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How does it come about that alongside of the idea of
ponderable matter, which is derived by abstraction from everyday
life, the physicists set the idea of the existence of another
kind of matter, the ether? The explanation is probably to be sought
in those phenomena which have given rise to the theory of action
at a distance, and in the properties of light which have led to
the undulatory theory. Let us devote a little while to the consideration
of these two subjects.
Outside of physics we know nothing of action at a distance.
When we try to connect cause and effect in the experiences which
natural objects afford us, it seems at first as if there were
no other mutual actions than those of immediate contact, e.g.
the communication of motion by impact, push and pull, heating
or inducing combustion by means of a flame, etc. It is true that
even in everyday experience weight, which is in a sense action
at a distance, plays a very important part. But since in daily
experience the weight of bodies meets us as something constant,
something not linked to any cause which is variable in time or
place, we do not in everyday life speculate as to the cause of
gravity, and therefore do not become conscious of its character
as action at a distance. It was Newton's theory of gravitation
that first assigned a cause for gravity by interpreting it as
action at a distance, proceeding from masses. Newton's theory
is probably the greatest stride ever made in the effort towards
the causal nexus of natural phenomena. And yet this theory evoked
a lively sense of discomfort among Newton's contemporaries, because
it seemed to be in conflict with the principle springing from
the rest of experience, that there can be reciprocal action only
through contact, and not through immediate action at a distance.
It is only with reluctance that man's desire for knowledge
endures a dualism of thls kind. How was unity to be preserved
in his comprehension of the forces of nature? Either by trying
to look upon contact forces as being themselves distant forces
which admittedly are observable only at a very small distance
and this was the road which Newton's followers, who were entirely
under the spell of his doctrine, mostly preferred to take; or
by assuming that the Newtonian action at a distance is only apparently
immediate action at a distance, but in truth is conveyed by a
medium permeating space, whether by movements or by elastic deformation
of this medium. Thus the endeavour toward a unified view of the
nature of forces leads to the hypothesis of an ether. This hypothesis,
to be sure, did not at first bring with it any advance in the
theory of gravitation or in physics generally, so that it became
customary to treat Newton's law of force as an axiom not further
reducible. But the ether hypothesis was bound always to play some
part in physical science, even if at first only a latent part.
When in the first half of the nineteenth century the far-reaching
similarity was revealed which subsists between the properties
of light and those of elastic waves in ponderable bodies, the
ether hypothesis found fresh support. 1t appeared beyond question
that light must be interpreted as a vibratory process in an elastic,
inert medium filling up universal space. It also seemed to be
a necessary consequence of the fact that light is capable of polarisation
that this medium, the ether, must be of the nature of a solid
body, because transverse waves are not possible in a fluid, but
only in a solid. Thus the physicists were bound to arrive at the
theory of the ``quas-irigid'' luminiferous ether, the parts of
which can carry out no movements relatively to one another except
the small movements of deformation which correspond to light-waves.
This theory also called the theory of the stationary luminiferous
ether moreover found a strong support in an experiment which is
also of fundamental importance in the special theory of relativity,
the experiment of Fizeau, from which one was obliged to infer
that the luminiferous ether does not take part in the movements
of bodies. The phenomenon of aberration also favoured the theory
of the quasi-rigid ether.
The development of the theory of electricity along the
path opened up by Maxwell and Lorentz gave the development of
our ideas concerning the ether quite a peculiar and unexpected
turn. For Maxwell himself the ether indeed still had properties
which were purely mechanical, although of a much more complicated
kind than the mechanical properties of tangible solid bodies.
But neither Maxwell nor his followers succeeded in elaborating
a mechanical model for the ether which might furnish a satisfactory
mechanical interpretation of Maxwell's laws of the electro-magnetic
field. The laws were clear and simple, the mechanical interpretations
clumsy and contradictory. Almost imperceptibly the theoretical
physicists adapted themselves to a situation which, from the standpoint
of their mechanical programme, was very depressing. They were
particularly influenced by the electro-dynamical investigations
of Heinrich Hertz. For whereas they previously had required of
a conclusive theory that it should content itself with the fundamental
concepts which belong exclusively to mechanics (e.g. densities,
velocities, deformations, stresses) they gradually accustomed
themselves to admitting electric and magnetic force as fundamental
concepts side by side with those of mechanics, without requiring
a mechanical interpretation for them. Thus the purely mechanical
view of nature was gradually abandoned. But this change led to
a fundamental dualism which in the long-run was insupportable.
