| "Ether and the
Theory of
Relativity" Albert Einstein
(1920) 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 presented 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 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 permanently 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
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 gmn), 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.
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