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Page 4
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.
As to the part which the new ether is to play in the physics of
the future we are not yet clear. We know that it determines the
metrical relations in the space-time continuum, e.g. the configurative
possibilities of solid bodies as well as the gravitational fields;
but we do not know whether it has an essential share in the structure
of the electrical elementary particles constituting matter. Nor do
we know whether it is only in the proximity of ponderable masses
that its structure differs essentially from that of the Lorentzian
ether; whether the geometry of spaces of cosmic extent is approximately
Euclidean. But we can assert by reason of the relativistic equations
of gravitation that there must be a departure from Euclidean
relations, with spaces of cosmic order of magnitude, if there exists
a positive mean density, no matter how small, of the matter in the
universe. In this case the universe must of necessity be spatially
unbounded and of finite magnitude, its magnitude being determined
by the value of that mean density.
If we consider the gravitational field and the electromagnetic field
from the stand-point of the ether hypothesis, we find a remarkable
difference between the two. There can be no space nor any part
of space without gravitational potentials; for these confer upon
space its metrical qualities, without which it cannot be imagined
at all. The existence of the gravitational field is inseparably
bound up with the existence of space. On the other hand a part of
space may very well be imagined without an electromagnetic field;
thus in contrast with the gravitational field, the electromagnetic
field seems to be only secondarily linked to the ether, the formal
nature of the electromagnetic field being as yet in no way determined
by that of gravitational ether. From the present state of theory
it looks as if the electromagnetic field, as opposed to the
gravitational field, rests upon an entirely new formal _motif_,
as though nature might just as well have endowed the gravitational
ether with fields of quite another type, for example, with fields
of a scalar potential, instead of fields of the electromagnetic
type.
Since according to our present conceptions the elementary particles
of matter are also, in their essence, nothing else than condensations
of the electromagnetic field, our present view of the universe
presents two realities which are completely separated from each other
conceptually, although connected causally, namely, gravitational ether
and electromagnetic field, or--as they might also be called--space
and matter.
Of course it would be a great advance if we could succeed in
comprehending the gravitational field and the electromagnetic field
together as one unified conformation. Then for the first time the
epoch of theoretical physics founded by Faraday and Maxwell would
reach a satisfactory conclusion. The contrast between ether and
matter would fade away, and, through the general theory of relativity,
the whole of physics would become a complete system of thought,
like geometry, kinematics, and the theory of gravitation. An
exceedingly ingenious attempt in this direction has been made by
the mathematician H. Weyl; but I do not believe that his theory will
hold its ground in relation to reality. Further, in contemplating
the immediate future of theoretical physics we ought not unconditionally
to reject the possibility that the facts comprised in the quantum
theory may set bounds to the field theory beyond which it cannot
pass.
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