THE NEW DYNAMICS 287
provided that( 15 .23)where p is a constant mass density. In this Einsteinian universe, the Newtonian
infinite no longer causes problems because it has been abolished; three-dimen-
sional space is spherically bounded and has a time-independent curvature. More-
over, if there is no matter, then there is no inertia, that is, for nonzero X, Eq. 15.21
cannot be satisfied if p = 0. Of course, this solution did not specifically associate
inertia with the distant stars, but it seemed a good beginning.
So strongly did Einstein believe at that time in the relativity of inertia that in
1918 he stated as being on equal footing three principles on which a satisfactory
theory of gravitation should rest [E42]:
- The principle of relativity as expressed by general covariance
- The principle of equivalence
- Mach's principle (the first time this term entered the literature): 'Das G-Feld
ist restlos durch die Massen der Korper bestimmt,' that is, the g^ are com-
pletely determined by the mass of bodies, more generally by T^. In 1922, Ein-
stein noted that others were satisfied to proceed without this criterion and
added, 'This contentedness will appear incomprehensible to a later generation,
however' [E42a].
In later years, Einstein's enthusiasm for Mach's principle waned and finally
vanished. I conclude with a brief chronology of his subsequent involvement with
cosmology.- Einstein never said so explicitly, but it seems reasonable to assume that
he had in mind that the correct equations should have no solutions at all in the
absence of matter. However, right after his paper appeared, de Sitter did find a
solution of Eq. 15.21 with p = 0 [S14, W19]. Thus the cosmological term X^
does not prevent the occurrence of 'inertia relative to space.' Einstein must have
been disappointed. In 1918 he looked for ways to rule out the de Sitter solution
[E42b], but soon realized that there is nothing wrong with it. - Einstein suggests [E43] that perhaps electrically-charged particles are
held together by gravitational forces. He starts from Eq. 15.21, assumes that T^
is due purely to electromagnetism so that 7£ = 0, and notes that this yields the
trace condition X = R/4. Thus electromagnetism constrains gravitation. This idea
may be considered Einstein's first attempt at a unified field theory. In 1927 he
wrote a further short note on the mathematical properties of this model [E44].
Otherwise, as is not unusual for him in his later years, a thought comes, is men-
tioned in print, and then vanishes without a trace.
(15.22)