THE NEW DYNAMICS 285Enter Mach.
In this note Einstein declared, 'This [conclusion] lends plausibility to the con-
jecture that the total inertia of a mass point is an effect due to the presence of all
other masses, due to a sort of interaction with the latter.... This is just the point
of view asserted by Mach in his penetrating investigations on this subject.' From
that time on, similar references to Mach are recurrent. In the Einstein-Gross-
mann paper we read of 'Mach's bold idea that inertia originates in the interaction
of [a given] mass point with all other [masses]' [E37]. In June 1913, Einstein
wrote to Mach about the induction effect as well as about the bending of light,
adding that, if these effects were found, it would be 'a brilliant confirmation of
your ingenious investigations on the foundations of mechanics' [E38]. In his
Vienna lecture given in the fall of 1913, Einstein referred again to Mach's view
of inertia and named it 'the hypothesis of the relativity of inertia' [E39]. He men-
tioned neither this hypothesis nor the problem of inertia in any of his subsequent
articles until February 1917, when he submitted a paper [E40] which once again
marks the beginning of a new chapter in physics: general relativistic cosmology.
A few days before presenting this paper to the Prussian Academy, Einstein had
written to Ehrenfest, 'I have... again perpetrated something about gravitation
theory which somewhat exposes me to the danger of being confined in a madhouse'
[E41]. In the paper itself, he mentions the 'indirect and bumpy road' he had fol-
lowed to arrive at the first cosmological model of the new era, an isotropic, homo-
geneous, unbounded, but spatially finite static universe. It must have taken him
a relatively long time to formulate this theory, since already in September 1916
de Sitter mentions a conversation with Einstein about the possibility 'of an entirely
material origin of inertia' and the implementation of this idea in terms of 'a world
which of necessity must be finite' [SI2].
Einstein's paper is no doubt motivated by Machian ideas. However, he begins
with a re-analysis of another problem, the difficulties with a static Newtonian
universe.* He remarked that the Newton-Poisson equation
permits only (average) mass densities p which tend to zero faster than 1/r^2 for r
—* oo, since otherwise the gravitational potential would be infinite and the force
on a particle due to all the masses in the universe undetermined. (He realized soon
afterward that this reasoning is incorrect [E41a].) He also argued that even if 0
remains finite for large r, there still are difficulties. For it is still impossible to
have a Boltzmann equilibrium distribution of stars as long as the total stellar
energy is larger than the energy needed to expel stars one by one to infinity as the
result of collisions with other stars during the infinite time the universe has lived.
On the other hand (he notes), if Eq. 15.17 is replaced by
*For details and references to cosmology in the nineteenth century, see especially [P7] and [N6]. For
broader historial reviews, see [Ml] and [Ml2].(15.18)(15.17)