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The Quantum (Undemystified)

© Wesley Colley

Last time, I tried to demystify special relativity a bit and motivate it from an intuitive standpoint. Quantum mechanics, unfortunately, is much, much harder to motivate intuitively, and even its most schooled practitioners have fundamental philosophical differences over what's really going on. Therefore, I shall report the necessity for quantum mechanics and leave the demystification behind (for now, at least).

First of all, what is quantum mechanics? Quantum mechanics arose around the turn of the century and was necessary to answer (among other things) this very fundamental, very simple problem: Why is a hot stove red, not blue? That a hot stove is red, then orange, then yellow, then perhaps even white when hotter is something three-year-olds seem to grasp intuitively, but scientists in 1900 remained unable to explain this phenomenon.

The prevailing theory at the time was due to Rayleigh and Jeans, who correctly understood the long wavelenth part of the thermal spectrum (which a stove very accurately produces). They noted simply that the number of states available as a function of energy simply went as the fourth power of energy (I'll omit that calculation for brevity). Therefore, any thermal source should have a spectrum that brightens simply as energy (1/wavelength) to the fourth power. While this formula worked brilliantly for the very red side of the spectrum, it predicted bizarre consequences in the blue. For instance, in the ultraviolet (wavelength of 0.1 microns), there should be 10,000 times as much light as in the infrared (wavelength of 1 micron), or 16 times as much light in blue as in red (making for a very blue stove), no matter the temperature. Worse, the X-ray intensity from a stove would be 10 quadrillion times greater than infrared intensity! Easily enough to kill a person quickly! We know stoves look red and change color as temperture changes; and we know that they don't kill us by X-raying us to death. This problem was called the ultraviolet catastrophe.

Another, seemingly unrelated, principle known in those days was the distibution of energies of simple systems, such as vibrations on a string and a mass on a spring. In the absence of outside forces, a string will vibrate just due to thermal (temperature) fluctuations. Maxwell and Boltzmann had described the mathematical distribution of such vibrations as a simple exponential form (f(E) = Ce^-E/kT), where E is the energy, T is the temperature, k is a constant called the Boltzmann constant and C is just some normalization constant.

It took Max Planck to unite these ideas and put forth his own profound idea in 1900. First, he set out simply to make careful measurements of the spectrum

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