284 RELATIVITY, THE GENERAL THEORY
The third theme, Mach's conjecture on the dynamic origins of inertia, leads us
to Einstein's work on cosmology.
- Einstein and Mach 's Principle. The central innovation in Mach's mechan-
ics is the abolition of absolute space in the formulation of the law of inertia. Write
this law as: A system on which no forces act is either at rest or in uniform motion
relative to xxx. Then
xxx = absolute space Newton
xxx = the fixed stars
idealized as a
rigid system Mach
'When ... we say that a body preserves unchanged its direction and velocity in
space, our assertion is nothing more or less than an abbreviated reference to the
entire universe' [M10]. Those are Mach's words and italics. He argued further
that the reference to the entire universe could be restricted to the heavy bodies at
large distances which make up the fixed stars idealized as a rigid system, since the
relative motion of the body with regard to nearby bodies averages out to zero.
Mach goes on to raise a new question.* Newton's law of inertia refers to
motions that are uniform relative to an absolute space; this law is a kinematic first
principle. By contrast, his own version of the law of inertia refers to motions of
bodies relative to the fixed stars. Should one not seek a dynamic explanation of
such motions, just as one explains dynamically the planetary orbits by means of
gravitational dynamics or the relative motion of electrically-charged particles by
means of electrodynamics? These are not Mach's own words. However, this
dynamic view is implicit in his query: 'What would become of the law of inertia
if the whole of the heavens began to move and the stars swarmed in confusion?
How would we apply it then? How would it be expressed then? ... Only in the
case of a shattering of the universe [do] we learn that all bodies [his italics] each
with its share are of importance in the law of inertia' [Mil]. We do not find in
Mach's book how this importance of all bodies manifests itself; he never proposed
an explicit dynamic scheme for his new interpretation of the law of inertia. Mach
invented Mach's law of inertia, not Mach's principle. Reading his discourse on
inertia is not unlike reading the Holy Scriptures. The text is lucid but one senses,
perhaps correctly, perhaps wrongly, a deeper meaning behind the words. Let us
see how Einstein read Mach.
Soon after Einstein arrived in Prague and broke his long silence on gravitation,
he published a short note entitled 'Does There Exist a Gravitational Action Anal-
ogous to the Electrodynamical Induction Effect?' [E36]. In this paper (based on
the rudimentary gravitation theory of the Prague days), he showed that if a hol-
low, massive sphere is accelerated around an axis passing through its center, then
the inertial mass of a mass point located at the sphere's center is increased, an
effect which foreshadows the Lense-Thirring effect [T6].
*Seealso[Hll].
