The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power. Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ... For other uses, see Radiation (disambiguation). ...

The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, although the concept goes back to 1905; the word "ultraviolet" refers to the fact that the problem appears in the short wavelength region of the electromagnetic spectrum. Since the first appearance of the term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence. Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 – Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ... For other uses, see Ultraviolet (disambiguation). ... Although some radiations are marked as N for no in the diagram, some waves do in fact penetrate the atmosphere, although extremely minimally compared to the other radiations The electromagnetic (EM) spectrum is the range of all possible electromagnetic radiation. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. ... In physics, an ultraviolet divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very high energy approaching infinity, or, equivalently, because of physical phenomena at very short distances. ...

Problem

The ultraviolet catastrophe results from the equipartition theorem of classical statistical mechanics which states that all modes (degrees of freedom) of a system at equilibrium have an average energy of kT / 2. Figure 1. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

An example, from Mason's A History of the Sciences^[1], is a piece of string. As a natural vibrator, the string will oscillate with specific modes (the standing waves of a string in harmonic resonance), dependent on the length of the string. In classical physics, a radiator of energy will act as a natural vibrator. And, since each mode will have the same energy, most of the energy in a natural vibrator will be in the smaller wavelengths and higher frequencies, where most of the modes are. Vibration and standing waves in a string, The fundamental and the first 6 overtones A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ... Approximate harmonic overtones on a string An overtone is a natural resonance or vibration frequency of a system. ...

According to classical electromagnetism, the number of electromagnetic modes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the Rayleigh-Jeans law, and be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power is unlimited as higher and higher frequencies are considered: this is clearly unphysical as the total radiated power of a cavity is not observed to be infinite, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in the year 1905. Comparison of Rayleigh-Jeans law with Wiens law and Plancks law, for a body of 8 mK temperature. ... “Einstein” redirects here. ... See also Rayleigh fading Rayleigh scattering Rayleigh number Rayleigh waves Rayleigh-Jeans law External links Nobel website bio of Rayleigh About John William Strutt MacTutor biography of Lord Rayleigh Categories: People stubs | 1842 births | 1919 deaths | Nobel Prize in Physics winners | Peers | British physicists | Discoverer of a chemical element ... Sir James Hopwood Jeans (born Ormskirk, September 11, 1877, died Dorking, September 16, 1946) was a British physicist, astronomer and mathematician who was the first to propose the theory of continuous creation of matter in the universe. ...

Solution

Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. Planck postulated that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to the frequency , as given by Planck's law. This has the effect of reducing the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy at those frequencies by application of the equipartition theorem. The radiated power eventually goes to zero at infinite frequencies, and the total predicted power is finite. The formula for the radiated power for the idealized system (black body) was in line with known experiments, and came to be called Planck's law of black body radiation. Based on past experiments, Planck was also able to determine the value of its parameter, now called Planck's constant. The packets of energy later came to be called photons, and played a key role in the quantum description of electromagnetism. “Einstein” redirects here. ... Planck redirects here. ... Black body spectrum For a general introduction, see black body. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...

In Popular Culture

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In this version, the "catastrophe" was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental — his motivation for introducing "quanta" was entirely different. That Planck's proposal happened to provide a solution for it was realized much later, as stated above.^[2] Figure 1. ... In physics, a quantum (plural: quanta) is an indivisible entity of energy. ...

Though this has been known by historians for many decades, the historically incorrect version persists, in part because Planck's actual motivations for the proposal of the quantum are complicated and less easy to summarize to a modern audience.^[3]

References

• Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company, Chapter 4. ISBN 0-7167-1088-9. 
• Cohen-Tannoudji, Claude; Diu, Bernard; Laloë, Franck (1977). Quantum Mechanics: Volume One. Hermann, Paris, 624–626. ISBN 0-4711-6433-X.