1 3 8 D O C . 3 1 I D E A S A N D M E T H O D S
The experimental fact of the same fall of all bodies therefore can, in the spirit of
Newtonian mechanics, also be viewed as the equality of the inertial and gravitation-
al mass, which from the point of view of Newtonian mechanics is by no means self-
This theorem has been confirmed with extraordinary precision by the tests of
which are based upon the following. A body on the surface of the earth
is under the influence of the gravitational force of the earth and of the centrifugal
force of the earth’s rotation. The first force is proportional to the gravitational mass,
the latter to the inertial mass. The resultant of both forces is independent of the ma-
terial only if the ratio of inertial and gravitational mass is independent of the mate-
rial. Eötvös attached masses of different material to the ends of the horizontal
balance beam of a torsion scale. In case of an incomplete proportionality of inertial
and gravitational mass, the resulting forces acting upon the two masses could not
be exactly parallel; i.e., there should have been a torsion moment acting upon the
system when the balance beam was oriented in the east-west direction. The nega-
tive outcome was registered with such precision that the relative difference between
inertial and gravitational mass had to be smaller than .
16. General Reasons for a General Postulate of Relativity
Classical mechanics and the theory of special relativity know of admissible coor-
dinate systems (inertial systems) and nonadmissable coordinate systems. Relative
to the first ones, the laws of nature (e.g., the law of inertia and the theorem of the
constancy of the speed of light) are supposed to hold; relative to the latter, they do
not. In vain one asks for an objective reason for the different quality of systems;
and one is forced to explain them as an independent, very strange property of the
space-time continuum. Newton was only very reluctantly content with this opinion
(of “absolute space”), but he believed that in centrifugal effects he had an objective
proof for it in hand.
However, E. Mach was the first to recognize the weakness of this argument. Per-
haps it was not a physical quality of space that determined the inertial behavior of
bodies; it could also be possible that inertia was not a reaction against a (conceptu-
ally empty) acceleration with respect to space, but rather against an acceleration
with respect to the rest of gravitating matter in the world. Such a hypothesis ap-
peared more satisfactory to Mach than the old concept of inertia, because it did not
inertial mass gravitational mass =
[p. 23]
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