This paper presents Chapter
III, section 4 from the book THE EVOLUTION
OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original
publication of this book by Simon and Schuster, New York (1942).
The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.
The heading below is linked to
the original materials.
The
electromagnetic wave is a transverse one and is propagated with the velocity of
light in empty space. The fact that their velocities are the same suggests a close
relationship between optical and electromagnetic phenomena.
The electromagnetic wave is not like the material wave. The
electromagnetic wave is “transverse” in the sense that its “density” does not
change as it propagates. The optical and electromagnetic phenomena have about
the same velocity because both are massless.
When
we had to choose between the corpuscular and the wave theory, we decided in
favour of the wave theory. The diffraction of light was the strongest argument
influencing our decision. But we shall not contradict any of the explanations
of the optical facts by also assuming that the light wave is an electromagnetic one. On the contrary, still other
conclusions can be drawn. If this is really so, then there must exist some connection
between the optical and electrical properties of matter that can be deduced
from the theory. The fact that conclusions of this kind can really be drawn and
that they stand the test of experiment is an essential argument in favour of
the electromagnetic theory of light.
A fast moving particle behaves like a wave that does not change
in “density”. For all practical purposes, it behaves like a wave but it is
called a “particle” because it has density. This description satisfies both the
corpuscular and the wave theory of light. The difference between optical and
electromagnetic wave phenomenon is primarily in terms of their densities.
This
great result is due to the field theory. Two apparently unrelated branches of
science are covered by the same theory. The same Maxwell’s equations describe
both electric induction and optical refraction. If it is our aim to describe
everything that ever happened or may happen with the help of one theory, then
the union of optics and electricity is, undoubtedly, a very great step forward.
From the physical point of view, the only difference between an ordinary
electromagnetic wave and a light wave is the wave-length: this is very small
for light waves, detected by the human eye, and great for ordinary
electromagnetic waves, detected by a radio receiver.
I shall differentiate between the field theory of Faraday, and
the electromagnetic theory of Maxwell. The electromagnetic theory is a special case
of the field theory. A field wave is very different from a material wave. The
concept of material wave-length may not apply to a field wave the same way. A
better concept shall be field density. The field density is many degrees of
magnitude smaller than material density.
The
old mechanical view attempted to reduce all events in nature to forces acting
between material particles. Upon this mechanical view was based the first naive
theory of the electric fluids. The field did not exist for the physicist of the
early years of the nineteenth century. For him only substance and its changes were
real. He tried to describe the action of two electric charges only by concepts
referring directly to the two charges.
The concept of field filling the space does not exist in the
mechanical view.
In
the beginning, the field concept was no more than a means of facilitating the
understanding of phenomena from the mechanical point of view. In the new field language
it is the description of the field between the two charges, and not the charges
themselves, which is essential for an understanding of their action. The
recognition of the new concepts grew steadily, until substance was overshadowed
by the field. It was realized that something of great importance had happened
in physics. A new reality was created, a new concept for which there was no
place in the mechanical description. Slowly and by a struggle the field concept
established for itself a leading place in physics and has remained one of the
basic physical concepts. The electromagnetic field is, for the modern
physicist, as real as the chair on which he sits.
The field is the new substance that is quite real.
But
it would be unjust to consider that the new field view freed science from the
errors of the old theory of electric fluids or that the new theory destroys the
achievements of the old. The new theory shows the merits as well as the
limitations of the old theory and allows us to regain our old concepts from a
higher level. This is true not only for the theories of electric fluids and
field, but for all changes in physical theories, however revolutionary they may
seem. In our case, we still find, for example, the concept of the electric charge
in Maxwell’s theory, though the charge is understood only as a source of the
electric field. Coulomb’s law is still valid and is contained in Maxwell’s equations
from which it can be deduced as one of the many consequences. We can still
apply the old theory, whenever facts within the region of its validity are
investigated. But we may as well apply the new theory, since all the known
facts are contained in the realm of its validity.
The new theory shows the merits as well as the limitations of
the old theory and allows us to regain our old concepts from a higher level.
The concept of charge now belongs to the old theory. The electrostatic field
originates from the unbalanced particle-void interface.
