The speech by Albert Einstein

The speech by Albert Einstein

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 insuportable. 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 ß-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 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 world-threads. 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 vacua 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

gµ?), 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 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.

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.