◽  
Light Quantum ◽  
Quantum Hypothesis ◽  
Specific Heats ◽  
Light Quanta ◽  
Physics Community ◽  
Equipartition Theorem

After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Einstein relied heavily on arguments from statistical mechanics in the most revolutionary of his famous 1905 papers, the one introducing the light‐quantum hypothesis. He showed that the equipartition theorem inescapably leads to the classical Rayleigh‐Jeans law for black‐body radiation and the ultraviolet catastrophe (as Ehrenfest later called it). Einstein and Ehrenfest were the first to point this out but the physics community only accepted it after the venerable H.A. Lorentz, came to the same conclusion in 1908. The central argument for light quanta in Einstein’s 1905 paper involves a comparison between fluctuations in black‐body radiation in the Wien regime and fluctuations in an ideal gas. From this comparison Einstein inferred that black‐body radiation in the Wien regime behaves as a collection of discrete, independent, and localized particles. We show that the same argument works for non‐localized quantized wave modes. Although nobody noticed this flaw in Einstein’s reasoning at the time, his fluctuation argument, and several others like it, failed to convince anybody of the reality of light quanta. Even Millikan’s verification of Einstein formula for the photoelectric effect only led to the acceptance of the formula, not of the theory behind it. Einstein’s quantization of matter was better received, especially his simple model of a solid consisting of quantized oscillators. This model could explain why the specific heats of solids fall off sharply as the temperature is lowered instead of remaining constant as it should according to the well‐known Dulong‐Petit law, which is a direct consequence of the equipartition theorem. The confirmation of Einstein’s theory of specific heats by Nernst and his associates was an important milestone in the development of quantum theory and a central topic at the first Solvay conference of 1911, which brought the fledgling theory to the attention of a larger segment of the physics community. Returning to the quantum theory after spending a few years on the development of general relativity, Einstein combined his light‐quantum hypothesis with elements of Bohr’s model of the atom in a new quantum radiation theory.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

William H. Bragg's Corpuscular Theory of X-Rays and γ-Rays

1971 ◽  
Vol 5 (3) ◽  
pp. 258-281 ◽  
Author(s):  
Roger H. Stuewer
Keyword(s):  
Ultra Violet ◽  
Black Body ◽  
Black Body Radiation ◽  
Electromagnetic Spectrum ◽  
Light Quantum ◽  
X Rays ◽  
Ultra Violet Light ◽  
Violet Light ◽  
History Of ◽  
Γ Rays

The modern corpuscular theory of radiation was born in 1905 when Einstein advanced his light quantum hypothesis; and the steps by which Einstein's hypothesis, after years of profound scepticism, was finally and fully vindicated by Arthur Compton's 1922 scattering experiments constitutes one of the most stimulating chapters in the history of recent physics. To begin to appreciate the complexity of this chapter, however, it is only necessary to emphasize an elementary but very significant point, namely, that while Einstein based his arguments for quanta largely on the behaviour of high-frequency black body radiation or ultra-violet light, Compton experimented with X-rays. A modern physicist accustomed to picturing ultra-violet light and X-radiation as simply two adjacent regions in the electromagnetic spectrum might regard this distinction as hair-splitting. But who in 1905 was sure that X-rays and γ-rays are far more closely related to ultra-violet light than to α-particles, for example ? This only became evident after years of painstaking research, so that moving without elaboration from Einstein's hypothesis to Compton's experiments automatically eliminates from consideration an important segment of history—a segment in which a major role was played by William Henry Bragg.

Guiding Principles

2019 ◽  
pp. 205-258
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Theory ◽  
Classical System ◽  
Special Role ◽  
Quantum Numbers ◽  
Adiabatic Principle ◽  
Old Quantum Theory ◽  
Underlying Principle ◽  
Guiding Principles ◽  
Action Variables

The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement of asymptotic coincidence of quantum and classical theory in the limit of large quantum numbers, originally introduced by Bohr in 1913 as a supporting argument for his quantization of angular momentum in his theory of the hydrogen atom, was extended by Bohr and Kramers to provide selection rules and approximate intensity predictions evening the regime low quantum numbers.

