All movements must be referred to definite sets of co-ordinate axes. If
there is any change of axes, the numerical magnitude of the movements
will also change. But according to Newtonian dynamics, such alteration
in physical movements can only be due to the effect of certain forces in
the field.[5] Thus any change of axes will introduce new “geometrical”
forces in the field which are quite independent of the nature of the
body acted on. Gravitational forces also have this same remarkable
property, and gravitation itself may be of essentially the same nature
as these “geometrical” forces introduced by a change of axes. This leads
to Einstein’s famous Principle of Equivalence. _A gravitational field of
force is strictly equivalent to one introduced by a transformation of
co-ordinates and no possible experiment can distinguish between the
two._
Thus it may become possible to “transform away” gravitational effects,
at least for sufficiently small regions of space, by referring all
movements to a new set of axes. This new “framework” may of course have
all kinds of very complicated movements when referred to the old
Galilean or “rectangular unaccelerated system of co-ordinates.”
But there is no reason why we should look upon the Galilean system as
more fundamental than any other. If it is found simpler to refer all
motion in a gravitational field to a special set of co-ordinates, we may
certainly look upon this special “framework” (at least for the
particular region concerned), to be more fundamental and more natural.
We may, still more simply, identify this particular framework with the
special local properties of space in that region. That is, we can look
upon the effects of a gravitational field as simply due to the local
properties of space and time itself. The very presence of matter implies
a modification of the characteristics of space and time in its
neighbourhood. As Eddington says “matter does not cause the curvature of
space-time. It is the curvature. Just as light does not cause
electromagnetic oscillations; it is the oscillations.”
We may look upon this from a slightly different point of view. The
General Principle of Relativity asserts that all motion is merely
relative motion between matter and matter, and as all movements must be
referred to definite sets of co-ordinates, the ground of any possible
framework must ultimately be material in character. It _is_ convenient
to take the matter actually present in a field as the fundamental ground
of our framework. If this is done, the special characteristics of our
framework would naturally depend on the actual distribution of matter in
the field. But physical space and time is completely defined by the
“framework.” In other words the “framework” itself _is_ space and time.
Hence we see how _physical_ space and time is actually defined by the
local distribution of matter.
Public-domain text, read in full here on John Shaqi.
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