include my efforts to put things together in their calculations (I was only
four years old at the time), and so I think I’ll leave the construction of
home quantum erasers to those with demonstrated mechanical ability.The Uncertainty Principle
Some branches of mathematics, such as geometry, are highly visual; oth-
ers, such as algebra, are highly symbolic, although many important re-
sults have been obtained by looking at algebraic problems geometrically
or geometric problems algebraically. Nonetheless, most of us have a pref-
erence for looking at things one way or the other. Einstein had a beautiful
way of expressing this: in his later years, he remarked that he hardly ever
thought about physics by using words. Possibly, he saw pictures; possibly,
he saw relationships between concepts. I marvel at this facility—while I
sometimes think in terms of pictures, they are almost always derived
from words describing them.
As physics probed ever deeper into the subatomic world in the first few
decades of the twentieth century, it became harder and harder to visual-
ize the phenomena that were occurring. As a result, some physicists,
including Werner Heisenberg, preferred to treat the subatomic world
through symbolic representation alone.
The Heisenberg who tackled this complex problem was very different
from the Heisenberg who, at the end of World War I, was a “street-fight-
ing man,” engaging in pitched battles with Communists in the streets of
Munich after the collapse of the German government following the war.
Heisenberg was only a teenager at the time, and after the rebellious phase
subsided, he switched his focus from politics to physics, displaying such
talent that he became one of Niels Bohr’s assistants. As a result, Heisen-
berg was thoroughly familiar with Bohr’s “solar system” model of the
atom, in which electrons were viewed as orbiting the nucleus much as
planets orbit the sun. At that time, Bohr’s model was running into cer-
tain theoretical difficulties, and several physicists were trying to resolve
them. One was Erwin Schrödinger, whom we have already met.
Schrödinger’s solution entailed treating the subatomic world as consist-
ing of waves, rather than particles. Heisenberg adopted a different ap-
proach. He devised a mathematical system consisting of quantities called
matrices (a matrix is a little like a spreadsheet—a rectangular array of
numbers arranged in rows and columns) that could be manipulated in
such a fashion as to generate known experimental results. Both
Schrödinger’s and Heisenberg’s approaches worked, in the sense that
they accounted for more phenomena than Bohr’s atomic model. In fact,
All Things Great and Small 55