To
use a comparison, we could say that creating a new theory is not like
destroying an old barn and erecting a skyscraper in its place. It is rather
like climbing a mountain, gaining new and wider views, discovering unexpected
connections between our starting-point and its rich environment. But the point
from which we started out still exists and can be seen, although it appears
smaller and forms a tiny part of our broad view gained by the mastery of the
obstacles on our adventurous way up.
This paragraph is quite a poetic expression by Einstein.
It
was, indeed, a long time before the full content of Maxwell’s theory was
recognized. The field was at first considered as something which might later be
interpreted mechanically with the help of ether. By the time it was realized
that this programme could not be carried out, the achievements of the field
theory had already become too striking and important for it to be exchanged for
a mechanical dogma. On the other hand, the problem of devising the mechanical
model of ether seemed to become less and less interesting and the result, in
view of the forced and artificial character of the assumptions, more and more
discouraging.
The field theory of Faraday and Maxwell has finally overcome the
mechanical dogma.
Our
only way out seems to be to take for granted the fact that space has the
physical property of transmitting electromagnetic waves, and not to bother too much
about the meaning of this statement. We may still use the word ether, but only
to express some physical property of space. This word ether has changed its meaning
many times in the development of science. At the moment it no longer stands for
a medium built up of particles. Its story, by no means finished, is continued by
the relativity theory.
Aether no longer stands for a mechanical medium built up by
particles. It now fills the space with the physical property of transmitting
field waves.
.
FINAL COMMENTS
A fast moving particle behaves like a wave. The lighter it
becomes, the faster it moves, and the more wave-like properties it acquires.
After shrinking down in size to the nucleus of an atom, the particle starts to
lessen in density and becomes diffused; and so we have the quantum particles
like electron. Such particles diffuse further in density to become a field and the
wave-like xsdc disturbance in it.
The property of a fast moving quantum particle is that it does
not change in its density; and so it appears like a transverse wave. Its wave
characteristics are very different from that of a material wave. It is diffused
in its density and spread out in space.
An electromagnetic wave that exists among the nuclei of atoms is
much denser than the light that exists in space. Both are field waves. The “electromagnetic
spectrum” is more properly characterized as “field spectrum”.
The electromagnetic theory of Maxwell applies more specifically
to the electromagnetic wave that has a certain uniform density among the nuclei
of atoms. It does not apply to all the field waves because their specific characteristics
are based on their densities, which differ throughout the field spectrum.
The concept of field filling the space is very similar to the
concept of aether filling the space, except that field, unlike the aether, is
not mechanical. The mechanical view applies to solid particles, whereas the
field view applies to diffused quanta.
The field is the new substance that is quite real. It now fills
the space with the physical property of transmitting field waves.
This paper presents Chapter
III, section 3 from the book THE EVOLUTION
OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original
publication of this book by Simon and Schuster, New York (1942).
The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.
The heading below is linked to
the original materials.
The
quantitative, mathematical description of the laws of the field is summed up in
what are called Maxwell’s equations. The facts mentioned so far led to the
formulation of these equations, but their content is much richer than we have
been able to indicate. Their simple form conceals a depth revealed only by
careful study.
The
formulation of these equations is the most important event in physics since
Newton’s time, not only because of their wealth of content, but also because they
form a pattern for a new type of law.
The
characteristic features of Maxwell’s equations, appearing in all other
equations of modern physics, are summarized in one sentence. Maxwell’s
equations are laws representing the structure
of the field.
Maxwell’s equations are laws representing the structure of the
field.
Why do Maxwell’s equations differ in form and character from the equations of classical mechanics? What does it mean that these equations describe the structure of the field? How is it possible that, from the results of Oersted’s and Faraday’s experiments, we can form a new type of law, which proves so important for the further development of physics?
We
have already seen, from Oersted’s experiment, how a magnetic field coils itself
around a changing electric field. We have seen, from Faraday’s experiment, how
an electric field coils itself around a changing magnetic field. To outline
some of the characteristic features of Maxwell’s theory, let us, for the
moment, focus all our attention on one of these experiments, say, on that of
Faraday. We repeat the drawing in which an electric current is induced by a
changing magnetic field. We already know that an induced current appears if the
number of lines of force, passing the surface bounded by the wire, changes.
