Ether and the Theory of Relativity
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. 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
inay 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. 1n 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 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, 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.
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