is more important to have the correct answer later than an incorrect
answer now.
I’d like to give the same advice to readers of this book— especially in this
chapter—but sometimes the answers are not known, even to the best
minds in physics, and certainly not to me. So I would ask for a certain
measure of indulgence on the part of the reader. What quantum mechan-
ics has shown us about the nature of reality and the limitations of knowl-
edge is truly fascinating—but the final version of this saga is a long way
from being written, and may never be written. Unquestionably, though,
what we have learned via quantum mechanics about reality and the limi-
tations of knowledge is so fascinating and compelling that this book
would be incomplete without a discussion of this subject.
Max Planck and the Quantum Hypothesis
As the nineteenth century came to a close, physicists around the world
were beginning to feel their time had come and gone. One physicist ad-
vised his students to pursue other careers, feeling that the future of phys-
ics would consist of the rather mundane task of measuring the physical
constants of the universe (such as the speed of light) to ever-increasing
levels of accuracy.
Still, there were (apparently) minor problems that had yet to be resolved.
One of the unsettled questions concerned how an object radiates. When
iron is heated on a forge, it first glows a dull red, then a brighter red, and
then white; in other words, the color changes in a consistent way with in-
creasing temperature. Classical physics was having a hard time account-
ing for this. In fact, the prevailing Rayleigh-Jeans theory predicted that
an idealized object called a blackbody would emit infinite energy as the
wavelength falling on it became shorter and shorter. Short-wavelength
light is ultraviolet; the failure of the Rayleigh-Jeans theory to predict fi-
nite energy for a radiating blackbody exposed to ultraviolet light came to
be known as the “ultraviolet catastrophe.”^2
When a scientific theory encounters an obstacle, several different things
can happen. The theory can overcome the obstacle; this frequently occurs
when broader ramifications of a new theory are discovered. The theory
can undergo minor revisions; like software, the alpha version of a theory
is often in need of fine-tuning. Finally, since any scientific theory is capa-
ble of explaining only a limited number of phenomena, it may be neces-
sary to come up with a new theory.
The Rayleigh-Jeans theory operated under a very commonsense
premise—that energy could be radiated at all frequencies. An analogy
44 How Math Explains the World