The development of quantum mechanics in the first decades of the twentieth century came as a shock to many physicists. Today, despite the great successes of quantum mechanics, arguments continue about its meaning, and its future.

1.

The first shock came as a challenge to the clear categories to which physicists by 1900 had become accustomed. There were particles—atoms, and then electrons and atomic nuclei—and there were fields—conditions of space that pervade regions in which electric, magnetic, and gravitational forces are exerted. Light waves were clearly recognized as self-sustaining oscillations of electric and magnetic fields. But in order to understand the light emitted by heated bodies, Albert Einstein in 1905 found it necessary to describe light waves as streams of massless particles, later called photons.

Then in the 1920s, according to theories of Louis de Broglie and Erwin Schrödinger, it appeared that electrons, which had always been recognized as particles, under some circumstances behaved as waves. In order to account for the energies of the stable states of atoms, physicists had to give up the notion that electrons in atoms are little Newtonian planets in orbit around the atomic nucleus. Electrons in atoms are better described as waves, fitting around the nucleus like sound waves fitting into an organ pipe.1 The world’s categories had become all muddled.

Worse yet, the electron waves are not waves of electronic matter, in the way that ocean waves are waves of water. Rather, as Max Born came to realize, the electron waves are waves of probability. That is, when a free electron collides with an atom, we cannot in principle say in what direction it will bounce off. The electron wave, after encountering the atom, spreads out in all directions, like an ocean wave after striking a reef. As Born recognized, this does not mean that the electron…