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When we speak here of aether, we are, of course, not referring to
the corporeal aether of mechanical wave-theory that underlies Newtonian
mechanics, whose individual points each have a velocity assigned to
them. This theoretical construct has, in my opinion, been superseded
by the special theory of relativity. Rather the discussion concerns,
much more generally, those things thought of as physically real which,
besides ponderable matter consisting of electrical elementary particles,
play a role in the causal nexus of physics. Instead of ‘aether’,
one could equally well speak of ‘the physical qualities of space’.
Now, it might be claimed that this concept covers all objects of physics,
for according to consistent field theory, even ponderable matter,
or its constituent elementary particles, are to be understood as fields
of some kind or particular ‘states of space’. But it must
be admitted that such a view would be premature, since, thus far,
all efforts directed toward this goal have foundered. So we are effectively
forced by the current state of things to distinguish between matter
and aether, even though we may hope that future generations will transcend
this dualistic conception and replace it with a unified theory, as
the field theoreticians of our day have tried in vain to accomplish.

It is usually believed that aether is foreign to Newtonian physics
and that it was only the wave theory of light which introduced the
notion of an omnipresent medium influencing, and affected by, physical
phenomena. But this is not the case. Newtonian mechanics had its ‘aether’
in the sense indicated, albeit under the name ‘absolute space’.
To get a clear understanding of this and, at the same time, to explore
more fully the concept of aether, we must take a step back.

We will consider first a branch of physics which makes do without
any notion of aether, namely the geometry of Euclid, understood as
the study of the possible ways of bringing essentially rigid bodies
into contact with each other. (For now, we will set to one side light
rays, which may also contribute to the development of geometrical
concepts and theorems.) The laws concerning the placement of rigid
bodies, excluding relative motion, temperature and the influence of
deformations, as laid down in an idealised way in Euclid’s geometry,
derive from the concept of a rigid body. Any environmental influence
which could be thought of as existing independently of those bodies
and as acting on them and influencing the laws governing their placement
is unknown to Euclidean geometry. The same holds for the non-Euclidean
geometries of constant curvature if these are understood as conceivable
laws of nature. It would be different if we were to find ourselves
forced to adopt a geometry of variable curvature. This would mean
that the laws governing the ways essentially rigid bodies can be brought
into contact would be different in different cases, depending on environmental
influences. Here we would have to say that, in the sense we are considering,
such a theory would require an aether hypothesis. Its aether would
be something every bit as physically real as matter. If the laws of
placement were impervious to the influence of physical factors, such
as the accumulation and state of motion of bodies in the environment,
but irrevocably given, then we would call this aether ‘absolute’,
i.e. by its nature independent of any influence.

The kinematics, or phoronomy, of classical physics had as little
need of an aether as (physically interpreted) Euclidean geometry has.
For its laws have a clear physical meaning only if we assume that
the special-relativistic influences of motion on rulers and clocks
do not exist. Not so in the dynamics of Galileo and Newton. The law
of motion ‘force equals mass times acceleration’, does
not consist only of a statement about material systems, not even if,
according to Newton’s fundamental law of astronomy, the force
is expressed at a distance, i.e. by quantities whose ‘real definition’
[*definitio realis*, a definition in terms of the object’s
distinguishing properties] can be based on measurements involving
rigid bodies. For the ‘real definition’ of acceleration
cannot be completely reduced to observations of rigid bodies and clocks.
It cannot be reduced to the measurable distances between the points
that make up the mechanical system. Its definition requires also a
coordinate system or reference body having some suitable state of
motion. If a different coordinate system is chosen, the Newtonian
equations do not hold with respect to this new coordinate system.
With those equations, the milieu in which the bodies move appears
as an implicit, real factor in the laws of motion, alongside the real
bodies themselves and the distances that massive bodies define. In
contrast to geometry and kinematics, the ‘space’ of Newton’s
theory of motion possesses physical reality. We will call this physical
reality which enters the Newtonian law of motion alongside the observable,
ponderable real bodies, the aether of mechanics. The occurrence of
centrifugal effects with a (rotating) body, whose material points
do not change their distances from one another, shows that this aether
is not to be understood as a mere hallucination of the Newtonian theory,
but rather that it corresponds to something real that exists in nature.

We see that, for Newton, ‘space’ was something physically
real, in spite of the curiously indirect way this real thing reaches
our awareness. Ernst Mach, the first after Newton to subject the foundations
of mechanics to a deep analysis, perceived this clearly. He sought
to escape this hypothesis of the ‘mechanical aether’ by
reducing inertia to immediate interaction between the perceived mass
and all other masses of the universe. This view was certainly a logical
possibility but, as a theory involving action at a distance, cannot
be taken seriously today. The mechanical aether--which Newton called
‘absolute space’--must remain for us a physical reality.
Of course, one must not be tempted by the expression aether into thinking
that, like the physicists of the 19th century, we have in mind something
analogous to ponderable matter.