Quantum theory and the electromagnetic world-view

2004 ◽  
Vol 35 (1) ◽  
pp. 67-93 ◽  
Author(s):  
SUMAN SETH
Keyword(s):  
Quantum Theory ◽  
Research Agenda ◽  
World View ◽  
Black Body ◽  
Electromagnetic Theory ◽  
Electron Theory ◽  
Arnold Sommerfeld ◽  
Quantum Hypothesis ◽  
Levels Of Explanation ◽  
Planetary Model

ABSTRACT: This paper has two goals: to use the electromagnetic world-view as a means of probing what we now know as the quantum theory, and to use the case of the quantum theory to explicate the practices of the electromagnetic program. It focuses on the work of Arnold Sommerfeld (1868––1951) as one of the leading theorists of the so-called ““older”” quantum theory. By 1911, the year he presented a paper on the ““Quantum of action”” at the Solvay Conference, Sommerfeld vocally espoused the necessity of some form of a quantum hypothesis. In his earlier lectures, however, his reservations about Max Planck's position were far more apparent. Section 1 argues that Sommerfeld's hostility towards Planck's derivation of the Black-body law, and his support for the result achieved by James Jeans and rederived using the electron theory by Lorentz, can be traced to his commitment to the programmatic aims of the electromagnetic world-view. Section 2 suggests that this conclusion has deep implications for our understanding of the ““conversion”” of several leading physicists to the quantum theory after around 1908. Section 3 traces a partial continuation of Sommerfeld's deeply held beliefs. Sommerfeld's Solvay paper is best understood as an attempt to reconcile the programmatic aims of the electromagnetic world-view with the necessity of recourse to the quantum hypothesis. No longer a universalizing vision, the attempt to prove the necessity of electromagnetic theory at all levels of explanation remained a key element of Sommerfeld's research agenda until (and even beyond) the advent of Niels Bohr's ““planetary”” model of the atom in 1913.

Distilled shock conditions for ideal magneto-acoustic shock waves in an optically thick medium

2012 ◽  
Vol 79 (5) ◽  
pp. 457-465
Author(s):  
D. ONIĆ
Keyword(s):  
Shock Waves ◽  
Thermal Radiation ◽  
Total Pressure ◽  
Fixed Ratio ◽  
Black Body ◽  
Black Body Radiation ◽  
Ideal Gas ◽  
Specific Heats ◽  
Special Case ◽  
Thick Medium

AbstractThe shock waves are important features in the analysis of transonic magnetohydrodynamical (MHD) flows where thermal radiation could also be significant. In this paper the effects of black-body radiation on non-relativistic shock waves in an ideal radiation MHD model for the optically thick case are discussed. Distilled shock conditions were derived and discussed for the case of a fixed ratio of specific heats of an ideal gas (γ) and ratio of gas to total pressure (b). The special case, when jumps in γ and/or b are allowed, was also considered.

The Wave Theory of Heat: A Forgotten Stage in the Transition from the Caloric Theory to Thermodynamics

1970 ◽  
Vol 5 (2) ◽  
pp. 145-167 ◽  
Author(s):  
Stephen G. Brush
Keyword(s):  
Twentieth Century ◽  
Quantum Theory ◽  
Essential Role ◽  
Wave Theory ◽  
Radiant Heat ◽  
Black Body ◽  
Black Body Radiation ◽  
Modern Physics ◽  
Caloric Theory

Research on thermal “black-body” radiation played an essential role in the origin of the quantum theory at the beginning of the twentieth century. This is a well-known fact, but historians of science up to now have not generally recognized that studies of radiant heat were also important in an earlier episode in the development of modern physics: the transition from caloric theory to thermodynamics. During the period 1830–50, many physicists were led by these studies to accept a “wave theory of heat”, although this theory subsequently faded into obscurity.

scholarly journals The mathematical representation of a light pulse

1914 ◽  
Vol 89 (612) ◽  
pp. 399-404
Keyword(s):  
Light Pulse ◽  
White Light ◽  
Black Body ◽  
Black Body Radiation ◽  
Mathematical Representation ◽  
Light Quantum ◽  
Concrete Case ◽  
Know How ◽  
New Class ◽  
The Subject

In recent years, owing to the work of Rayleigh, Schuster, and others, our views as to the nature of white light have undergone a change, and it is now universally accepted that white light consists of irregular pulses which are transformed into trains of sine waves by their passage through a prism. But the method of this transformation is not clearly understood, as the reasoning on the subject is unfortunately somewhat general, the only concrete case well known being the pulse Rayleigh represented by e - c 2 t 2 . Had the nature of a light pulse been better understood, there might possibly never have been any talk of the “Light Quantum” or unit theory of light. The object of this note is to call attention to a new class of expressions representing the initial form and dispersion of a light pulse. They are both simple and elegant, and one of them gives the energy distribution required by Wien’s law for black body radiation. They have been suggested by one of Kelvin’s hydrodynamical papers. They do not depend on the Fourier analysis and this is an advantage, for we never know how much of the latter is subjective.

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