Drop a single drop of ink into a glass of clear water and leave it alone, and even though no one stirs it, the ink slowly spreads until it tints all the water. That is because something invisible is constantly pushing the ink around. The phenomenon that first brought this invisible motion into plain view is Brownian motion.
Put simply, Brownian motion is ‘the irregular movement of tiny particles suspended in a liquid or gas as they constantly collide with the molecules around them.’ This tiny jiggling became decisive evidence that atoms and molecules really exist.
This article explains, in easy-to-understand terms, how Brownian motion was discovered and what it is, Einstein's explanation of how it works, Perrin's experiments that proved atoms exist, and how it is used today.
The Discovery and Principles of Brownian Motion
What Is Brownian Motion?
Brownian motion is named after the Scottish botanist Robert Brown. In 1827, while observing pollen suspended in water under a microscope, he noticed that the minute particles released from the pollen grains kept moving restlessly this way and that, as if trembling.
At first it was natural to suspect that this motion might be a sign of life. But Brown confirmed that the same movement appeared not only in old plant specimens but also in finely ground powders of glass and rock. That showed the motion was not caused by life, yet what actually moved the particles remained a mystery for more than 70 years.
- Randomness: The direction and distance of movement change unpredictably from moment to moment.
- Persistence: No matter how much time passes, the motion never stops.
- Temperature dependence: The higher the temperature, the more vigorous the motion.
- Size dependence: The smaller the particle, the more it jiggles.
How Einstein Explained Brownian Motion
The person who solved the mystery was a young Albert Einstein in 1905. In the very same year he published his papers on the photoelectric effect and special relativity, he also put out a paper explaining Brownian motion.
(1) Collisions with invisible molecules
Water molecules are too small to see even with a microscope, but heat keeps them moving rapidly and constantly. A tiny particle floating in water is struck from all sides by countless water molecules every second.
(2) Imbalance created by chance
If collisions happened equally from every direction, the particle would not move. But at any given instant, it happens to be hit a bit more on one side, and that small imbalance pushes the particle.
(3) Distance grows with the square root of time
Einstein expressed in an equation how far particles spread out in one direction. The mean squared displacement equals 2Dt, where D is the diffusion coefficient and t is time. So even when four times as much time passes, a particle spreads on average only twice as far. It is like a drunkard's zigzag walk, wandering back and forth and getting only a little farther away.
(4) Temperature and size determine the motion
Einstein also expressed the diffusion coefficient as D = kT / (6πηr), where T is the temperature, η is the viscosity of the liquid, r is the radius of the particle, and k is the Boltzmann constant. This single line captures the observations that the motion becomes more vigorous at higher temperatures and more sluggish when the liquid is thicker or the particle is larger. Large objects such as a ball do not jiggle in water because the collisions from all sides cancel out almost perfectly.
Around the same time, the Polish physicist Marian Smoluchowski independently reached the same conclusion in 1906.
Perrin's Experiments That Proved Atoms Exist
As late as the early 20th century, some scientists still regarded atoms as merely a hypothesis used to make calculations convenient and considered it uncertain whether they actually existed. Einstein's theory opened the way to settle this debate by experiment.
Starting around 1908, the French physicist Jean Perrin prepared tiny particles of uniform size and recorded their positions under a microscope at regular time intervals. The results agreed well with Einstein's predictions, and on that basis he obtained a value for Avogadro's number, the number of particles in one mole of a substance, close to the value known today (about 6.02 × 10²³).
As values obtained by several independent methods came out close to one another, the voices doubting that atoms were real lost their force. Perrin received the 1926 Nobel Prize in Physics for this work.
Three Fields Where Brownian Motion Is Used
Beyond physics textbooks, Brownian motion has become the basic framework for describing ‘random motion’ in many fields.
[Field 1] Life and chemistry
Diffusion, through which nutrients and signaling molecules spread inside cells, arises from the Brownian motion of molecules. The same principle explains why sugar in unstirred coffee eventually spreads evenly.
[Field 2] Precision measurement
By measuring how much particles jiggle, you can work backward to calculate their size. Instruments that measure the size of nanoparticles and proteins use this principle.
[Field 3] Finance
In 1900, the French mathematician Louis Bachelier described the movement of stock prices as a random walk like Brownian motion. This idea later became the foundation of financial theories used to price options.
Starting as a tiny jiggle seen under a microscope, Brownian motion grew into a theory that proved the existence of atoms and explains movement everywhere from living cells to financial markets. The motion of the smallest things turned out to be one of the biggest keys to understanding the world.
Stopping to look closely at small movements that seem unremarkable: that is the first step of discovery into the invisible world.
