When staring into a cup of freshly-brewed tea, you may notice that all the little tea leaf particles are moving around inside the cup. You may even be tempted to ask yourself the question, 'Why, exactly, are they swirling around?'.

Way back in 1785, Jan Ingenhousz noticed the movement of small particles suspended in a liquid. However, as is often the case in scientific circles, very little attention was paid to the discovery. Then, in 1827, the English botanist Robert Brown noticed that pollen grains suspended in water jiggled about under the close scrutiny of a microscope. Brown made a bigger fuss about this phenomenon, and in honour of his discovery¹, the phenomenon was named Brownian Motion. The discovery of this phenomenon has greatly contributed to the study of physics, chemistry and mathematics. It was used as the basis to power the infinite improbability drive in Douglas Adams' book, The Hitchhiker's Guide to the Galaxy.

Experiments showed that the motion became more rapid and the particles moved farther in a given time interval when the temperature was raised, when the viscosity of the fluid was lowered, or when the average particle size was reduced. All of these discoveries helped to develop the kinetic theory of gasses which states something to the effect that the atoms or molecules that make up a liquid or gas are in constant thermal motion, and their velocity distribution is determined by the temperature of the system. Thus, the particle in the liquid really is moving because it is being constantly bombarded with other particles that are far too small for the eye to see.

The first mathematical theory of Brownian motion was developed independently by both Marian Smoluchowski and Albert Einstein (1879 - 1955)² in 1905. Einstein received a Nobel Prize³ for this work, although Smoluchowski received absolutely nothing. The theory states that a particle experiencing Brownian Motion moves at a speed that's the square of the time elapsed since moving away from its starting point. This is called the diffusion constant. Einstein derived this fact using kinetic theory and expressed it in terms of the fundamental parameters of particles and of liquid. Jean-Baptiste Perin⁴ then used this work to derive Boltzmann's Constant which is 1.3807 x 10^-23 JK^-1.

Brownian trajectories are continuous but of infinite length between any two points. This hints at the fractal nature of the 'reality' we live in. One should also note that very large objects are still subject to the forces that cause Brownian Motion, but do not move enough to be noticed. For instance, your car does not drift from its parking spot at a rate proportional to the square of the time elapsed since you parked it. Imagine if it did; you would have to remember when you parked it and calculate how far it could have gone in order to know which area to search for it in. Parking lots would certainly be a far scarier place.