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348 CONTRIBUTIONS TO SCIENCE
ons transformations of the coordinates. This is the principle
of general relativity.
The procedure just described overcomes a deficiency in the
foundations of mechanics which had already been noticed by
Newton and was criticized by Leibnitz and, two centuries later,
by Mach: inertia resists acceleration, but acceleration relative
to what? Within the frame of classical mechanics the only answer
is: inertia resists acceleration relative to space. This is a
physical property of space-space acts on objects, but objects
do not act on space. Such is probably the deeper meaning of
Newton's assertion spatium est abso/utum (space is absolute).
But the idea disturbed some, in particular Leibnitz, who did
not ascribe an independent existence to space but considered it
merely a property of "things" (contiguity of physical objects).
Had his justified doubts won out at that time, it hardly would
have been a boon to physics, for the empirical and theoretical
foundations necessary to follow up his idea were not available
in the seventeenth century.
According to general relativity, the concept of space detached
from any physical content does not exist. The physical reality
of space is represented by a field whose components are continuous
functions of four independent variables-the coordinates of
space and time. It is just this particular kind of dependence that
expresses the spatial character of physical reality.
Since the theory of general relativity implies the representation
of physical reality by a continuous field, the concept of particles
or material points cannot play a fundamental part, nor
can the concept of motion. The particle can only appear as a
limited region in space in which the field strength or the energy
density are particularly high.
A relativistic theory has to answer two questions: (1) What is
the mathematical character of the field? (2) What equations
hold for this field?
Concerning the first question: from the mathematical point
of view the field is essentially characterized by the way its components
transform if a coordinate transformation is applied.
Concerning the second question: the equations must determine
the field to a sufficient extent while satisfying the postulates of