Problem
The ultraviolet catastrophe results from the equipartition theorem of classical statistical mechanics which states that all harmonic oscillator modes (degrees of freedom) of a system at equilibrium have an average energy of .
An example, from Mason's A History of the Sciences, illustrates multi-mode vibration via 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.
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.
Read more about this topic: Ultraviolet Catastrophe
Famous quotes containing the word problem:
“The great problem of American life [is] the riddle of authority: the difficulty of finding a way, within a liberal and individualistic social order, of living in harmonious and consecrated submission to something larger than oneself.... A yearning for self-transcendence and submission to authority [is] as deeply rooted as the lure of individual liberation.”
—Wilfred M. McClay, educator, author. The Masterless: Self and Society in Modern America, p. 4, University of North Carolina Press (1994)
“Every reform was once a private opinion, and when it shall be a private opinion again, it will solve the problem of the age.”
—Ralph Waldo Emerson (1803–1882)
“Great speeches have always had great soundbites. The problem now is that the young technicians who put together speeches are paying attention only to the soundbite, not to the text as a whole, not realizing that all great soundbites happen by accident, which is to say, all great soundbites are yielded up inevitably, as part of the natural expression of the text. They are part of the tapestry, they aren’t a little flower somebody sewed on.”
—Peggy Noonan (b. 1950)