Then the current will appear if the magnetic field changes or the circuit is
deformed or moved: if the number of magnetic lines passing through the surface
is changed, no matter how this change is caused. To take into account all these
various possibilities, to discuss their particular influences, would necessarily
lead to a very complicated theory. But can we not simplify our problem? Let us try
to eliminate from our considerations everything which refers to the shape of
the circuit, to its length, to the surface enclosed by the wire. Let us imagine
that the circuit in our last drawing becomes smaller and smaller, shrinking
gradually to a very small circuit enclosing a certain point in space. Then
everything concerning shape and size is quite irrelevant. In this limiting
process where the closed curve shrinks to a point, size and shape automatically
vanish from our considerations and we obtain laws connecting changes of
magnetic and electric field at an arbitrary point in space at an arbitrary
instant.
Thus,
this is one of the principal steps leading to Maxwell’s equations. It is again
an idealized experiment performed in imagination by repeating Faraday’s
experiment with a circuit shrinking to a point.
The Maxwell equations are obtained from repeating Faraday’s
experiment, in imagination, with a circuit shrinking to a point.
We
should really call it half a step rather than a whole one. So far our attention
has been focused on Faraday’s experiment. But the other pillar of the field theory,
based on Oersted’s experiment, must be considered just as carefully and in a similar
manner. In this experiment the magnetic lines of force coil themselves around
the current. By shrinking the circular magnetic lines of force to a point, the
second half-step is performed and the whole step yields a connection between the
changes of the magnetic and electric fields at an arbitrary point in space and
at an arbitrary instant.
Here the point must be continuous with its neighboring points
and not discrete as it sounds.
But
still another essential step is necessary. According to Faraday’s experiment,
there must be a wire testing the existence of the electric field, just as there
must be a magnetic pole, or needle, testing the existence of a magnetic field
in Oersted’s experiment. But Maxwell’s new theoretical idea goes beyond these
experimental facts. The electric and magnetic field or, in short, the electromagnetic field is, in Maxwell’s
theory, something real. The electric field is produced by a changing magnetic
field, quite independently, whether or not there is a wire to test its existence;
a magnetic field is produced by a changing electric field, whether or not there
is a magnetic pole to test its existence.
This electromagnetic field must exist even when there are no
instruments to test their presence.
Thus
two essential steps led to Maxwell’s equations. The first: in considering
Oersted’s and Rowland’s experiments, the circular line of the magnetic field
coiling itself around the current and the changing electric field had to be
shrunk to a point; in considering Faraday’s experiment, the circular line of
the electric field coiling itself around the changing magnetic field had to be shrunk
to a point. The second step consists of the realization of the field as
something real; the electromagnetic field once created exists, acts, and changes
according to Maxwell’s laws.
Maxwell’s
equations describe the structure of the electromagnetic field. All space is the
scene of these laws and not, as for mechanical laws, only points in which
matter or charges are present.
The electromagnetic field once created exists, acts, and changes
in space according to Maxwell’s laws in the absence of even matter and charges.
We
remember how it was in mechanics. By knowing the position and velocity of a
particle at one single instant, by knowing the acting forces, the whole future path
of the particle could be foreseen. In Maxwell’s theory, if we know the field at
one instant only, we can deduce from the equations of the theory how the whole
field will change in space and time. Maxwell’s equations enable us to follow
the history of the field, just as the mechanical equations enabled us to follow
the history of material particles.
Maxwell’s equations enable us to follow the history of the
field, just as the mechanical equations enabled us to follow the history of
material particles.
But
there is still one essential difference between mechanical laws and Maxwell’s
laws. A comparison of Newton’s gravitational laws and Maxwell’s field laws will
emphasize some of the characteristic features expressed by these equations.
With
the help of Newton’s laws we can deduce the motion of the earth from the force
acting between the sun and the earth. The laws connect the motion of the earth
with the action of the far-off sun. The earth and the sun, though so far apart,
are both actors in the play of forces.
In
Maxwell’s theory there are no material actors. The mathematical equations of
this theory express the laws governing the electromagnetic field. They do not, as
in Newton’s laws, connect two widely separated events; they do not connect the
happenings here with the conditions there.