When Newton referred to the space of physics as ‘absolute’,
he was thinking of yet another property of what we call here aether.
Every physical thing influences others and is, it its turn, generally
influenced by other things. This does not however apply to the aether
of Newtonian mechanics. For the inertia-giving property of this aether
is, according to classical mechanics, not susceptible to any influence,
neither from the configuration of matter nor anything else. Hence
the term ‘absolute’.

Only in recent years has it become clear to physicists that the preferred
nature of initial systems, as opposed to non-inertial systems, requires
a real cause. Viewed historically, the aether hypothesis has emerged
in its present form by a process of sublimation from the mechanical
aether hypothesis of optics. After long and fruitless efforts, physicists
became convinced that light was not to be understood as the motion
of an inertial, elastic medium, that the electromagnetic fields of
Maxwell’s theory could not be construed as mechanical. So under
the pressure of this failure, the electromagnetic fields had gradually
come to be regarded as the final, irreducible physical reality, as
states of the aether, impervious to further explanation. What remained
of the mechanical theory was its definite state of motion; it somehow
embodied a state of absolute rest. While at least in Newtonian mechanics
all inertial systems were equivalent, it seemed that, in the Maxwell-Lorentz
theory, the state of motion of the preferred coordinate system (at
rest with respect to the aether) was completely determined. It was
accepted implicitly that this preferred coordinate system was also
an inertial system, i.e. that the principle of inertia [Newton’s
first law] applied relative to the electromagnetic aether.

There was another way too in which the Maxwell-Lorentz theory set
back physicists’ basic understanding. Since electromagnetic
fields were seen as fundamental, irreducible entities, they seemed
destined to rob ponderable masses, possessing inertia, of their primary
meaning. It was shown by Maxwell’s equations that a moving,
electrically charged body is surrounded by a magnetic field whose
energy is, to first approximation, a quadratic function of speed.
It seemed only natural to conceive of all kinetic energy as electromagnetic
energy. Thus one could hope to reduce mechanics to electromagnetism,
since efforts to reduce electromagnetic phenomena to mechanics had
failed. Indeed this looked all the more promising as it became apparent
that all ponderable matter was composed of electromagnetic elementary
particles. But there were two difficulties that could not be overcome.
Firstly the Maxwell-Loretz equations could not explain how the electric
charge constituting an electrical elementary particle can exist in
equilibrium in spite of the forces of electrostatic repulsion. Secondly
electromagnetic theory could not give a reasonably natural and satisfactory
explanation of gravitation. Nevertheless the results that electromagnetic
theory achieved for physics were so significant they came to be regarded
as a completely secured possession, indeed as its most firmly established
success.

The Maxwell-Lorentz theory eventually influenced our view of the
theoretical basis to the extent that it led to the creation of the
special theory of relativity. It was recognised that the equations
of electromagnetism did not, in fact, single out one particular state
of motion, but rather that, in accordance with these equations, just
as with those of classical mechanics, there exists an infinite multitude
of coordinate systems in mutually equivalent states of motion, providing
the appropriate transformation formulas are used for the spatial and
temporal coordinates. It is well known that this realisation entailed
a profound modification, not only in our ideas about space and time,
but also to kinematics and dynamics. No longer was a special state
of motion to be ascribed to the electromagnetic aether. Now, like
the aether of classical mechanics, it resulted not in the favoring
of a particular state of motion, only the favoring of a particular
state of acceleration. Because it was no longer possible to speak,
in any absolute sense, of simultaneous states at different locations
in the aether, the aether became, as it were, four dimensional, since
there was no objective way of ordering its states by time alone. According
to special relativity too, the aether was absolute, since its influence
on inertia and the propogation of light was thought of as being itself
independent of physical influence. While classical physics took it
for granted that the geometry of bodies was independent of their state
of motion, the special theory of relativity stated that the laws of
Euclidean geometry only apply to the positioning of bodies at rest
with respect to one another when these bodies are at rest with respect
to an inertial coordinate system.[1] This can
be easily concluded from the so-called Lorentz contraction. Thus geometry,
like dynamics, came to depend on the aether.

The general theory of relativity rectified a mischief of classical
dynamics. According to the latter, inertia and gravity appear as quite
different, mutually independent phenomena, even though they both depend
on the same quantity, mass. The theory of relativity resolved this
problem by establishing the behaviour of the electrically neutral
point-mass by the law of the geodetic line, according to which inertial
and gravitational effects are no longer considered as separate. In
doing so, it attached characteristics to the aether which vary from
point to point, determining the metric and the dynamic behaviour of
material points, and determined, in their turn, by physical factors,
namely the distribution of mass/energy.

