1 4 0 D O C . 1 7 G R AV I T Y A N D M AT T E R
43). If they could be derived in this way, the divergence (in the sense of eq. (2)) of the left-hand side
of the equations should vanish identically on account of Noether’s theorem. Sending page proofs of
the document presented here to Felix Klein, Einstein emphasized that “Hamilton’s principle” needs
to be given up in the new theory (Einstein to Felix Klein, 14 April 1919, GyGöU, Nachlaß F. Klein
The divergence of the left-hand side of eq. (1a) reduces to the divergence of . Substitut-
ing for in eq. (2), the definition of the divergence, and using the relation
, one finds that the divergence of is equal to . The diver-
gence of the right-hand side of eq. (1a) is given by (see eq. (4) above). is defined as
(see eq. (7) below). David Hilbert had trouble following the derivation of eq. (4a). He wrote to
Einstein asking for clarification, which Einstein promptly supplied (see David Hilbert to Einstein, 9
June 1919, and Einstein to David Hilbert, 11 June 1919, GyGöU, Cod. Ms. D. Hilbert 92b).
These field equations were introduced in Einstein 1917b (Vol. 6, Doc. 43). In them, repre-
sents the energy-momentum tensor for both the electromagnetic field and the charge-carrying parti-
cles generating this field, whereas in eq. (9) represents the energy-momentum tensor for the
electromagnetic field only.
What is meant, presumably, is that the trace of vanishes in such regions.
The argument following eq. (4) establishes the same result (i.e., is constant except on the
worldlines of particles) for the theory based on the new field equations in eqs. (1a) and (9).
Intended are the field equations of eq. (1) with the addition of the cosmological term, as given
in the third equation on this page.
Given the interpretation of as a constant negative pressure term (see p. 352 of the docu-
ment), the interpretation of the cosmological constant in Einstein’s new theory is similar to the inter-
pretation offered in Schrödinger 1918b and rejected in Einstein 1918d (Doc. 3). Schrödinger’s
proposal, however, amounted to no more than adding a universal constant to the right-hand side of the
field equations rather than to the left-hand side as was done in Einstein 1917b (Vol. 6, Doc. 43). In the
theory presented in this document, the pressure term emerges as a by-product of a new solution to the
problem of the stability of charge-carrying particles.
A year earlier, Einstein had already made an attempt to recover the cosmological constant as a con-
stant of integration (see Einstein to Michele Besso, 29 July 1918 [Vol. 8, Doc. 591]). When the attempt
failed, he took the position that, since the world is only given once, there is no fundamental difference
between a new universal constant and a constant of integration (see Einstein to Michele Besso, 20 Au-
gust 1918 [Vol. 8, Doc. 604]). However, Einstein continued to be dissatisfied with the fact that there
was no intrinsic connection between the three terms—gravitational, electromagnetic, and cosmolog-
ical—entering into his field equations (see Einstein to Hermann Weyl, 27 September 1918 [Vol. 8,
Here and in the calculation below, instead of P and , Einstein presumably intended Ρ and
(Greek capital rho), the notation used in Weyl 1918b (cited on p. 355 of the document). Weyl used
Greek letters for quantities constructed out of the spatial part of the metric.
Eq. (14) is the trace of eq. (13).
Weyl 1918b, p. 224, eq. (59).
In eq. (19), “–” should be “+.”
As pointed out in Pauli 1921, p. 773, in the electron model of Lorentz and Poincaré, the elec-
tromagnetic energy also accounts for three-quarters of the total energy, while the energy of the non-
electromagnetic stabilizing mechanism accounts for the remaining quarter.
In the fourth edition of Einstein 1917a (Vol. 6, Doc. 42), published in 1919, Einstein added a
footnote to his remarks about the impossibility of a purely electromagnetic account of the stability of
the electron, saying that general relativity suggests that electrons are held together by gravity (see Vol.
6, Doc. 42, note 26). In his correspondence, Einstein was more cautious, expressing his doubts about
the correctness of the theory (see, e.g., Einstein to Paul Ehrenfest, 12 September 1919, and Einstein
to Théophile de Donder, 11 August 1920, BBU, 95PP 2).
-- - –g------