9 8 D O C . 1 2 R E L A T I V I T Y L E C T U R E N O T E S

1918, title page), but Einstein left Berlin in early January. His comment, “Ende des Kollegs am

Heftende (in Zürich notiert)” (see note 28) suggests that at least part of the notes were written for the

course in Zurich which he held from 20 January until the second half of February 1919 (see notes 20

and 28).

[2]The exposition of special relativity and covariant electrodynamics in these lecture notes follows

rather closely the treatment in an unpublished manuscript on special relativity from 1912 to 1914 (see

Vol. 4, Doc. 1). In the following, this manuscript will be referred to as “Vol. 4, Doc. 1.” These lecture

notes also show many similarities to the course on special relativity given by Einstein at the University

of Berlin in the winter semester of 1914–1915 (see Einstein’s notes for this course in Vol. 6, Doc. 7).

The lectures are dated. The first two dates given were Fridays, followed by one date on a Sunday, and

the remainder on Saturdays. The order of topics covered shows one notable change over that of the

lecture course given in 1914–1915 (Vol. 6, Doc. 7). In the earlier course the first two lectures covered

a philosophical defense of the relativity principle, followed by the experimental underpinning for the

ideas of special relativity, in particular the experiment of Fizeau concerning the velocity of light in

moving water. Unlike previous expositions, in the present course Einstein begins with Maxwell’s

equations and the theoretical formalism of Lorentzian electrodynamics, and he dispenses with the

need to convince his audience of the complete integration of special relativity into the fundamental

theory of electromagnetism. Only after this theoretical introduction does he go on to discuss the

Fizeau experiment in the second lecture.

[3]Heaviside 1892, p. 199. See also Vol. 4, Doc. 1, p. 9.

[4]The rather dense calculation of an expression for the magnetic polarization current below is

probably based on Lorentz 1904b, secs. 15, 28, 31, and 48. Note that in Vol. 4, Doc. 1, p. 18, Einstein

avoids this more rigorous approach in favor of a simpler one based on a direct analogy with the case

of an electrically polarized dielectric. In the following, q is the magnetic dipole moment. Further down

the page, when writing down the Maxwell-Lorentz equations for stationary matter, Einstein changes

q to m, his usual notation for the magnetic polarization vector.

[5]This should read .

[6]Here Einstein considers a magnetic element consisting of a current loop with circulating current

I, area f, and normal n. From this he derives the magnetic dipole moment of the loop, . On

the next line, following the notation of Lorentz 1904a, sec. 28, he multiplies by N the number of mag-

netic elements, or current loops, per unit volume to write the magnetic dipole moment density of the

material in question (the current loops representing bound electrons). The brackets around the q may

represent the averaged dipole moment per unit volume, presuming that the current loops are all iden-

tical, and (N) the average number of elements per unit volume. On the right in the next line is the

expression for q projected onto another normal (see the accompanying figure) whose angle to the first

normal is written nα.

[7]Here and in the line below Einstein calculates the current through an element of area ds, averag-

ing over the orientation of the loops, and argues that it is equal to the averaged magnetic dipole density

calculated in the line above (see note 6). A factor of c is missing in the right-hand side of the equation.

[8]On this line Einstein invokes Stokes’s theorem to show that the total current through a given sur-

face area in a material, calculated two lines above (see note 7), can be rewritten in terms of a line inte-

gral around a closed curve surrounding the surface, with line element dS. The factor of c on the right-

hand side of the equation should be omitted. This gives directly, on the next line, an expression for

the magnetic polarization current of a material in terms of q (see note 6), which should read

.

[9]Rowland 1878, Rowland and Hutchinson 1889 (see Vol. 4, Doc. 1, note 8).

[10]Röntgen 1888 and Eichenwald 1903, 1904 (see Vol. 4, Doc. 1, p. 17, note 21, and Vol. 6, Doc.

7, note 11). See, for example, Laue 1913, §2, and Pauli 1921, sec. 36, for discussions of these exper-

iments as well as Wilson’s (see note 11).

[11]Wilson, H. 1904 (Vol. 4, Doc. 1, p. 17, note 22, and Vol. 6, Doc. 7, note 8).

[12]Fizeau 1851. See Doc. 31, [pp. 1–2] and [p. 13], for a discussion of the importance of Fizeau’s

experiment.

m

crot =

c

-- - n =

m

crot =