Ether and the Theory of Relativity
___________________________

by Albert Einstein, 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 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. 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 ``quas-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 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. 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 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 
characteristicwhich 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 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 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 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 magnitude being 
determined by the value of that mean 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 media, as consisting of parts which may be tracked 
through time. The idea of motion may not be applied to it. 

------------------
 
Kindly communicated by Gerald Y. Chin 
ger.chin@juno.com


Excerpts (by M. Luttgens)
________

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.

More careful reflection teaches us, however, that the special theory of
relativity does not compel us to deny ether.

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 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.

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.

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 media, as consisting of parts which may be tracked
through time. The idea of motion may not be applied to it.