HERE IS THE ADDRESS IN ITS ENTIRETY
ETHER AND THE THEORY OF RELATIVITY
An address delivered on May 5th, 1920, in the University of Leyden
<< 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 this 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. It 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 "quasi rigid" 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 beta-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. It 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 modeled 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
I 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 movable 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
material 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 is not 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 these 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 ultimately to
assume 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, must 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
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
spacetime 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[greek subscript mu, nu]), 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 held
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 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 held 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 would 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 media, as
consisting of parts which may be tracked through time. The idea of
motion may not be applied to it. >> ------ Albert Einstein
