product of the uncertainties of two related variables, called conjugate vari-
ables, must be greater than some predetermined set amount. Possibly the
most familiar conjugate variables are the duration of a musical note and its
frequency—the longer the note is held the more accurately we can deter-
mine its frequency. A note played for an infinitesimally short period of
time simply sounds like a click; its frequency is impossible to determine.
However, the devil in the details of the uncertainty principle comes
from the fact that position and momentum (momentum is the product of
mass and velocity) are conjugate variables. The more accurately we can
determine the position of a particle, the less information we have about
its momentum—and if we can determine its momentum to a high de-
gree of accuracy, we have only a limited idea of where it is. Since momen-
tum is the product of mass and velocity, a microscopic quantity of
momentum that would amount to almost no velocity at all if allocated to
an automobile will result in a lot of velocity if allocated to an electron.
Heisenberg’s uncertainty principle is sometimes erroneously inter-
preted as an inability on the part of fallible humans to measure phenom-
ena sufficiently accurately. Rather, it is a statement about the limitations
of knowledge, and is a direct consequence of the quantum-mechanical
view of the world. As a fundamental part of quantum mechanics, the
uncertainty principle has real-world ramifications for the construction of
such everyday items as lasers and computers. It has also banished the
simple cause-and-effect view of the universe that had been unquestioned
since the Greek philosophers first enunciated it. Heisenberg stated one of
the consequences of the uncertainty principle as follows:
It is not surprising that our language should be incapable of de-
scribing the processes occurring within the atoms, for, as has
been remarked, it was invented to describe the experiences of daily
life, and these consist only of processes involving exceedingly large
numbers of atoms. Furthermore, it is very difficult to modify our
language so that it will be able to describe these atomic processes,
for words can only describe things of which we can form mental
pictures, and this ability, too, is a result of daily experience.... In
the experiments about atomic events we have to do with things
and facts, with phenomena that are just as real as any phenomena
in daily life. But the atoms or the elementary particles themselves
are not as real; they form a world of potentialities or possibilities
rather than one of things or facts... Atoms are not things.^7
If atoms are not things, what are they? More than seventy-five years af-
ter Heisenberg’s revelation, physicists—and philosophers—are stillAll Things Great and Small 57