The physics behind the song
h
v

For millennia, people have wondered about the nature of light. In the late 1600's, debate intensified, with Isaac Newton proposing that light was made of particles, while Robert Hooke and Christian Huygens thought instead that light was a wave phenomenon.

The matter seemed to be settled in 1801, when Thomas Young published his "two-slit experiment", showing interference effects when light passed through two narrow, closely-spaced slits. This could only occur for a wave.

However, later in the 1800s, a serious problem developed. Classical physics predicts that the energy of "blackbody radiation" (the light emitted by objects due to their thermal energy) should increase without limit at short wavelengths (ultraviolet light, x-rays, etc.). This nonsensical result was dubbed the "ultraviolet catastrophe".

Max Planck realized that the experimentally-observed relation between the intensity of emitted light and its wavelength could be explained by assuming that light could only be emitted in discrete bundles, each carrying energy h v, where h is "Planck's constant", and v (pronounced "nu") is the frequency of the light, which is inversely related to its wavelength. He published this result in 1900; in 1918, he won the Nobel prize for it.

It appears that Planck and others of the time thought of this idea mostly as a mathematical trick; they assumed that later theories would bring more detailed understanding. After all, these light bundles or "photons" seemed to lie in opposition to the wave theory which had been proved by Young's two-slit experiment.

However, in 1905 Albert Einstein showed that the photon theory also explained the photoelectric effect (for which he won the Nobel prize in 1920). This left us with our current understanding: light has a dual nature. Sometimes, it behaves like a wave (as in the two-slit experiment), and sometimes like a particle (as in the emission of photons in blackbody radiation or in the photoelectric effect). This perplexing situation is reflected in the last verse of the song. (At this point, we've had decades to get used to this peculiar idea, but when Stead wrote the song around 1920, these notions were still quite new.)

In fact, it turns out that essentially everything has this dual nature, and essentially everything obeys the relation E = h v, where E is the energy. For example, electrons sometimes behave as particles, and sometimes as waves. The oscillation frequency v of the electron wave obeys E = h v. Another important example is the vibrations of a solid material. Like light, these vibrations can only occur with a minimum energy, E = h v. As mentioned in the 3rd verse of the song, this quantization of vibrational energy strongly affects the "specific heat" of solids. (The specific heat is the amount of energy needed to raise the temperature of one gram of a solid by one degree.)

The transition from wave behavior to particle behavior, known as the "collapse of the wavefunction", is a subject of significant current research. (At one time, many popularizations contended that the collapse was related to observation by a conscious intelligence, but this has been shown to be incorrect.)

--Walter F. Smith Aug. 15, 2005

The links below lead to external sites where you can explore more about each person or topic.


Isaac Newton in 1689


Memorial window for Robert Hooke

(This window is an idealization; there are no surviving actual images of Hooke.)


Click the image to see a movie of two-slit interference

"I knew the formula that reproduces the energy distribution in the normal spectrum; a theoretical interpretation had to be found at any cost, no matter how high."

A fun, short animated lecture by Neil Turok (of the Perimeter Institute) and MinutePhysics about the ultraviolet catastrophe and the discovery of E = h v for the case of light. One error: even with the best incandescent light bulbs (the type discussed here), most of the energy radiated is in the infrared, where it is invisible.

 
The development of lasers depended completely on an understanding of E = h v. In this entertaining hour-long lecture, Philip Bucksbaum of Stanford Univeristy walks us through from candles to "real world light sabers", and to the world's most powerful lasers at the cutting edge of current research.

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