The background of Einstein’s 1905 Brownian motion paper is discussed, including the work of people like Brown, Boltzmann, and Bachelier. The paper is discussed as is its aftermath. The question is raised as to whether atoms exist.

1.
A.
Einstein
, “
Die von der molekularkinetischen Theorie der Wärme gefordete Bewegung von der ruhenden Flüssigkeiten suspendierten Teilchen
,”
Ann. Phys.
17
,
549
560
(
1905
).
2.
A.
Einstein
, “
On the electrodynamics of moving bodies
,”
Ann. Phys.
17
(
10
),
891
921
(
1905
).
3.
These attitudes are discussed by Gerald Holton, “
Einstein and the crucial Experiment
,”
Am. J. Phys.
37
,
968
82
(
1969
). Einstein himself gave various responses, but he insisted that the experiment played no role in his discovery of relativity.
4.

There are three English translations of this paper known to me. Einstein’s Miraculous Year, edited and introduced by John Stachel (Princeton University Press, Princeton, NJ, 1998); Albert Einstein: Investigations on the Theory of the Brownian Movement, edited by R. Fürth (Dover Publications, Mineola, NY, 1956); and The Collected Papers of Albert Einstein, translated by Anna Beck (Princeton University Press, Princeton, NJ, 1989), Vol. 2. I will use the translations in Stachel. The quotation can be found on p. 85.

5.
M.
von Smoluchowski
, “
Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen (On the kinetic theory of Brownian motion and their suspensions)
,”
Ann. Phys.
21
,
756
780
(
1906
). I am grateful to Kryzsztof Fialkowski of the Jagiellonian University in Krakow, where Smoluchowski taught at the end of his career, and who made an electronic archive of Smoluchowski’s papers, for sending me this paper. I am also grateful to Helmut Rechenberg for sending me a copy from the Annalen.
6.
Albert Einstein: Philosopher-Scientist
, edited by
Paul
Arthur Schilpp
(
MJF Books
, NY,
1970
), p.
19
.
7.
Ludwig
Boltzmann
,
Lectures on Gas Theory
, translated by
Stephen G.
Brush
(
Dover Publications
, NY,
1995
), p.
27
.
8.

Reference 7, p. 216.

9.

Reference 7, p. 318.

10.
Ernst
Mach
,
The Science of Mechanics
(
The Open Court Publishing Company
, Lasalle, Illinois,
1960
).
11.
This quotation along with a brief profile of Mach can be found in my
Cranks, Quarks and the Cosmos
(
Basic Books
, NY,
1993
). Both quotations can be found on p.
34
.
12.
For a discussion of these issues, see
Thomas S.
Kuhn
,
Black-Body Theory and the Quantum Discontinuity, 1894-1912
(
The University of Chicago Press
, Chicago,
1978
).
13.
H.
Poincare’
, “
Sur le problème des trois corps et les équations de la dynamique
,”
Acta Math.
13
,
1
270
(
1890
).
14.
See, for example, ⟨en.wikipedia.org/wiki/Brownian_Motion⟩, and references therein.
15.
Robert
Brown
, “
A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies
,”
Philos. Mag.
4
,
161
173
(
1828
).
16.
Robert
Brown
, “
Additional remarks on active molecules
,” privately printed (
1829
).
17.
This reference to
K.
von Nägeli
,
Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl.
9
,
389
453
(
1879
),
and others, can be found in
Jurgen
Renn
, “
Einstein’s invention of Brownian motion
,”
Ann. Phys.
14
, Supplement, 23–37 (
2005
).
18.
F. M.
Exner
, “
Notiz zu Brown’s Molecularbewegung,
Ann. Phys.
2
,
843
847
(
1900
).
19.
A.
Einstein
, “
Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik (Kinetic theory of the heat equilibrium and the second fundamental theorem of the thermodynamics)
,”
Ann. Phys.
4
(
9
),
417
433
(
1902
);
A.
Einstein
, “
Eine Theorie der Grundlagen der Thermodynamik (A theory on the basics of thermodynamics)
,”
Ann. Phys.
4
(
11
),
170
187
(
1903
).
20.

I am grateful to Arthur Miller for supplying this quotation.

21.
A.
Einstein
, “
Algemeine molekulare Theorie der Wärme (The general molecular theory of heat)
,”
Ann. Phys.
4
(
14
),
354
362
(
1904
).
22.

Reference 1, Stachel, p. 71.

23.

Reference 7, pp. 58

24.

This relation can be found in Gibbs’s Elementary Principles in Statistical Mechanics which was published in 1901. In the Ox Bow Press edition (Ox Bow Press, Woodbridge, Connecticut, 1981), the relation is on p. 72. Gibbs applied it to a Maxwell gas for which E¯=nkT. He did not consider radiation.

25.

In modern notation E¯=v4cσT4, where σ=5.670×108wattsm2K4

26.

Reference 1, Stachel, p. 77.

27.
The title of Einstein’s thesis is “
Eine neue Bestimmung der Moleküldimensionen (A new determination of molecular dimensions)
.” It was published in
Ann. Phys.
4
(
19
),
289
306
(
1906
).
28.

Reference 1, Stachel, p. 105.

29.

See A. Pais, Subtle is the Lord (Oxford University Press, New York, 1981).

30.

This error is very lucidly described in Ref. 1, Stachel, where the detailed errors and corrections can be found.

32.
The book in question was
G.
Kirchoff
,
Vorlesungen Uber Mechanic (Lectures on Mechanics)
(
B. G. Teubner
, Leipzig,
1897
).
33.
Reference 1, Stachel,
p.
69
.
34.

In his paper Einstein omitted the time argument under the integral sign which I have added.

35.

Reference 1, Stachel, p. 134.

36.
A profile of Smoluchowski can be found in
S.
Ulam
, “
Marian Smuluchowski and the theory of probabilities in physics
,”
Am. J. Phys.
25
,
475
481
(
1957
).
37.
Paul
Langevin
, “
Sur la theorie du mouvement brownien (On the theory of Brownian motion)
,”
C. R. Acad. Sci. (Paris)
146
,
530
533
(
1908
).
A translation by Anthony Gythiel with commentary by Don S. Lemons is in
Am. J. Phys.
65
(
11
),
1079
1081
(
1997
).
38.
Louis
Bachelier
,
Theory of Speculation: The Origins of Modern Finance
, translated by Mark Davis and Alison Etheridge (
Princeton University Press
,
2006
).
39.
For a brief profile of Bachelier and his work, see
Jeremy
Bernstein
, “
Bachelier
,”
Am. J. Phys.
73
(
5
),
395
398
(
2005
).
40.
A.
Einstein
, “
Zur Theorie der Brownschen Bewegung (On the theory of Brownian motion)
,”
Ann. Phys.
20
,
199
206
(
1906
);
Theoretische Bemerkungen über die Brownschen Bewegung (Theoretical Remarks on Brownian Motion)
,”
Z. Elektrochem. Angew. Phys. Chem.
13
,
41
42
(
1906
).
41.
A.
Einstein
, “
Theoretical remarks on the Brownian movement
,”
Z. Elektrochem. Angew. Phys. Chem.
13
,
41
42
(
1907
).
42.
Reference 1, Stachel,
p.
231
.
43.
The original reference is
J.
Perrin
, “
Mouvement brownien et réalité moléculaire (Brownian movement and molecular reality)
,”
Ann. Phys.
18
,
5
114
(
1909
). A partial translation with commentary can be found in The World of the Atom, edited by Henry A. Boorse and Lloyd Motz (Basic Books, NY, 1966), pp. 628–640.
44.

Reference 39, p. 36.

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