Editing Brownian motion (section)

==History==
[[File:PerrinPlot2.svg|thumb|Reproduced from the book of [[Jean Baptiste Perrin]], ''Les Atomes'', three tracings of the motion of colloidal particles of radius 0.53&nbsp;μm, as seen under the microscope, are displayed. Successive positions every 30 seconds are joined by straight line segments (the mesh size is 3.2&nbsp;μm).<ref>{{cite book | last = Perrin | first = Jean | year = 1914 | title = Atoms | url = https://archive.org/stream/atomsper00perruoft#page/115/mode/1up | page = 115| publisher = London : Constable }}</ref>]]

The Roman philosopher-poet [[Lucretius]]' scientific poem ''[[On the Nature of Things]]'' ({{circa|60 BC}}) has a remarkable description of the motion of [[dust]] particles in verses 113–140 from Book II. He uses this as a proof of the existence of atoms:

{{Blockquote|Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.}}

Although the mingling, tumbling motion of dust particles is caused largely by air currents, the glittering, jiggling motion of small dust particles is caused chiefly by true [[Brownian dynamics]]; Lucretius "perfectly describes and explains the Brownian movement by a wrong example".<ref>{{cite book | last = Tabor | first = D. | title = Gases, Liquids and Solids: And Other States of Matter | url = https://books.google.com/books?id=bTrJ15y2IksC&pg=PA120 | edition = 3rd | year = 1991 | publisher = Cambridge University Press | location = Cambridge | isbn = 978-0-521-40667-3 | page = 120}}</ref>

While [[Jan Ingenhousz]] described the irregular motion of [[coal]] [[dust]] particles on the surface of [[ethanol|alcohol]] in 1785, the discovery of this phenomenon is often credited to the botanist [[Robert Brown (botanist, born 1773)|Robert Brown]] in 1827. Brown was studying [[pollen]] grains of the plant ''[[Clarkia pulchella]]'' suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he was able to rule out that the motion was life-related, although its origin was yet to be explained.

The mathematics of much of stochastic analysis including the mathematics of Brownian motion was introduced by [[Louis Bachelier]] in 1900 in his PhD thesis "The theory of speculation", in which he presented an analysis of the stock and option markets. However this work was largely unknown until the 1950s.<ref>{{Cite book |last=Davis |first=Mark H. A. |title=Louis Bachelier's Theory of Speculation: The Origins of Modern Finance |last2=Bachelier |first2=Louis |last3=Etheridge |first3=Alison |date=2011 |publisher=Princeton University Press |isbn=978-1-4008-2930-9 |location=Princeton}}</ref><ref name=Morters-2001/>{{rp|33}}

[[Albert Einstein]] (in one of his [[Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen|1905 papers]]) provided an explanation of Brownian motion in terms of atoms and molecules at a time when their existence was still debated. Einstein proved the relation between the probability distribution of a Brownian particle and the diffusion equation.<ref name=Morters-2001/>{{rp|33}} These equations describing Brownian motion were subsequently verified by the experimental work of [[Jean Baptiste Perrin]] in 1908, leading to his Nobel prize.<ref name=Grigoryan-1999>{{Cite journal |last=Grigor’yan |first=Alexander |date=1999-02-19 |title=Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds |url=https://www.ams.org/bull/1999-36-02/S0273-0979-99-00776-4/ |journal=Bulletin of the American Mathematical Society |language=en |volume=36 |issue=2 |pages=135–249 |doi=10.1090/S0273-0979-99-00776-4 |issn=0273-0979|doi-access=free }}</ref> [[Norbert Wiener]] gave the first complete and rigorous mathematical analysis in 1923, leading to the underlying mathematical concept being called a [[Wiener process]].<ref name=Morters-2001>{{Cite book |last=Mörters |first=Peter |url=https://www.cambridge.org/core/product/identifier/9780511750489/type/book |title=Brownian Motion |last2=Peres |first2=Yuval |date=2001-01-01 |publisher=Cambridge University Press |isbn=978-0-521-76018-8 |edition=1 |doi=10.1017/cbo9780511750489}}</ref>

The instantaneous velocity of the Brownian motion can be defined as {{math|1=''v'' = Δ''x''/Δ''t''}}, when {{math|Δ''t'' << ''τ''}}, where {{mvar|τ}} is the momentum relaxation time. 
In 2010, the instantaneous velocity of a Brownian particle (a glass microsphere trapped in air with [[optical tweezers]]) was measured successfully. The velocity data verified the [[Maxwell–Boltzmann distribution|Maxwell–Boltzmann velocity distribution]], and the equipartition theorem for a Brownian particle.<ref name=Velocity-2010>{{cite journal | last1 = Li | first1 = Tongcang | last2 = Kheifets | first2 = Simon | last3 = Medellin | first3 = David | last4 = Raizen | first4 = Mark | year = 2010 | title = Measurement of the instantaneous velocity of a Brownian particle | journal = [[Science (journal)|Science]] | volume = 328 | issue = 5986 | pages = 1673–1675 | bibcode = 2010Sci...328.1673L | doi = 10.1126/science.1189403 | pmid = 20488989 | url = http://chaos.utexas.edu/wp-uploads/2010/06/science.1189403v1.pdf | archive-url = https://wayback.archive-it.org/all/20110331172407/http://chaos.utexas.edu/wp-uploads/2010/06/science.1189403v1.pdf | url-status = dead | archive-date = 2011-03-31 | citeseerx = 10.1.1.167.8245 | s2cid = 45828908 }}</ref>