The Great Atom Debate by Paul Halpern is a truly fun dual biography about two eminent 19th-century scientists who had a long-running, almost cutthroat rivalry centered on the question of whether atoms exist. Ernst Mach and Ludwig Boltzmann were friends and mutually respectful colleagues. But when it came to the question of whether atoms were real, they functioned—loudly, and in public—as archenemies. Both held prestigious faculty positions at the University of Vienna, Boltzmann as a professor of theoretical physics and Mach in a newly created chair in “Philosophy, in particular the History and Theory of the Inductive Sciences.”

Routinely, these two chums made conversational sparks fly.

Mach believed that scientific reasoning should confine itself to phenomena that can be directly observed. Although he was deeply skeptical of speculative physics, he recognized that Newton’s ideas didn’t adequately address every problem confronting Industrial Age scientists. One was why heat traveled so readily from a steam pipe to a colder, immediately adjacent piece of equipment.

Mach thought that the idea of the atom was a useful construct in theorizing about such matters. He just didn’t believe that atoms had been demonstrated to actually exist, and he didn’t think that his fellow physicists should waste their time or their students’ time insisting on the existence of tiny particles that no one could see.

Where he succeeded spectacularly as a theoretician and experimenter was in his work with shock waves and supersonic motion. He was able to photograph shock waves produced by projectiles traveling at supersonic speed. Mach’s name has survived into the 21st century in what we now call the Mach number: the ratio between an object’s speed and the local speed of sound. Perhaps a simpler way to explain it is this: When Tom Cruise claims that his jet is traveling at Mach 2, what he’s really saying is, “My jet is traveling at twice the speed that sound is traveling through the air around me right now.” (Halpern makes a strong Tom Cruise reference in his book.)

Of course, Mach did not live long enough to see what fun Hollywood would eventually have with his number. Also, to his credit—and despite his ability to argue with enormous ego in favor of his limited view of physics—Mach didn’t believe there is any such thing as an independent, permanent ego. Instead, there are streams of experience. Maybe it’s fitting, then, that Mach didn’t name his speed-of-sound number after himself. The term “Mach number” was coined in his honor in 1929, thirteen years after his death—and long after his anti-atomist views had begun losing ground in physics.

Having taken a statistical approach to physics, Ludwig Boltzmann is best known today for his work in thermodynamics and entropy. Boltzmann approached the problem of heat traveling from hot objects to immediately adjacent cold ones by speculating that heat is the motion of enormous numbers of entirely invisible atoms and molecules. The atoms and molecules of a hot object move around more energetically than do the atoms and molecules of a cold one. Bouncing off the slower particles, the fast-moving ones transfer some of their energy to them. The hot ones cool as the cold ones warm.

Regarding entropy, he theorized that, over time, nature tends to move particles from less probable, highly organized arrangements to more probable, messy ones.

In any race against Mach for reputational longevity, Boltzmann would have won, hands down. Yes, the name “Mach” is used on a daily basis by test pilots and movie stars. But Boltzmann’s name is on an impressive list of equations, laws, distributions, constants, and concepts:

  • Boltzmann equation — describes statistically how particles in a gas move and collide.
  • Boltzmann constant — connects temperature with energy at the level of individual particles.
  • Boltzmann entropy formula — connects entropy to the number of possible microscopic arrangements of a system.
  • Boltzmann distribution — describes how particles are distributed among different possible energy states.
  • Boltzmann factor — the mathematical factor underlying that distribution.
  • Maxwell–Boltzmann distribution — describes the range of speeds or energies among particles in a gas.

Boltzmann was a colorful guy. He would chase his bowling ball down the alley. He told fascinating stories. He was a virtuoso pianist. He seems, however, to have had longstanding problems with depression and anxiety. In 1906, he was on vacation with his family. While his wife and daughter were at the beach, he hanged himself in his hotel room. He left no note, and people have long speculated that he had been made weary by his battles over atomic theory.

But the scientific tide was already beginning to turn. Einstein’s 1905 work on Brownian motion had shown how the atomic hypothesis could be subjected to quantitative experimental testing. Within a few years, Jean Perrin’s experiments would provide powerful empirical evidence for the existence of atoms. The pendulum of scientific opinion was swinging away from Mach and toward Boltzmann.

I won’t tell you more because I don’t want to spoil your reading fun. Paul Halpern’s The Great Atom Debate is a dual biography that should be of interest even to people who don’t care a whit about physics but love a good story, especially one showcasing two fascinating, driven characters.

After all, it’s set in Vienna close to the turn of the 20th century. This was Sigmund Freud’s era, and that of the painter Gustav Klimt and the composer Gustav Mahler. Physicists, philosophers, physicians, artists, and musicians were dismantling old ideas about matter, mind, art, and reality while they constructed new ones.

Truly, call in the movie producers!

The Great Atom Debate: Enst Mach, Ludwig Boltzmann, and the Battle for the Essence of Reality By Paul Halpern Basic Books Publication Date: December 1, 2026 (though pre-order pages are already available at online retailers and at the Basic Books site) 336 pages ISBN 9781541607224 Hardcover $32.00