The field here and now depends on the field in the immediate neighbourhood at a time just past. The equations allow us to
predict what will happen a little farther in space and a little later in time, if
we know what happens here and now. They allow us to increase our knowledge of
the field by small steps. We can deduce what happens here from that which happened
far away by the summation of these very small steps. In Newton’s theory, on the
contrary, only big steps connecting distant events are permissible. The experiments
of Oersted and Faraday can be regained from Maxwell’s theory, but only by the
summation of small steps each of which is governed by Maxwell’s equations.
In Newton’s theory there are material actors that influence each
other in big steps. But in Maxwell’s theory there are no material actors and
influence occurs in very small steps. In my opinion there are unexpressed
quanta in Maxwell’s theory that are spread uniformly throughout the field.
A
more thorough mathematical study of Maxwell’s equations shows that new and
really unexpected conclusions can be drawn and the whole theory submitted to a
test on a much higher level, because the theoretical consequences are now of a
quantitative character and are revealed by a whole chain of logical arguments.
Let
us again imagine an idealized experiment. A small sphere with an electric
charge is forced, by some external influence, to oscillate rapidly and in a
rhythmical way, like a pendulum. With the knowledge we already have of the
changes of the field, how shall we describe everything that is going on here,
in the field language?
The
oscillation of the charge produces a changing electric field. This is always
accompanied by a changing magnetic field. If a wire forming a closed circuit is
placed in the vicinity, then again the changing magnetic field will be
accompanied by an electric current in the circuit. All this is merely a
repetition of known facts, but the study of Maxwell’s equations gives a much
deeper insight into the problem of the oscillating electric charge. By
mathematical deduction from Maxwell’s equations we can detect the character of
the field surrounding an oscillating charge, its structure near and far from
the source and its change with time. The outcome of such deduction is the electromagnetic wave. Energy radiates
from the oscillating charge travelling with a definite speed through space; but
a transference of energy, the motion of a state, is characteristic of all wave
phenomena.
Maxwell’s equations predict that an oscillating charge shall
produce an electromagnetic wave that travels with a definite speed through
space.
Different
types of waves have already been considered. There was the longitudinal wave
caused by the pulsating sphere, where the changes of density were propagated
through the medium. There was the jellylike medium in which the transverse wave
spread. A deformation of the jelly, caused by the rotation of the sphere, moved
through the medium. What kind of changes are now spreading in the case of an
electromagnetic wave? Just the changes of an electromagnetic field! Every
change of an electric field produces a magnetic field; every change of this
magnetic field produces an electric field; every change of…, and so on. As
field represents energy, all these changes spreading out in space, with a
definite velocity, produce a wave. The electric and magnetic lines of force
always lie, as deduced from the theory, on planes perpendicular to the
direction of propagation. The wave produced is, therefore, transverse. The
original features of the picture of the field we formed from Oersted’s and
Faraday’s experiments are still preserved, but we now recognize that it has a
deeper meaning.
Energy is the property of a substance that has become dynamic. A
field is, therefore, a substance that is changing rapidly. The electric field
seems to be changing in the direction of propagation like the electric current.
And the magnetic field is changing perpendicular to that direction. But
Maxwell’s equations seem to give a different picture as described above.
The
electromagnetic wave spreads in empty space. This, again, is a consequence of
the theory. If the oscillating charge suddenly ceases to move, then its field becomes
electrostatic. But the series of waves created by the oscillation continues to
spread. The waves lead an independent existence and the history of their changes
can be followed just as that of any other material object.
The field also is its own medium. The waves lead an independent
existence and the history of their changes can be followed just as that of any
other material object.
We
understand that our picture of an electromagnetic wave, spreading with a
certain velocity in space and changing in time, follows from Maxwell’s
equations only because they describe the structure of the electromagnetic field
at any point in space and for any instant.
There
is another very important question. With what speed does the electromagnetic
wave spread in empty space? The theory, with the support of some data from simple
experiments having nothing to do with the actual propagation of waves, gives a
clear answer: the velocity of an
electromagnetic wave is equal to the velocity of light.
There are two distinct velocities: The velocity in material
domain, and the velocity in radiation domain. The inertia of these two domains
is very far apart, and so are their velocities. All the velocities in the radiation
domain appear to be the same from the perspective of material domain. So, it is
no surprise that the velocity of electromagnetic wave is same as the velocity
of light.
Oersted’s
and Faraday’s experiments formed the basis on which Maxwell’s laws were built.
