In 1905, atoms were still controversial. Not in the way that new scientific ideas are usually controversial, argued over at conferences and then gradually accepted. Atoms were controversial in a deeper way. Some of the most respected physicists and chemists in the world genuinely believed they did not exist.
Ernst Mach, the Austrian physicist and philosopher whose work influenced Einstein himself, dismissed atoms as a “mental artifice.” Wilhelm Ostwald, who would win the Nobel Prize in Chemistry in 1909, argued that energy, not matter, was the fundamental reality, and that atoms were just a convenient fiction for balancing chemical equations. These were not fringe figures. They represented a serious intellectual tradition that demanded direct evidence before accepting invisible entities.
The evidence arrived in Einstein’s second paper of his miracle year. In May 1905, he submitted a paper titled “On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat.” The title was dry. The content was revolutionary. Einstein had figured out how to make the invisible visible, not by building a better microscope, but by doing mathematics.
Robert Brown and the Dancing Pollen
The story begins 78 years earlier, in the summer of 1827, with a Scottish botanist named Robert Brown. Brown was examining pollen grains from the plant Clarkia pulchella under a microscope when he noticed something strange. Tiny particles ejected from the pollen grains were jittering around in the water, moving in a constant, seemingly random dance.
Brown’s first thought was that the particles might be alive. Pollen, after all, is involved in reproduction, perhaps these dancing specks were some kind of primitive life form. But when he repeated the experiment with pollen from plants that had been dead for decades (including specimens from a herbarium collection over a century old), the jittering was identical. Dead pollen danced just as vigorously as fresh pollen.
Then he tried inorganic materials. Tiny fragments of ground-up glass, granite, even a piece of the Sphinx (Brown was well-connected) all showed the same erratic motion when suspended in water. Whatever was causing the dance, it had nothing to do with life.
Brown published his observations but offered no explanation. For the next seven decades, Brownian motion, as it came to be called, remained a curiosity. Various explanations were proposed: convection currents, electrical effects, temperature gradients, vibrations in the building. None of them held up. The motion was too persistent, too random, too indifferent to external conditions. You could isolate the sample from vibration, wait for temperature to equilibrate perfectly, and the particles still danced.
The Atomic Hypothesis
By the mid-1800s, some scientists had a pretty good guess about what was happening. If matter is made of atoms and molecules in constant thermal motion, then a tiny particle suspended in water is being bombarded from all sides by water molecules. Most of the time, the impacts from different directions roughly cancel out. But because the particle is so small, there are random fluctuations, sometimes a few more molecules hit from the left than from the right, and the particle lurches sideways. A moment later, the imbalance goes the other way. The result is a continuous, unpredictable zigzag.
This qualitative explanation was proposed by several people, but it remained handwavy. The anti-atomists were unimpressed. “You claim invisible particles are pushing things around,” they essentially said. “Show me the math. Give me a prediction I can test. Otherwise, this is just storytelling.”
They had a point. In science, a qualitative story is not enough. You need quantitative predictions, numbers that can be measured and either confirmed or refuted. Without them, the atomic explanation of Brownian motion was just a plausible narrative, no more rigorous than the convection current theory or the vibration theory.
Einstein’s Calculation
This is where Einstein came in. He approached the problem with a characteristic combination of physical intuition and mathematical precision. His paper did not start from Brownian motion at all, it started from the kinetic theory of heat and asked: if atoms are real and behave as the theory says, what observable consequences should follow?
Einstein imagined a large number of tiny particles suspended in a fluid. Each particle is being hit by molecules from all sides. He treated the problem statistically, not trying to track individual molecular collisions (which would be hopelessly complicated) but instead asking about the average behavior of many particles over time.
His central result was elegant. The mean squared displacement of a suspended particle, the average of the square of the distance it wanders from its starting point, grows linearly with time. A particle that has been wandering for four times as long will, on average, be twice as far from where it started (not four times, because the random walk keeps doubling back on itself). The precise relationship depended on:
- The temperature of the fluid (hotter means more vigorous molecular bombardment)
- The viscosity of the fluid (thicker fluids slow the particles down)
- The size of the suspended particles (smaller particles are pushed around more easily)
- Avogadro’s number, the number of molecules in a mole of substance
That last item was the key. Avogadro’s number appears in Einstein’s formula, which means you can measure the displacement of particles under a microscope, plug the numbers into Einstein’s equation, and calculate how many molecules are in a mole. If you get a sensible answer, a number consistent with other estimates, then the atomic theory is confirmed. If you get nonsense, the theory is wrong.
Einstein even told experimentalists exactly what to look for. He calculated that particles about one thousandth of a millimeter in diameter, suspended in water at room temperature, should move about six thousandths of a millimeter in one minute. This was well within the range of existing microscopes. He was essentially handing experimentalists a recipe.
Perrin’s Beautiful Experiments
The French physicist Jean Perrin took up the challenge with extraordinary skill and patience. Between 1908 and 1913, he and his students performed a series of meticulous experiments that rank among the most beautiful in the history of physics.
Perrin’s approach was painstaking. He prepared uniform suspensions of tiny particles (gamboge resin and mastic) of known, consistent sizes. He tracked individual particles through a microscope, recording their positions at regular time intervals. He measured how the density of suspended particles decreased with height in a vertical column, the “sedimentation equilibrium”, which Einstein’s theory also predicted.
