Albert Einstein.

$a Äther und Relativitäts-Theorie + Geometrie und Erfahrung $l Englisch online

. (page 1 of 3)
Online LibraryAlbert Einstein$a Äther und Relativitäts-Theorie + Geometrie und Erfahrung $l Englisch → online text (page 1 of 3)
Font size
QR-code for this ebook


Produced by David Starner, William Fishburne and the Online
Distributed Proofreading Team.










SIDELIGHTS ON RELATIVITY

By Albert Einstein

Contents

ETHER AND THE THEORY OF RELATIVITY

An Address delivered on May 5th, 1920, in the University of Leyden

GEOMETRY AND EXPERIENCE

An expanded form of an Address to the Prussian Academy of Sciences
in Berlin on January 27th, 1921.





ETHER AND THE THEORY OF RELATIVITY

An Address delivered on May 5th, 1920, in the University of Leyden



How does it come about that alongside of the idea of ponderable
matter, which is derived by abstraction from everyday life, the
physicists set the idea of the existence of another kind of matter,
the ether? The explanation is probably to be sought in those phenomena
which have given rise to the theory of action at a distance, and
in the properties of light which have led to the undulatory theory.
Let us devote a little while to the consideration of these two
subjects.

Outside of physics we know nothing of action at a distance. When
we try to connect cause and effect in the experiences which natural
objects afford us, it seems at first as if there were no other mutual
actions than those of immediate contact, e.g. the communication of
motion by impact, push and pull, heating or inducing combustion by
means of a flame, etc. It is true that even in everyday experience
weight, which is in a sense action at a distance, plays a very
important part. But since in daily experience the weight of bodies
meets us as something constant, something not linked to any cause
which is variable in time or place, we do not in everyday life
speculate as to the cause of gravity, and therefore do not become
conscious of its character as action at a distance. It was Newton's
theory of gravitation that first assigned a cause for gravity by
interpreting it as action at a distance, proceeding from masses.
Newton's theory is probably the greatest stride ever made in
the effort towards the causal nexus of natural phenomena. And yet
this theory evoked a lively sense of discomfort among Newton's
contemporaries, because it seemed to be in conflict with the
principle springing from the rest of experience, that there can be
reciprocal action only through contact, and not through immediate
action at a distance. It is only with reluctance that man's desire
for knowledge endures a dualism of this kind. How was unity to
be preserved in his comprehension of the forces of nature? Either
by trying to look upon contact forces as being themselves distant
forces which admittedly are observable only at a very small
distance - and this was the road which Newton's followers, who were
entirely under the spell of his doctrine, mostly preferred to
take; or by assuming that the Newtonian action at a distance is
only _apparently_ immediate action at a distance, but in truth is
conveyed by a medium permeating space, whether by movements or by
elastic deformation of this medium. Thus the endeavour toward a
unified view of the nature of forces leads to the hypothesis of an
ether. This hypothesis, to be sure, did not at first bring with it
any advance in the theory of gravitation or in physics generally,
so that it became customary to treat Newton's law of force as an
axiom not further reducible. But the ether hypothesis was bound
always to play some part in physical science, even if at first only
a latent part.

When in the first half of the nineteenth century the far-reaching
similarity was revealed which subsists between the properties of
light and those of elastic waves in ponderable bodies, the ether
hypothesis found fresh support. It appeared beyond question that
light must be interpreted as a vibratory process in an elastic, inert
medium filling up universal space. It also seemed to be a necessary
consequence of the fact that light is capable of polarisation that
this medium, the ether, must be of the nature of a solid body,
because transverse waves are not possible in a fluid, but only in
a solid. Thus the physicists were bound to arrive at the theory
of the "quasi-rigid" luminiferous ether, the parts of which can
carry out no movements relatively to one another except the small
movements of deformation which correspond to light-waves.

This theory - also called the theory of the stationary luminiferous
ether - moreover found a strong support in an experiment which is
also of fundamental importance in the special theory of relativity,
the experiment of Fizeau, from which one was obliged to infer
that the luminiferous ether does not take part in the movements of
bodies. The phenomenon of aberration also favoured the theory of
the quasi-rigid ether.

