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The physics behind
the song
“h v”
For millenia, 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 situtation 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
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Isaac
Newton in 1689
Memorial window for Robert
Hooke
(This window is an idealization; there are no surviving
actual images of Hooke.) |
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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."
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