Brownian Motion
Observe the random walk of a macroscopic "pollen" particle suspended in a fluid. Its erratic motion is driven by the relentless, invisible bombardment of countless smaller, fast-moving fluid molecules.
The Physics of Brownian Motion
In 1827, botanist Robert Brown observed pollen grains jiggling erratically in water under a microscope. He initially thought they were alive, but later found that inanimate dust particles did the same thing. This phenomenon became known as Brownian motion.
Einstein's Explanation
In 1905, Albert Einstein provided the theoretical explanation that definitively proved the existence of atoms and molecules. He showed that the visible pollen grain was being constantly bombarded from all sides by invisible, rapidly moving water molecules.
Because the impacts are random, they don't perfectly cancel out at any given moment. This slight imbalance of forces pushes the pollen grain in a random direction, causing it to perform a random walk.
Mathematical Description
Einstein derived a formula relating the mean squared displacement $\langle x^2 \rangle$ of the particle to time $t$ and temperature $T$:
Where $D$ is the diffusion coefficient, $k_B$ is the Boltzmann constant, $T$ is absolute temperature, $\eta$ is the fluid viscosity, and $r$ is the particle radius. This was one of the first times a macroscopic observable (diffusion) was directly linked to microscopic atomic properties.