Random walks span a gamut from watching winnings fluctuate in games of chance, to simple brownian diffusion, to modern studies of nonlinear dynamics. As with many important concepts in twentieth-century physics, random walks had a boost from Einstein who, in 1905, was focusing on brownian motion. In 1785, Jan Ingenhauz had placed charcoal powder on an alcohol film and saw the grains move randomly; in 1828, the botanist Robert Brown had reported erratic dancing of small particles in fluids at rest. Einstein considered these fluids to be composed of discrete molecules whose many collisions with a brownian particle caused them to jump in random directions — a random walk. His analysis not only explained brownian motion, but also bolstered the case for the existence of atoms (which at that time was not universally accepted).

Einstein's approach was founded on the principal that noise, like other natural phenomena, is an expression of physical law. He showed that the brownian particle obeys the diffusion equation; his formula for the mean-squared displacement involved Avogadro's number as a factor in the diffusion constant. Jean Perrin's careful observations of brownian motion allowed him to calculate Avogadro's number in this manner and hence to win the 1926 Nobel prize.

Enjoying our latest content?
Log in or create an account to continue

  • Access the most recent journalism from Nature's award-winning team
  • Explore the latest features & opinion covering groundbreaking research
Access through your institution

or

Sign in or create an account
Continue with Google
Continue with ORCiD