First described in 1827 by the Scottish botanist who also named the cell nucleus (1827)
Robert Brown, watching particles from pollen of Clarkia pulchella
Science · Physics
Brownian motion
1827; explained 1905
Physics — statistical mechanics
The restless, random jiggling of tiny particles suspended in a fluid, caused by the ceaseless bombardment of the particles by the fluid's own molecules. The Scottish botanist Robert Brown described it in 1827 while watching particles ejected from pollen grains of the plant Clarkia pulchella, and showed that even ground-up rock behaved the same way, so it was not a sign of life. Einstein gave the quantitative theory in 1905, Marian Smoluchowski independently in 1906, and Jean Perrin's experiments confirmed it — which finally convinced the remaining sceptics that atoms exist. In mathematics it became the Wiener process, the foundation of stochastic calculus and the Black–Scholes model.
How to spot them
- ▸First described in 1827 by a Scottish botanist watching pollen grains under a microscope
- ▸The 1905 Einstein paper that is not relativity and not the photoelectric effect
- ▸The experimental proof that atoms and molecules really exist, confirmed by Jean Perrin
- ▸Known to mathematicians as the Wiener process, and to finance as the random walk behind Black–Scholes
Key facts
The third of Einstein's 1905 papers, alongside relativity and the light quantum (1905)
It predicted how far a suspended particle drifts in a given time
Jean Perrin's experiments won him the 1926 Nobel Prize and settled the reality of atoms (1908–09)
He measured Avogadro's number from the jiggling
Named in mathematics after Norbert Wiener, who put it on a rigorous footing in 1923 (1923)
The Wiener process, the cornerstone of stochastic calculus
The random walk underlying the Black–Scholes option-pricing formula (1973)
Anticipated by Louis Bachelier's 1900 thesis on the Paris Bourse
Brown showed ground-up rock and even a fragment of the Sphinx did the same, ruling out a vital force
The decisive control experiment against a 'life force' explanation
Key ideas
- A speck of dust is hit by fluid molecules from every direction; at any instant the hits do not quite cancel, and the imbalance shoves the speck about.
- Einstein's key insight was statistical: the average squared displacement grows in proportion to time, so measuring the drift of visible particles yields the size and number of invisible molecules.
Quick-fire facts
- •Named for Robert Brown (1773–1858), Scottish botanist, who observed it in 1827 and published in 1828
- •He was watching particles ejected from pollen grains of Clarkia pulchella suspended in water — not the pollen grains themselves, a common misreading
- •Brown also named the cell nucleus, and sailed as naturalist on Matthew Flinders's voyage to Australia
- •The Dutch physician Jan Ingenhousz had described similar motion in coal dust on alcohol in 1785
- •Einstein's paper of May 1905 was one of his four annus mirabilis papers; he did not know it explained Brown's observation when he wrote it
- •Marian Smoluchowski published an independent theory in 1906
- •Jean Perrin's confirming experiments earned the 1926 Nobel Prize in Physics and effectively ended scientific doubt about atoms
- •The mean squared displacement grows linearly with time, not the distance itself — so a particle wanders slowly
- •Rigorously formalised by Norbert Wiener in 1923; the mathematical object is the Wiener process
- •Louis Bachelier applied the same mathematics to share prices in his 1900 thesis, five years before Einstein
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Sources
- APS News, American Physical Society — August 1827: Robert Brown and Molecular Motion in a Pollen Grain
- The Nobel Foundation — The Nobel Prize in Physics 1926 Jean Perrin, for work on the discontinuous structure of matter