Chapter 5 described quantum mechanics in the context of particles moving in a potential. This application of quantum mechanics led to great advances in the 1920s and 1930s in our understanding of atoms, molecules, and much else. But, starting around 1930 and increasingly since then, theoretical physicists have become aware of a deeper description of matter, in terms of fields. Just as Einstein and others had much earlier recognized that the energy and momentum of the electromagnetic field is packaged in bundles, the particles later called photons, so also there is an electron field whose energy and momentum is packaged in particles, observed as electrons, and likewise for every other sort of elementary particle. Indeed, in practice this is what we now mean by an elementary particle: it is the quantum of some field that appears as an ingredient in whatever seem to be the fundamental equations of physics at any stage in our progress.

The successful uses of atomic theory described in Chapter 1 did not settle the existence of atoms in all scientists’ minds. This was in part because of the appearance in the first half of the nineteenth century of an attractive competitor, the physical theory of thermodynamics. With thermodynamics one may derive powerful results of great generality, without ever committing oneself to the existence of atoms or molecules. But thermodynamics could not do everything. This chapter describes the advent of kinetic theory, which is based on the assumption that matter consists of very large numbers of particles, and its generalization to statistical mechanics. From these, thermodynamics could be derived and, together with the atomic hypothesis, it yielded results far more powerful than could be obtained from thermodynamics alone. Even so, it was not until the appearance of direct evidence for the graininess of matter that the existence of atoms became almost universally accepted.

The serious scientific application of the atomic theory began in the eighteenth century, with calculations of the properties of gases, which had been studied experimentally since the century before. This is the topic with which we begin this chapter. Applications to chemistry and electrolysis followed in the nineteenth century, and are considered in subsequent sections. The final section of this chapter describes how the nature of atoms began to be clarified with the discovery of the electron.

This chapter covers the early years of quantum theory, a time of guesswork, inspired by problems presented by the properties of atoms and radiation and their interaction. Later, in the 1920s, this struggle led to the systematic theory known as quantum mechanics, the subject of Chapter 5. Quantum mechanics started with the problem of understanding radiation in thermal equilibrium at a non-zero temperature. It was not possible to make progress in applying quantum ideas to atoms without some understanding of what atoms are. The growth of this understanding began with the discovery of radioactivity.

Atoms were at the center of physicists’ interests in the 1920s. It was largely from the effort to understand atomic properties that modern quantum mechanics emerged in this decade. In the 1930s physicists’ concerns expanded to include the nature of atomic nuclei. The constituents of the nucleus were identified, and a start was made in learning what held them together. And as everyone knows, world history was changed in subsequent decades by the military application of nuclear physics.

Our modern understanding of atoms, molecules, solids, atomic nuclei, and elementary particles is largely based on quantum mechanics. Quantum mechanics grew in the mid-1920s out of two independent developments: the matrix mechanics of Werner and the wave mechanics of Erwin Schrödinger. For the most part this chapter follows the path of wave mechanics, which is more convenient for all but the simplest calculations. The general principles of the wave mechanical formulation of quantum mechanics are laid out and provide a basis for the discussion of spin, identical particles. and scattering processes. The general principles are supplemented with the canonical formalism to work out the Schrödinger equation for charged particles in a general electromagnetic field. The chapter ends with the unification of the approaches of wave and matrix mechanics by Paul Dirac, and a modern approach, known as Hilbert space, is briefly described.

This chapter covers the Special Theory of Relativity, introduced by Einstein in a pair of papers in 1905, the same year in which he postulated the quantization of radiation energy and showed how to use observations of diffusion to measure constants of microscopic physics. Special relativity revolutionized our ideas of space, time, and mass, and it gave the physicists of the twentieth century a paradigm for the incorporation of conditions of invariance into the fundamental principles of physics.