D O C U M E N T 1 2 O N K A L U Z A ’ S T H E O R Y 7 3

Published in Scripta Universitatis atque Bibliothecae Hierosolymitanarum. Mathematica et Physica

1 (1923), VII, pp. 1–5. Kitvei ha-Universita ve-Beth-ha-Sfarim bi-Yerushalayim. Mathematica u’Fi-

sica. A (5684), VII: 1–4 (Hebrew). Received 10 January 1922. A manuscript version is also available

[120 763]. Significant variations between the manuscript and the published version are noted.

[1]Two volumes of the Scripta were published under the imprint of the Hebrew University Library:

Orientalia et Judaica and Mathematica et Physica. Einstein agreed to act as editor of the latter vol-

ume, but it is unclear what part he actually played in the editorial process. The papers contained in

each of these volumes were published both in their original language and in Hebrew translation; the

present paper was translated into Hebrew by Jakob Grommer himself (Einstein and Grommer 1923b).

Immanuel Velikovsky played a major role in the compilation and production of the volumes, and was

responsible for editing in Palestine. For his account of his work on these volumes, see Velikovsky

1978. Heinrich Löwe was responsible for editing in Europe (see undated form letter by Heinrich

Löwe [IsJCZA/A146/116]).

[2]See Weyl 1918a and 1918c, 1919b; for a summary of Weyl’s approach see, e.g., Hermann Weyl

to Einstein, 1 March 1918 (Vol. 8, Doc. 472).

[3]For Einstein’s initial critique, especially with regard to the behavior of rods and clocks, see, e.g.,

Einstein 1918g and Einstein et al. 1920 (Vol. 7, Docs. 8 and 46), as well as Einstein to Walter Dällen-

bach, after 15 June 1918 (Vol. 8, Doc. 565), for a particularly clear statement of the objection.

[4]Theodor Kaluza (1885–1954) was Privatdozent in Mathematics at the University of Königsberg.

In spring 1919, Einstein had reacted enthusiastically to Theodor Kaluza’s original suggestion of a

five-dimensional extension of the general theory of relativity to include electromagnetism, as

becomes clear from his response to the letter Kaluza sent him together with the original draft paper,

Einstein to Theodor Kaluza, 21 April 1919 (Vol. 9, Doc. 26). Yet, in the two following weeks, Einstein

had been pondering on the consequences of Kaluza’s proposal in detail (see Einstein to Theodor

Kaluza, 28 April, 5 May, and 14 May 1919 [Vol. 9, Docs. 30, 35, and 40]). In a letter at the end of

May (Einstein to Theodor Kaluza, 29 May 1919 [Vol. 9, Doc. 48]), Einstein finally withdrew his ear-

lier offer to submit the paper for publication in the Sitzungsberichte. More than three years later, Ein-

stein changed his mind and offered to submit Kaluza’s paper for publication after all (Einstein to

Theodor Kaluza, 14 October 1921 [Vol.12, Doc. 270]). Only one week after this, Einstein received a

letter from Jakob Grommer of 25 October 1921 (Vol. 12, Doc. 283), which contains the mathematical

argument of the present paper.

[5]For a history of five-dimensional theories, see Vizgin 1994, pp. 149–161, and Goenner 2004,

secs. 4.2 and 6.3; for a biography of Kaluza, see Wuensch 2007.

[6]Einstein argues here that, because of the cylinder condition, the introduction of a fifth dimension

should not be interpreted realistically. Einstein and Peter Bergmann would, much later, criticize in

detail Kaluza’s original approach as not allowing for a realistic interpretation of the fifth dimension.

In consequence, they proposed a five-dimensional theory that allows for a periodic dependence on

the fifth coordinate, which, they argue, makes possible a realistic interpretation (see Einstein and

Bergmann 1938; Einstein et al. 1941).

[7]See Einstein to Kaluza, 5 May 1919 (Vol. 9, Doc. 35).

[8]Just like Kaluza (see Kaluza 1921, p. 968), Einstein and Grommer only look at the linearized

field equations corresponding to Kaluza’s full five-dimensional field equations, , where

is the Ricci tensor of the metric-compatible five-dimensional connection. In contrast to Kaluza,

Einstein and Grommer argue (on the previous page) that a five-dimensional (dust) energy-momentum

tensor should not be introduced; instead, elementary particles are supposed to be described by

solutions to the field equations.

[9]Einstein already in 1909 had considered the possibility of reducing particles to solutions of field

equations in electromagnetic theory (see Einstein to Hendrik A. Lorentz, 23 May 1909 [Vol. 5,

Doc. 163]). In Einstein 1919a (Vol. 7, Doc. 17), he then tried to reduce particles to configurations of

(nonunified) electromagnetic and gravitational fields. The present document gives Einstein’s first def-

inition of the necessary and sufficient conditions that a solution to the field equations has to fulfill to

be interpretable as representing a material particle. At the same time, the document gives the first for-

mulation of the criterion that such particle solutions must exist in a satisfactory physical theory based

Rμν 0=

Rμν

Tμν