In some of the past BMC posts, I have blogged about how statistical mechanics, in the 19th century, came perilously close to uncovering quantum mechanics early. A number of “problems” with statistical mechanics arose due to the classical treatment used. One of the most serious was the Ultraviolet Catastrophe. This problem was not easily solved with the hand-wavey pseudo-quantum explanations used in some previous cases. It took a full-on, quantized description of electromagnetism, and helped usher in quantum mechanics to being the foremost theory in subatomic physics.
Black body Radiation
The catastrophe arises from considering a phenomena called black body radiation. A black body is a perfect absorber, and a perfect emitter of radiation. What that means, is that all the light, x-rays, microwaves, etc. (all forms of electromagnetic radiation) striking the object are completely absorbed (increasing its temperature), and that it is a perfect radiator (it glows because of its temperature). The glow it gives off increases in frequency as the object heats up (which is why a hot steel will go from red to yellow to white as it heats). A black body can be used as an approximation for most physical objects, from stars to people, but is one of the many non-physical objects used in physics like massless strings and frictionless planes. Perhaps Hotblack Desiato could make one, but we haven’t yet.
The Ultraviolet Catastrophe
The problem arose when trying to determine how much power was radiated by the black body. When physicists in the 19th century attempted to calculate this, they turned to two tools: classical harmonic oscillators (things like vibrations on a string), and the equipartition theorem. The classical harmonic oscillator theory of radiation told them that the number of oscillation modes in a 3D box is proportional to the frequency of the wave squared, and that the power of a wave was dependent on the frequency of it. The equipartition theorem told them that each mode of vibration was a degree of freedom, and that it stored a fixed amount of energy, dependent on the temperature. BIG SCIENCY WARNING BELLS WENT OFF. These two things give you that as you increase the vibration mode, you get a massive increase in degrees of freedom, and therefore energy, all the way up to infinity. These calculations told them that any object above absolute zero emits an infinite amount of radiation, most of it in ultra-high energy gamma rays (ultraviolet was the whiz-bang high energy light of the time, hence the name).
Planck Saves the Day
The solution to this catastrophe came from none other than Max Planck. He modified the idea of using classical harmonic oscillators as a model for radiation by introducing quantized emission. In other words, the photon: a discrete “packet” of EM radiation. These packets have energy proportional to their frequency, which means that as you approach infinite frequency, their energy expands to infinity as well. This dropped the number of available modes in the cavity for higher frequencies, causing the emission to go to zero at very high frequencies (rather than ballooning to infinity). The result of this modification was a change in how radiation was viewed (which, along with Einstein’s photoelectric effect helped cement the idea of photons) from a classical oscillator to a gas of Bosons (non-excluding, indistinguishable particles). The result of Planck’s work was Planck’s Law of black body radiation, which accurately describes the spectrum of hot objects, allowing us to easily gauge the temperature of objects by examining their radiation.