The development of the theory of electricity along the path opened
up by Maxwell and Lorentz gave the development of our ideas concerning
the ether quite a peculiar and unexpected turn. For Maxwell himself
the ether indeed still had properties which were purely mechanical,
although of a much more complicated kind than the mechanical
properties of tangible solid bodies. But neither Maxwell nor his
followers succeeded in elaborating a mechanical model for the ether
which might furnish a satisfactory mechanical interpretation of
Maxwell's laws of the electro-magnetic field. The laws were clear
and simple, the mechanical interpretations clumsy and contradictory.
Almost imperceptibly the theoretical physicists adapted themselves
to a situation which, from the standpoint of their mechanical
programme, was very depressing. They were particularly influenced
by the electro-dynamical investigations of Heinrich Hertz. For
whereas they previously had required of a conclusive theory that
it should content itself with the fundamental concepts which belong
exclusively to mechanics (e.g. densities, velocities, deformations,
stresses) they gradually accustomed themselves to admitting electric and
magnetic force as fundamental concepts side by side with those of
mechanics, without requiring a mechanical interpretation for them.
Thus the purely mechanical view of nature was gradually abandoned.
But this change led to a fundamental dualism which in the long-run
was insupportable. A way of escape was now sought in the reverse
direction, by reducing the principles of mechanics to those
of electricity, and this especially as confidence in the strict
validity of the equations of Newton's mechanics was shaken by the
experiments with beta-rays and rapid kathode rays.

This dualism still confronts us in unextenuated form in the theory
of Hertz, where matter appears not only as the bearer of velocities,
kinetic energy, and mechanical pressures, but also as the bearer of
electromagnetic fields. Since such fields also occur _in vacuo_ - i.e.
in free ether - the ether also appears as bearer of electromagnetic
fields. The ether appears indistinguishable in its functions from
ordinary matter. Within matter it takes part in the motion of matter
and in empty space it has everywhere a velocity; so that the ether
has a definitely assigned velocity throughout the whole of space.
There is no fundamental difference between Hertz's ether and
ponderable matter (which in part subsists in the ether).

The Hertz theory suffered not only from the defect of ascribing
to matter and ether, on the one hand mechanical states, and on the
other hand electrical states, which do not stand in any conceivable
relation to each other; it was also at variance with the result of
Fizeau's important experiment on the velocity of the propagation
of light in moving fluids, and with other established experimental
results.

Such was the state of things when H. A. Lorentz entered upon the
scene. He brought theory into harmony with experience by means of
a wonderful simplification of theoretical principles. He achieved
this, the most important advance in the theory of electricity since
Maxwell, by taking from ether its mechanical, and from matter its
electromagnetic qualities. As in empty space, so too in the interior
of material bodies, the ether, and not matter viewed atomistically,
was exclusively the seat of electromagnetic fields. According to
Lorentz the elementary particles of matter alone are capable of
carrying out movements; their electromagnetic activity is entirely
confined to the carrying of electric charges. Thus Lorentz succeeded
in reducing all electromagnetic happenings to Maxwell's equations
for free space.

As to the mechanical nature of the Lorentzian ether, it may be said
of it, in a somewhat playful spirit, that immobility is the only
mechanical property of which it has not been deprived by H. A.
Lorentz. It may be added that the whole change in the conception
of the ether which the special theory of relativity brought about,
consisted in taking away from the ether its last mechanical quality,
namely, its immobility. How this is to be understood will forthwith
be expounded.

The space-time theory and the kinematics of the special theory
of relativity were 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 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_(mn)), 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 stand-point 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.




GEOMETRY AND EXPERIENCE

An expanded form of an Address to the Prussian Academy of Sciences
in Berlin on January 27th, 1921.



One reason why mathematics enjoys special esteem, above all other
sciences, is that its laws are absolutely certain and indisputable,
while those of all other sciences are to some extent debatable and
in constant danger of being overthrown by newly discovered facts.
In spite of this, the investigator in another department of science
would not need to envy the mathematician if the laws of mathematics
referred to objects of our mere imagination, and not to objects
of reality. For it cannot occasion surprise that different persons
should arrive at the same logical conclusions when they have already
agreed upon the fundamental laws (axioms), as well as the methods
by which other laws are to be deduced therefrom. But there is another
reason for the high repute of mathematics, in that it is mathematics
which affords the exact natural sciences a certain measure of
security, to which without mathematics they could not attain.

At this point an enigma presents itself which in all ages has agitated
inquiring minds. How can it be that mathematics, being after all
a product of human thought which is independent of experience, is
so admirably appropriate to the objects of reality? Is human reason,
then, without experience, merely by taking thought, able to fathom
the properties of real things.

In my opinion the answer to this question is, briefly, this: - As far
as the laws of mathematics refer to reality, they are not certain;
and as far as they are certain, they do not refer to reality.
It seems to me that complete clearness as to this state of things
first became common property through that new departure in mathematics
which is known by the name of mathematical logic or "Axiomatics."
The progress achieved by axiomatics consists in its having neatly
separated the logical-formal from its objective or intuitive
content; according to axiomatics the logical-formal alone forms
the subject-matter of mathematics, which is not concerned with the
intuitive or other content associated with the logical-formal.

Let us for a moment consider from this point of view any axiom of
geometry, for instance, the following: - Through two points in space
there always passes one and only one straight line. How is this
axiom to be interpreted in the older sense and in the more modern


1 3

Online LibraryAlbert Einstein$a Äther und Relativitäts-Theorie + Geometrie und Erfahrung $l Englisch → online text (page 1 of 3)