The results were stunning. Perrin’s measurements of Brownian motion matched Einstein’s predictions precisely. More importantly, every different method of measuring, whether tracking horizontal displacement, vertical sedimentation, or rotational diffusion, gave the same value for Avogadro’s number. The consistency was overwhelming.
Perrin published his definitive results in his 1913 book Les Atomes, which laid out the evidence with such clarity and force that the remaining opposition crumbled. Ostwald publicly changed his mind. Mach went to his grave unconvinced, but he found himself increasingly alone. Perrin won the Nobel Prize in Physics in 1926, specifically for his work confirming the atomic nature of matter through Brownian motion studies.
Why This Mattered So Much
It is tempting to think of the debate over atoms as a strange historical quirk, of course atoms are real, everyone knows that now. But the anti-atomists were not stupid, and their demand for evidence was actually good scientific practice. They were insisting on a standard that science should insist on: do not accept invisible entities without proof that they produce visible, measurable effects.
Einstein’s paper met that standard. He did not prove atoms exist by showing you a photograph of one (that would not come until the scanning tunneling microscope in the 1980s). He proved atoms exist by showing that their existence has unavoidable, mathematically precise, experimentally testable consequences in the visible world. If atoms are real, then Brownian motion must look like this, with these specific numbers. The numbers matched.
This methodological approach, using statistical mechanics to bridge the gap between the microscopic world of atoms and the macroscopic world of observable phenomena. It became a cornerstone of 20th-century physics. It is the same logic that underlies thermodynamics, statistical mechanics, and much of modern chemistry and molecular biology.
The Random Walk and Beyond
Einstein’s mathematical treatment of Brownian motion also had consequences far beyond physics. His description of random walks, the mathematical structure of a particle taking random steps in random directions, turned out to apply to an astonishing range of phenomena:
- Stock market prices and financial modeling (the Black-Scholes equation for option pricing is a direct descendant of Einstein’s diffusion equation)
- The spread of diseases through populations
- The diffusion of molecules through cell membranes, fundamental to biology
- The behavior of polymers in solution, where long-chain molecules coil and uncoil like random walks in three dimensions
- Ecology and animal foraging patterns, where organisms sometimes follow paths that resemble Brownian motion
The mathematics Einstein developed for pollen grains jittering in water now runs Wall Street trading algorithms, drug delivery models, and climate simulations. Few scientific papers have had such a wide reach across disciplines.
Marie Curie and the Atomic World
Einstein’s proof that atoms exist arrived at a moment when the atomic world was revealing itself in other dramatic ways. Marie Curie’s research on radioactivity, conducted in the years just before Einstein’s paper, was demonstrating that atoms were not the simple, indivisible spheres that the word “atom” (from the Greek for “uncuttable”) implied. Atoms had internal structure. They could decay, emit radiation, and transform into other elements.
Curie’s meticulous experimental work, documented in her doctoral thesis, provided another powerful strand of evidence for the reality of the atomic world. Her measurements of radioactive emissions gave independent estimates of atomic quantities that aligned with Einstein’s and Perrin’s results. The Kronecker Wallis edition of Marie Curie’s Thesis preserves this foundational work in a form that honors both its scientific content and its historical significance.
From Dancing Pollen to Settled Science
Einstein’s Brownian motion paper is sometimes overshadowed by his more famous 1905 contributions, the photoelectric effect, special relativity, E=mc². It lacks the drama of relativity’s assault on space and time, or the practical implications of the photoelectric effect. But in some ways, it may have been his most important paper of that year.
It settled a fundamental question about the nature of reality. Are atoms real? Is matter truly made of tiny, discrete particles, or is that just a useful model? After Einstein’s paper and Perrin’s experiments, the answer was no longer a matter of opinion or philosophical preference. It was an empirical fact, supported by precise measurements that anyone with a good microscope could reproduce.
The broader framework of Einstein’s 1905 work, all four revolutionary papers, is reflected in the Kronecker Wallis edition of Einstein’s Relativity, which captures the later development of his ideas about space, time, and gravity. And the quantum revolution that Einstein helped ignite, building on Planck’s pioneering work, would go on to reveal an atomic world far stranger and more wonderful than even Einstein imagined.
The Jitter That Proved a Theory
There is something poetic about how the existence of atoms was ultimately established. Not through a dramatic experiment with expensive equipment. Not through a theoretical breakthrough of dazzling mathematical complexity. But through the patient observation of tiny specks dancing in a drop of water, a phenomenon first noticed by a botanist looking at pollen, explained by a patent clerk doing math on his lunch break, and confirmed by a physicist with a microscope and a great deal of patience.
Robert Brown saw the dance in 1827 and had no idea what caused it. Einstein explained the dance in 1905 without ever having observed it himself (he worked purely from theory). Perrin measured the dance between 1908 and 1913 and found that it matched the theory perfectly. Three very different scientists, three very different approaches, converging on a single truth: the world is made of atoms, and they never stop moving.
The next time you see dust motes drifting in a shaft of sunlight, watch their paths. They do not fall straight down. They wander, jitter, drift sideways, pause, and wander again. You are watching the air’s molecules push them around, one collision at a time. You are watching Brownian motion. You are watching the proof that atoms are real.
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