All our results so far have come from a careful study of these laws, expressed
in the field language. The theoretical discovery of an electromagnetic wave
spreading with the speed of light is one of the greatest achievements in the
history of science.
Experiment has confirmed the prediction of theory. Fifty years ago, Hertz proved, for the first time, the existence of electromagnetic waves and confirmed experimentally that their velocity is equal to that of light. Nowadays, millions of people demonstrate that electromagnetic waves are sent and received. Their apparatus is far more complicated than that used by Hertz and detects the presence of waves thousands of miles from their sources instead of only a few yards.
The electromagnetic wave produced by an oscillating charge is of
a different substantiality then that of the electromagnetic field existing among
the nuclei of the atoms.
.
FINAL COMMENTS
Maxwell’s equations provide laws for the structure of the
electromagnetic field. The electromagnetic field is continuous throughout the
space of the atom. The electric and magnetic components of the electromagnetic
field induce each other. It is as if the magnetic component is providing the
medium for the electric component to flow.
A field is a substance that is changing rapidly. This rapid
change is its energy. The electric component seems to be changing in the
direction of propagation like the electric current. The magnetic component
seems to be changing perpendicular to that direction acting as a medium for
that flow. Maxwell’s equations, however, mathematically, portray both electric
and magnetic components to be changing perpendicular to the direction of
propagation.
This electromagnetic field is as real as the nucleus of the
atom. It flows through the space among the nuclei of atoms. It has a certain
amount of substantiality, which is less than the substantiality of the nuclei.
This substantiality may be compared to the thick consistency of soup. It is continuous
throughout itself and with the mass of the nuclei.
The substantiality of the field may vary, but the Maxwell’s
equations assume it to be constant throughout. This is not the case, however,
as was discovered by Einstein later, and the word “quanta” was coined. The substantiality
or “quanta” varies with the frequency of the electromagnetic field.
In Newton’s theory the material actors influence each other in
big steps. But in Maxwell’s theory the quanta influences itself in small
continuous steps. This may be identified as the frequency of the field.
There are two distinct velocities: The velocity in material
domain, and the velocity in radiation domain. These velocities are poles apart
by many degrees of magnitude. It is no surprise that the velocity of electromagnetic
wave appears to be the same as the velocity of light from the perspective of
the material domain.
Maxwell’s equations enable us to follow the history of the
field, just as the mechanical equations enabled us to follow the history of
material particles (subject to its assumptions, of course).
This paper presents Chapter
III, section 2 from the book THE EVOLUTION
OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original
publication of this book by Simon and Schuster, New York (1942).
The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.
The heading below is linked to
the original materials.
“The
change of an electric field is accompanied by a magnetic field.” If we
interchange the words “magnetic” and “electric”, our
sentence reads: “The change of a magnetic field is accompanied by an
electric field.” Only an experiment can decide whether or not this statement
is true. But the idea of formulating this problem is suggested by the use of
the field language.
Just over a hundred years ago, Faraday performed an experiment which led to the great discovery of induced currents.
The
demonstration is very simple. We need only a solenoid or some other circuit, a
bar magnet, and one of the many types of apparatus for detecting the existence of
an electric current. To begin with, a bar magnet is kept at rest near a
solenoid which forms a closed circuit. No current flows through the wire, for
no source is present. There is only the magnetostatic field of the bar magnet
which does not change with time. Now, we quickly change the position of the
magnet either by removing it or by bringing it nearer the solenoid, whichever
we prefer. At this moment, a current will appear for a very short time and then
vanish. Whenever the position of the magnet is changed, the current reappears,
and can be detected by a sufficiently sensitive apparatus. But a current—from
the point of view of the field theory—means the existence of an electric field
forcing the flow of the electric fluids through the wire. The current, and
therefore the electric field, too, vanishes when the magnet is again at rest.
The lines of force seem to be fixed in space around a magnet. As
a closed circuit moves relative to these lines of force, the lines of force
move relative to the closed circuit, which then appear as a current through the
circuit.
Imagine
for a moment that the field language is unknown and the results of this
experiment have to be described, qualitatively and quantitatively, in the language
of old mechanical concepts. Our experiment then shows: by the motion of a
magnetic dipole a new force was created, moving the electric fluid in the wire.