Thus the aether of general relativity differs from those of classical
mechanics and special relativity in that it is not ‘absolute’
but determined, in its locally variable characteristics, by ponderable
matter. This determination is a complete one if the universe is finite
and closed. That there are, in general relativity, no preferred spacetime
coordinates uniquely associated with the metric is more characteristic
of its mathematical form than its physical framework.

Even using mathematical apparatus of general relativity it has not
been possible to reduce all of the inertia of mass to electromagnetic
fields, or to fields in general. Neither are we yet, in my view, at
the point of formally incorporating the electromagnetic forces into
the scheme of general relativity. On the one hand, the metric tensor,
which codetermines the phenomena of gravitation and inertia and, on
the other, the tensor of the electromagnetic field appear still as
different expressions of the state of the aether, whose logical independence
one is inclined to attribute rather to the incompleteness of our theoretical
ediface than to a complex structure of reality.

It is true that Weyl and Eddington have, by a generalisation of Riemannian
geometry, found a mathematical system, in which both kinds of field
appear to be unified under a single perspective. But the simplest
field laws which that theory provides seem to me not to advance physical
insight. On the whole, we seem to be much further now from an understanding
of the fundamental laws of electromagnetism than we did at the beginning
of this century. As justification for this opinion, I should here
like to briefly refer to the problem of the magnetic fields of the
earth and the sun, and also to the problem of light quanta, which
problems have some bearing on the gross and fine structure of the
electromagnetic field.

The earth and sun possess magnetic fields whose orientation and sense
are closely related to the spin axes of these bodies. According to
Maxwell’s theory, these fields may be due to electric currents
which flow in the opposite direction to the rotation of the earth
and sun about their axes. Even sunspots, which there are good grounds
to think of as vortices, posses analogous, and very powerful, magnetic
fields. But it is hardly conceivable that, in all these cases, circuits
or convection currents of sufficient strength are actually present.
Rather it looks as if cyclic motion of neutral masses generated magnetic
fields. Neither Maxwell’s theory as originally conceived nor
as extended in general relativity predict field generation of that
sort. Here nature seems to point us toward some fundamental connection,
not yet understood.[2]

If the case we have just discussed is one that field theory, in its
current form, seems not yet able to address, the facts and ideas subsumed
under quantum theory threaten to the blow the edifice of field theory
to bits. Specifically, we find increasing arguments suggesting that
the quanta of light are to be understood as physical reality, and
that the electromagnetic field cannot be seen as the final reality
to which all other physical objects can be reduced. As Planck’s
formula had already shown that the transmission of energy and momentum
by radiation happens as if the latter consisted of particles moving
at the speed of light, ,
with energy so
Compton demonstrated, by his research into the scattering of X-rays
by matter that scattering events occur in which quanta of light collide
with electrons and transmit to them a portion of their energy, as
a result of which the quanta of light undergo a change of energy and
direction. It is at least a fact that X-rays experience such changes
in frequency on scattering (in agreement with the predictions of Debye
and Compton) as quantum theory demands.

Recently there has appeared work by the Indian physicist Bose on
the derivation of Planck’s formula which is of particular significance
to our theoretical understanding for the following reasons: hitherto
all complete derivations of Planck’s formula made some use of
the hypothesis of the wave structure of radiation. So, for example,
in the well-known Ehrenfest-Debye derivation, the factor
in this formula was deduced by counting the eigenvibrations of the
cavity belonging to the frequency range .
Bose replaces this derivation based on the ideas of wave theory with
a gas-theoretical calculation which he applies to a quantum of light
conceived of like some sort of molecule present in the cavity. This
raises the question of whether it might perhaps also be possible to
link the phenomena of diffraction and interference to quantum theory
in such a way that the field-like concepts of the theory are presented
only as expressions of the interaction between quanta, so that independent
physical reality would no longer be ascribed to the fields.

The important fact that the radiation emitted is not, according to
Bohr’s frequency theory, determined by electrically charged
masses which periodically cycle through occurrences of the same frequency
can only strengthen this doubt of ours as to the independent reality
of the wave field.

But even if these possibilities do mature into an actual theory,
we will not be able to do without the aether in theoretical physics,
that is, a continuum endowed with physical properties; for general
relativity, to whose fundamental viewpoints physicists will always
hold fast, rules out direct action at a distance. But every theory
of local action assumes continuous fields, and thus also the existence
of an ‘aether’.

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