A way of escape was now sought in the reverse direction, by reducing
the principles of mechanics to those of electricity, and this
especially as confidence in the strict validity of the equations
of Newton's mechanics was shaken by the experiments with b-rays
and rapid kathode rays.
This dualism still confronts us in unextenuated form in
the theory of Hertz, where matter appears not only as the bearer
of velocities, kinetic energy, and mechanical pressures, but also
as the bearer of electromagnetic fields. Since such fields also
occur in vacuo i.e. in free ether the ether also appears as bearer
of electromagnetic fields. The ether appears indistinguishable
in its functions from ordinary matter. Within matter it takes
part in the motion of matter and in empty space it has everywhere
a velocity; so that the ether has a definitely assigned velocity
throughout the whole of space. There is no fundamental difference
between Hertz's ether and ponderable matter (which in part subsists
in the ether).
The Hertz theory suffered not only from the defect of ascribing
to matter and ether, on the one hand mechanical states, and on
the other hand electrical states, which do not stand in any conceivable
relation to each other; it was also at variance with the result
of Fizeau's important experiment on the velocity of the propagation
of light in moving fluids, and with other established experimental
results.
Such was the state of things when H. A. Lorentz entered
upon the scene. He brought theory into harmony with experience
by means of a wonderful simplification of theoretical principles.
He achieved this, the most important advance in the theory of
electricity since Maxwell, by taking from ether its mechanical,
and from matter its electromagnetic qualities. As in empty space,
so too in the interior of material bodies, the ether, and not
matter viewed atomistically, was exclusively the seat of electromagnetic
fields. According to Lorentz the elementary particles of matter
alone are capable of carrying out movements; their electromagnetic
activity is entirely confined to the carrying of electric charges.
Thus Lorentz succeeded in reducing all electromagnetic happenings
to Maxwell's equations for free space.
As to the mechanical nature of the Lorentzian ether, it
may be said of it, in a somewhat playful spirit, that immobility
is the only mechanical property of which it has not been deprived
by H. A. Lorentz. 1t may be added that the whole change in the
conception of the ether which the special theory of relativity
brought about, consisted in taking away from the ether its last
mechanical quality, namely, its immobility. How this is to be
understood will forthwith be expounded.
The space-time theory and the kinematics of the special
theory of relativity were modelled on the Maxwell-Lorentz theory
of the electromagnetic field. This theory therefore satisfies
the conditions of the special theory of relativity, but when viewed
from the latter it acquires a novel aspect. For if K be a system
of co-ordinates relatively to which the Lorentzian ether is at
rest, the Maxwell-Lorentz equations are valid primarily with reference
to K. But by the special theory of relativity the same equations
without any change of meaning also hold in relation to any new
system of co-ordinates K' which is moving in uniform translation
relatively to K. Now comes the anxious question: Why must I in
the theory distinguish the K system above all K' systems, which
are physically equivalent to it in all respects, by assuming that
the ether is at rest relatively to the K system? For the theoretician
such an asymmetry in the theoretical structure, with no corresponding
asymmetry in the system of experience, is intolerable. If we assume
the ether to be at rest relatively to K, but in motion relatively
to K', the physical equivalence of K and K' seems to me from the
logical standpoint, not indeed downright incorrect, but nevertheless
inacceptable.
The next position which it was possible to take up in face
of this state of things appeared to be the following. The ether
does not exist at all. The electromagnetic fields are not states
of a medium, and are not bound down to any bearer, but they are
independent realities which are not reducible to anything else,
exactly like the atoms of ponderable matter. This conception suggests
itself the more readily as, according to Lorentz's theory, electromagnetic
radiation, like ponderable matter, brings impulse and energy with
it, and as, according to the special theory of relativity, both
matter and radiation are but special forms of distributed energy,
ponderable mass losing its isolation and appearing as a special
form of energy.