The next question would be: upon what does this force depend? This would be
very difficult to answer. We should have to investigate the dependence of the force
upon the velocity of the magnet, upon its shape, and upon the shape of the
circuit. Furthermore, this experiment, if interpreted in the old language,
gives us no hint at all as to whether an induced current can be excited by the
motion of another circuit carrying a current, instead of by motion of a bar
magnet.
The old interpretation does not include what is going on in the space around a magnet, or in the space around a current.
It
is quite a different matter if we use the field language and again trust our
principle that the action is determined by the field. We see at once that a
solenoid through which a current flows would serve as well as a bar magnet. The
drawing shows two solenoids: one, small, through which a current flows, and the
other, in which the induced current is detected, larger. We could move the
small solenoid, as we previously moved the bar magnet, creating an induced
current in the larger solenoid. Furthermore, instead of moving the small
solenoid, we could create and destroy a magnetic field by creating and
destroying the current, that is, by opening and closing the circuit. Once
again, new facts suggested by the field theory are confirmed by experiment!
New facts suggested by the field theory are confirmed by experiment!
Let
us take a simpler example. We have a closed wire without any source of current.
Somewhere in the vicinity is a magnetic field. It means nothing to us whether
the source of this magnetic field is another circuit through which an electric
current flows, or a bar magnet. Our drawing shows the closed circuit and the
magnetic lines of force. The qualitative and quantitative description of the
induction phenomena is very simple in terms of the field language. As marked on
the drawing, some lines of force go through the surface bounded by the wire. We
have to consider the lines of force cutting that part of the plane which has
the wire for a rim. No electric current is present so long as the field does
not change, no matter how great its strength. But a current begins to flow
through the rim-wire as soon as the number of lines passing through the surface
surrounded by wire changes. The current is determined by the change, however it
may be caused, of the number of lines passing the surface. This change in the number
of lines of force is the only essential concept for both the qualitative and
the quantitative descriptions of the induced current. “The number of lines
changes” means that the density of the lines changes and this, we remember,
means that the field strength changes.
The current is determined by the change; however it may be
caused, of the number of lines passing the surface.
These
then are the essential points in our chain of reasoning: change of magnetic
field à
induced currentà motion
of charge à
existence of an electric field.
Therefore:
a changing magnetic field is accompanied
by an electric field.
Thus
we have found the two most important pillars of support for the theory of the
electric and magnetic field. The first is the connection between the changing electric
field and the magnetic field. It arose from Oersted’s experiment on the
deflection of a magnetic needle and led to the conclusion: a changing electric field is accompanied by a magnetic field.
The
second connects the changing magnetic field with the induced current and arose
from Faraday’s experiment. Both formed a basis for quantitative description.
Again
the electric field accompanying the changing magnetic field appears as
something real. We had to imagine, previously, the magnetic field of a current existing
without the testing pole. Similarly, we must claim here that the electric field
exists without the wire testing the presence of an induced current.
In
fact, our two-pillar structure could be reduced to only one, namely, to that
based on Oersted’s experiment. The result of Faraday’s experiment could be deduced
from this with the law of conservation of energy. We used the two-pillared
structure only for the sake of clearness and economy.
A changing electric field is accompanied by a magnetic field;
and a changing magnetic field is accompanied by an electric field. But the two
are the same phenomenon.
One
more consequence of the field description should be mentioned. There is a
circuit through which a current flows, with, for instance, a voltaic battery as
the source of the current. The connection between the wire and the source of
the current is suddenly broken. There is, of course, no current now! But during
this short interruption an intricate process takes place, a process which could
again have been foreseen by the field theory. Before the interruption of the
current, there was a magnetic field surrounding the wire. This ceased to exist
the moment the current was interrupted. Therefore, through the interruption of
a current, a magnetic field disappeared. The number of lines of force passing through
the surface surrounded by the wire changed very rapidly. But such a rapid
change, however it is produced, must create an induced current. What really
matters is the change of the magnetic field making the induced current stronger
if the change is greater. This consequence is another test for the theory. The
disconnection of a current must be accompanied by the appearance of a strong,
momentary induced current. Experiment again confirms the prediction. Anyone who
has ever disconnected a current must have noticed that a spark appears. This
spark reveals the strong potential differences caused by the rapid change of
the magnetic field.
