f led the country. Many others reacted with abhorrence to the Nazi re-
gime, and also departed. Planck, although deploring the Nazis, decided
to stay in Germany. It was to be a tragic decision. In 1945, Planck’s
younger son was executed for his part in the “Revolt of the Colonels,” the
unsuccessful attempt by several members of the German armed forces to
assassinate Hitler.
The Quantum Revolution Continues
Max Planck’s revolutionary idea did more than simply resolve the ultravi-
olet catastrophe. Possibly only one other moment in science has opened
the door to such an unexpected world—when Anton von Leeuwenhoek
took his primitive microscope and examined a drop of water, only to dis-
cover forms of life never suspected and never before seen.
The quantum revolution has changed our world—technologically, sci-
entifically, and philosophically. Much of the incredible technology that
has been developed since the 1930s—the computer, the medical scan-
ners, lasers, everything with a chip in it—are the result of the application
of quantum theory to understanding the behavior of the subatomic world.
Quantum mechanics has not only spawned sciences that did not exist
prior to its conception, it has also greatly enriched some of the more ven-
erable areas of study, such as chemistry and physics. Finally, quantum
mechanics has fostered discoveries so profound that they make us won-
der about the essential nature of reality, a topic that has been a matter of
fierce philosophical debate for millennia.
Libraries could be built housing only books devoted to discussions of
quantum mechanics, so I’ll just concern myself with three of the most
perplexing topics in quantum mechanics: wave-particle duality, the un-
certainty principle, and entanglement.
Is Light a Wave or a Particle?
Probably no question in science has created more controversy over a
longer period of time than the nature of light. Greek and medieval phi-
losophers alike puzzled over it, alternating between theories that light
was a substance and that light was a wave, a vibration in a surrounding
medium. Almost two millennia later, Isaac Newton entered the debate.
Newton, when he wasn’t busy with mathematics, mechanics, or gravita-
tion, found time to invent the science of optics. As had others, Newton
puzzled over the nature of light, but finally voted for the theory that light
was a substance.
46 How Math Explains the World