More careful reflection teaches us, however, that the special
theory of relativity does not compel us to deny ether. We may
assume the existence of an ether; only we must give up ascribing
a definite state of motion to it, i.e. we must by abstraction
take from it the last mechanical characteristic which Lorentz
had still left it. We shall see later that this point of view,
the conceivability of which shall at once endeavour to make more
intelligible by a somewhat halting comparison, is justified by
the results of the general theory of relativity.
Think of waves on the surface of water. Here we can describe
two entirely different things. Either we may observe how the undulatory
surface forming the boundary between water and air alters in the
course of time; or else with the help of small floats, for instance
we can observe how the position of the separate particles of water
alters in the course of time. If the existence of such floats
for tracking the motion of the particles of a fluid were a fundamental
impossibility in physics if, in fact, nothing else whatever were
observable than the shape of the space occupied by the water as
it varies in time, we should have no ground for the assumption
that water consists of inovable particles. But all the same we
could characterise it as a medium.
We have something like this in the electromagnetic field.
For we may picture the field to ourselves as consisting of lines
of force. If we wish to interpret these lines of force to ourselves
as something inaterial in the ordinary sense, we are tempted to
interpret the dynamic processes as motions of these lines of force,
such that each separate line of force is tracked through the course
of time. It is well known, however, that this way of regarding
the electromagnetic field leads to contradictions.
Generalising we must say this: There may be supposed to
be extended physical objects to which the idea of motion cannot
be applied. They may not be thought of as consisting of particles
which allow themselves to be separately tracked through time.
In Minkowski's idiom this is expressed as follows: Not every extended
conformation in the four-dimensional world can be regarded as
composed of worldthreads. The special theory of relativity forbids
us to assume the ether to consist of particles observable through
time, but the hypothesis of ether in itself in conflict with the
special theory of relativity. Only we must be on our guard against
ascribing a state of motion to the ether.
Certainly, from the standpoint of the special theory of
relativity, the ether hypothesis appears at first to be an empty
hypothesis. In the equations of the electromagnetic field there
occur, in addition to the densities of the electric charge, only
the intensities of the field. The career of electromagnetic processes
in vacuo appears to be completely determined by tliese equations,
uninfluenced by other physical quantities. The electromagnetic
fields appear as ultimate, irreducible realities, and at first
it seems superfluous to postulate a homogeneous, isotropic ether-medium,
and to envisage electromagnetic fields as states of this medium.
But on the other hand there is a weighty argument to be
adduced in favour of the ether hypothesis. To deny the ether is
nltimately to assuine that empty space has no physical qualities
whatever. The fundamental facts of mechanics do not harmonize
with this view. For the mechanical behaviour of a corporeal system
hovering freely in empty space depends not only on relative positions
(distances) and relative velocities, but also on its state of
rotation, which physically may be taken as a characteristic not
appertaining to the system in itself. In order to be able to look
upon the rotation of the system, at least formally, as something
real, Newton objectivises space. Since he classes his absolute
space together with real things, for him rotation relative to
an absolute space is also something real. Newton might no less
well have called his absolute space ``Ether''; what is essential
is merely that besides observable objects, another thing, which
is not perceptible, inust be looked upon as real, to enable acceleration
or rotation to be looked upon as something real.
It is true that Mach tried to avoid having to accept as
real something which is not observable by endeavouring to substitute
in inechanics 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 inore,
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), 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 inagnitude being determined by the
value of that inean density.
If we consider the gravitational field and the electromagnetic
field from the standpoint 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 electromagnctic 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.
Recapitulating, we may say that according to the general
theory of relativity space is endowed with physical qualities;
in this sense, therefore, there exists an ether. According to
the general theory of relativity space without ether is unthinkable;
for in such space there not only wonld be no propagation of light,
but also no possibility of existence for standards of space and
time (measuring-rods and clocks), nor therefore any space-time
intervals in the physical sense. But this ether may not be thought
of as endowed with the quality characteristic of ponderable inedia,
as consisting of parts which may be tracked through time. The
idea of motion may not be applied to it.