How Math Explains the World.pdf

(Marcin) #1

electrons had the same energy. Lenard also showed that the energy of the
emitted electrons depended upon the color of the incident light; if one
used light of shorter wavelengths, the energy of the emitted electrons was
higher than if one used light of longer wavelengths. This result also pro-
vides evidence how one’s adviser, and the interests of that adviser, often
inf luence the career of the student. Lenard’s adviser at the University of
Heidelberg was Robert Bunsen, who had discovered that the patterns of
light, recognizable as bands of different color, characterized each ele-
ment, and could be used to deduce the composition of the stars. This
seminal experiment earned Lenard the Nobel Prize in 1905, the same
year that Einstein was to explain the reasons behind the phenomena
Lenard had discovered.
Einstein explained the photoelectric effect by invoking Planck’s idea of
quanta. He assumed that light behaved as a collection of particles (each
particle is called a “photon”), with each photon carrying energy that de-
pended upon the frequency of the light. The shorter the wavelength, the
higher the energy of the associated photon. If you swing a bat faster, you
will impart more energy to a baseball—assuming you hit it. When the
short-wavelength (high-energy) photons hit an electron with enough en-
ergy to knock it out of the metal, that electron had more energy than one
hit with a higher-wavelength (lower energy) photon—a Barry Bonds home
run rather than a wind-assisted home run in Wrigley Field hit by a utility
infielder.
The explanation of the photoelectric effect won Einstein the Nobel
Prize in 1921. Great experiments such as Lenard’s win Nobel Prizes, but
great explanations such as Einstein’s not only win Nobel Prizes but also
make history. Perhaps unhappy at being upstaged by Einstein, possibly
exacerbated by his inability to find the explanation for the photoelectric
effect he had discovered (and on which he could have cornered both the
experimental and theoretical markets), Lenard disparaged Einstein’s
theory of relativity as “Jewish science” and became an ardent supporter
of the Nazis.


Is Matter a Wave or a Particle?
I have no idea how lengthy a typical doctoral dissertation is; I’m sure it
varies with the field. Mine was about seventy typewritten pages and con-
tained enough results that I was able to squeeze three published articles
out of it—all of which have long been forgotten. I’m sure there are other,
much lengthier doctoral dissertations, even in mathematics.
There are also shorter ones, much shorter. In 1924, Louis de Broglie

All Things Great and Small 49
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