D O C . 7 1 P R I N C E T O N L E C T U R E S 5 7 1
[12]In the manuscript, the following paragraph was started and then deleted at this point: “áDiese
Betrachtungen über den euklidischen Raum haben nur den Zweck, den Zusammenhang der physika-
lische Erfahrung mitñ.”
[13]In the manuscript, “zutreffend” replaces “árichtigñ.”
[14]The phrase “welche von Helmholtz herrührt” is not in the manuscript. The reference is to Helm-
holtz 1884.
[15]Here and in the footnote appended to this sentence, “ ” should be “ ” The error is
corrected in the first English edition (Einstein 1922d).
[16]In the manuscript, there is a deletion following “indem:” “ádie Fundamentalinvariante s ázweiñ
des Abstandes zweier Punkte sich bezüglich aller áTransformatiñ Bezugssysteme, dieñ.”
[17]In the manuscript, “áWenn sich eine Grösse bezüglich einerñ” precedes “Die rechte Seite:.”
[18]The summation convention was first introduced in print in Einstein 1916e (Vol. 6, Doc. 30), p.
781.
[19]In the manuscript, “Invariante” replaces “áSkalarñ.”
[20]The α on the left-hand side should be an index to the tensor T.
[21]In the manuscript, this paragraph forms the start of the second lecture (“Zweite Vorlesung”),
entitled “Raum und Zeit in der vor-relativistischen Physik (Fortsetzung)”
[22]In the manuscript, “postuliert” replaces “ásetzt vorausñ.”
[23]In the manuscript, “Range” replaces “áGewichteñ.”
[24]In the manuscript, the following passage is deleted at this point: “áDurch Vertauschung der
Indices μ und ν und Subtraktion beider Gleichungen erhält man die antisymmetrische Tensorglei-
chung ñ.”
[25]In the manuscript, this is the start of the third lecture, although there is no header (see notes 21
and 66). The content of this chapter corresponds to the lecture of 12 May 1921, which was summa-
rized as follows by Adams: “The third lecture was devoted to the mathematical formulation of the spe-
cial theory of relativity in the form given it by Minkowski. General theorems regarding the properties
of four-dimensional vectors and tensors were stated and the Maxwell-Lorentz equations of the
electro-magnetic field were written in terms of these quantities.
“It was shown how the ordinary electro-magnetic forces due to motions in the electro-magnetic
field followed as an immediate consequence of the special theory of relativity. Finally, the equivalence
of mass and energy resulting from this theory was brought out, as a consequence of which the two
laws of conservation of mass and energy become welded into a single law.” New York Evening Post,
12 May 1921, p. 7.
[26]The commas following “sind” and “Geometrie” are not in the manuscript.
[27]In the manuscript, “Bezugsraumes” replaces “áBezugssystemsñ.”
[28]Michelson and Morley 1887.
[29]Fizeau 1851 and De Sitter 1913a and 1913b.
[30]In the second German edition, “räumlich entfernter Ereignisse” is added following “Gleich-
zeitigkeit” in the first line of this footnote.
[31]In the manuscript, “zentrale” replaces “áausserordentlicheñ áwichtigeñ.”
[32]See Einstein 1910a (Vol. 3, Doc. 2), pp. 23–24, for more on processes used as clocks.
[33]See Minkowski 1908 for Minkowksi’s formulation of special relativity in four dimensions.
[34]Minkowski 1908.
[35]In the manuscript, “physikalischen” replaces “áanschaulichenñ.”
[36]“ ” should be „v.”
[37]In the manuscript, the following passage is deleted at this point (before “Ruht der . . .”):
“áDenken wir uns zwei koaxiale Zylinder die im Zustand relativer Ruhe denselben Radius haben.
Bewegen wir den zweiten gegen den ersten axial, mit der Geschwindigkeit q, so ist sein Radius
vom Standpunkt des ersten aus betrachtet.ñ”
[38]In the last of these equations, “x‰ should be “l.‰ The error is corrected in the first English edi-
tion (Einstein 1922d).
[39]See note 82 on the independence of the lengths of measurin- rods from their own prehistory.
n 2 – n 1. –
mè
dxμ
dt
------------------
d2xν
dt2
-
dxν
dt
-------------------ø
d2xμö
dt2
–
æ
=
v
R0
λ(q2) R0 ⋅