It is true that Mach tried to avoid having to accept as real something
which is not observable by endeavouring to substitute in mechanics
a mean acceleration with reference to the totality of the masses in
the universe in place of an acceleration with reference to absolute
space. But inertial resistance opposed to relative acceleration of
distant masses presupposes action at a distance; and as the modern
physicist does not believe that he may accept this action at
a distance, he comes back once more, if he follows Mach, to the
ether, which has to serve as medium for the effects of inertia. But
this conception of the ether to which we are led by Mach's way of
thinking differs essentially from the ether as conceived by Newton,
by Fresnel, and by Lorentz. Mach's ether not only _conditions_ the
behaviour of inert masses, but _is also conditioned_ in its state
by them.
Mach's idea finds its full development in the ether of the general
theory of relativity. According to this theory the metrical
qualities of the continuum of space-time differ in the environment
of different points of space-time, and are partly conditioned by the
matter existing outside of the territory under consideration. This
space-time variability of the reciprocal relations of the standards
of space and time, or, perhaps, the recognition of the fact that
"empty space" in its physical relation is neither homogeneous nor
isotropic, compelling us to describe its state by ten functions (the
gravitation potentials g_(mn)), has, I think, finally disposed of
the view that space is physically empty. But therewith the
conception of the ether has again acquired an intelligible content,
although this content differs widely from that of the ether of the
mechanical undulatory theory of light. The ether of the general
theory of relativity is a medium which is itself devoid of _all_
mechanical and kinematical qualities, but helps to determine
mechanical (and electromagnetic) events.
What is fundamentally new in the ether of the general theory of
relativity as opposed to the ether of Lorentz consists in this, that
the state of the former is at every place determined by connections
with the matter and the state of the ether in neighbouring places,
which are amenable to law in the form of differential equations;
whereas the state of the Lorentzian ether in the absence of
electromagnetic fields is conditioned by nothing outside itself,
and is everywhere the same. The ether of the general theory of
relativity is transmuted conceptually into the ether of Lorentz if
we substitute constants for the functions of space which describe
the former, disregarding the causes which condition its state.
Thus we may also say, I think, that the ether of the general theory
of relativity is the outcome of the Lorentzian ether, through
relativation.
Public-domain text, read in full here on John Shaqi.
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