Celebrating Einstein

"Seeing the Wind"


C.  Checking the idea against reality

From the preceding equation, Einstein deduced that, if the molecular theory of heat were true, and if the existing estimates of the number of particles in one mole were at least in the right ballpark, particles that are one micrometer wide (one millionth of a meter wide) and suspended in water at room temperature should move about 0.8 micrometers in one second, or 6 micrometers in 60 seconds.  The particles and their motion would thus be large enough to see with the kinds of microscopes that were available then.  On the other hand, if the size of one mole weren't assumed, but the particles' motions could be measured using a microscope, the motions could be used to determine more precisely than ever before how many molecules made one mole, and therefore determine the actual mass of any known molecule.

Several people took up the challenge of doing exactly that.  Within a few years, Jean Baptiste Perrin, with students of his at the Sorbonne, made the most careful and successful of these early measurements, and calculated that one mole contained 64 x 1022 units.  By that time, Einstein had also figured out how suspended particles would be rotated by the impacts of fluid molecules, but he didn't expect anyone to be able to measure the rotation; to his surprise, Perrin succeeded in this too. Later methods of determining the size of one mole have led to smaller numbers.

The exact number of units in a mole of substance can be calculated from other quantities only if all the other quantities are exactly measured themselves.  But we can partially test the theory behind Einstein's formula even without all these measurements.  Einstein's formula implies that the average square of a suspended particle's diffusion distance is proportional to the time it spends diffusing.  This proportionality is actually observed.

As Einstein himself noted in the Autobiographical Notes he wrote when he was 67 years old,

The agreement of these considerations with experience together with Planck's determination of the true molecular size from the law of radiation (for high temperatures) convinced the sceptics, who were quite numerous at that time . of the reality of atoms."

We noted one cause for such skepticism at the beginning of this article:  other experiments, in which matter behaved differently from what people expected of atoms.  Whenever theory and experiment disagree, it proves that something is wrong with the theory, although the disagreement by itself doesn't tell you exactly what's wrong with it.  In this case, the problem was not that atoms don't exist, but that people's assumptions about the nature of atoms were faulty.

A hundred years ago, physicists who tried to understand atoms were like visitors to a foreign country.  Foreign customs may make little sense at first, if one's initial understanding of human nature is based only on the habits of people in one's own country.  On the other hand, if one starts with both countries' customs, and infers facts about human nature from those instead of trying to make sense of either culture in terms of the other, one may arrive at a deeper understanding of human nature.  A hundred years ago, physicists observing phenomena that didn't fit their ideas of "atomic" nature were getting a taste of things that would eventually lead them to a more profound understanding of atoms.  But that's another story for another time.

Next article: Another Side of Light

References, Links, and Comments:

Einstein's Explanation of Brownian Motion" [exit federal site] ("Fowler's Physics Applets, [exit federal site] University of Virginia
"This Java applet is a simple demonstration of Einstein's explanation for Brownian Motion. It shows little particles batting about a more massive one and what it would look like if you could see only the massive one through a microscope."

Investigations on the Theory of Brownian Movement by Albert Einstein, edited by Reinhold Fürth, translated by A.D. Cowper.
Untersuchungen über die Theorie der "Brownschen Bewegung" by Albert Einstein, edited by Reinhold Fürth.
Collections (English translation, original German) of five papers by Einstein on Brownian motion, including his 1905 paper "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat".

Atom–from hypothesis to certainty [exit federal site] by Ales Lacina, in Physics Education, volume 34, number 6 (November 1999), pp. 397-402.
Brownian motion was one of the crucial demonstrations that atoms exist, but isn't the only one. This article traces the history of the concept of atoms from early speculation to current proof.

"History and progress in the accurate determination of the Avogadro constant" [exit federal site] by Peter Becker, in Reports on Progress in Physics, volume 64, number 12 (December 2001), pp. 1945-2008.
The number of entities per mole of something is known as the Avogadro constant, after Amedeo Avogadro. Page 1952 in this journal article shows a table of 35 different experimental determinations made during the years 1865 to 2001, and illustrates the increasing precision and accuracy of the results. Two of the determinations listed were based on Brownian motion: Jean Baptiste Perrin's (published 1909), and Harvey Fletcher's (published 1911). (Note: the table contains a typographical error, giving Fletcher's first initial as "T"; the reference on page 2006 correctly shows "H".)

Brownian motion using video capture" [exit federal site] by Reese Salmon, Candace Robbins and Kyle Forinash, in European Journal of Physics, volume 23, number 3 (May 2002), pp. 249-253.

Measuring Boltzmann's constant using video microscopy of Brownian motion" [exit federal site] by Paul Nakroshis, Matthew Amoroso, Jason Legere, and Christian Smith, in American Journal of Physics, volume 71, number 6 (June 2003), pp. 568-573.
Upper-level undergraduate laboratory experiments.

The Nobel Prize in Physics 1926" [exit federal site]
Jean Baptiste Perrin performed many experiments that demonstrated the reality of molecules besides those involving Brownian motion, and was awarded the Nobel Prize "for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium".  His Nobel Lecture [exit federal site] reviews his own and others' determinations of Avogadro's constant using various methods.

The Rise of the New Physics by Abraham D'Abro.
A detailed description in two volumes of the history of physical theory from its beginnings to the mid-20th century.  The last two chapters of Volume 1 are on "Thermodynamics" and "The Kinetic Theory of Gases".

Autobiographical Notes: A Centennial Edition by Albert Einstein; Paul Arthur Schlipp, translator and editor.  Corrected version of "Autobiographisches-Autobiographical Notes" published in Albert Einstein:  Philosopher-Scientist.
An autobiography that concentrates on the ideas Einstein was occupied with over his lifetime rather than other recollections.  In the original German with English translations on facing pages.  About halfway through, Einstein discussed the aim of his Brownian-motion analysis.


Prepared by Dr. William Watson, Physicist
DOE Office of Scientific and Technical Information
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