The
same process can be looked at from a different point of view, that of energy. A
magnetic field disappeared and a spark was created. A spark represents energy,
therefore so also must the magnetic field. To use the field concept and its
language consistently, we must regard the magnetic field as a store of energy. Only
in this way shall we be able to describe the electric and magnetic phenomena in
accordance with the law of conservation of energy.
Electric and magnetic lines of force are two different forms of
the same substance. They appear to transform into each other.
Starting
as a helpful model, the field became more and more real. It helped us to
understand old facts and led us to new ones. The attribution of energy to the field
is one step farther in the development in which the field concept was stressed
more and more, and the concepts of substances, so essential to the mechanical point
of view, were more and more suppressed.
The concept of substance is associated more with the mechanical
view, whereas, the concept of energy is associated with the field view.
.
FINAL COMMENTS
We associate matter with the mechanical view. Motion of this
matter is then viewed as mechanical energy. Substance is a more general form of
matter. Motion of substance may then be viewed as a more general form of
energy.
Substance is recognized by its substantiality of which the core
characteristic is force. As force becomes dynamic it appears as energy. We may
describe force and energy as the static and dynamic forms of substance. This
may help clear up the confusion that has come about from using Newton’s
terminology in describing the field concepts.
The magnetic lines of force seem to denote the substance, which when moved appears in its dynamic form as the electric lines of “energy”.
This paper presents Chapter
III, section 1 from the book THE EVOLUTION
OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original
publication of this book by Simon and Schuster, New York (1942).
The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.
The heading below is linked to
the original materials.
DURING
the second half of the nineteenth century new and revolutionary ideas were
introduced into physics; they opened the way to a new philosophical view, differing
from the mechanical one. The results of the work of Faraday, Maxwell, and Hertz
led to the development of modern physics, to the creation of new concepts,
forming a new picture of reality.
Our task now is to describe the break brought about in science by these new concepts and to show how they gradually gained clarity and strength. We shall try to reconstruct the line of progress logically, without bothering too much about chronological order.
The
new concepts originated in connection with the phenomena of electricity, but it
is simpler to introduce them, for the first time, through mechanics. We know that
two particles attract each other and that this force of attraction decreases
with the square of the distance. We can represent this fact in a new way, and
shall do so even though it is difficult to understand the advantage of this.
The small circle in our drawing represents an attracting body, say, the sun.
Actually, our diagram should be imagined as a model in space and not as a drawing
on a plane. Our small circle, then, stands for a sphere in space, say, the sun.
A body, the so-called test body,
brought somewhere within the vicinity of the sun will be attracted along the
line connecting the centres of the two bodies. Thus the lines in our drawing indicate
the direction of the attracting force of the sun for different positions of the
test body. The arrow on each line shows that the force is directed toward the
sun; this means the force is an attraction. These are the lines of force of the gravitational field. For the moment, this is
merely a name and there is no reason for stressing it further. There is one
characteristic feature of our drawing which will be emphasized later. The lines
of force are constructed in space, where no matter is present. For the moment,
all the lines of force, or briefly speaking, the field, indicate only how a test body would behave if brought into
the vicinity of the sphere for which the field is constructed.
Faraday’s lines of force are the earliest representation of
field. They exist in space where there is no matter.
The
lines in our space model are always perpendicular to the surface of the sphere.
Since they diverge from one point, they are dense near the sphere and become
less and less so farther away. If we increase the distance from the sphere
twice or three times, then the density of the lines, in our space model, though
not in the drawing, will be four or nine times less. Thus the lines serve a
double purpose. On the one hand, they show the direction of the force acting on
a body brought into the neighbourhood of the sphere-sun. On the other hand, the
density of the lines of force in space shows how the force varies with the
distance. The drawing of the field, correctly interpreted, represents the
direction of the gravitational force and its dependence on distance. One can
read the law of gravitation from such a drawing just as well as from a
description of the action in words, or in the precise and economical language
of mathematics. This field representation,
as we shall call it, may appear clear and interesting, but there is no reason
to believe that it marks any real advance. It would be quite difficult to prove
its usefulness in the case of gravitation. Some may, perhaps, find it helpful
to regard these lines as something more than drawings, and to imagine the real
actions of force passing through them. This may be done, but then the speed of
the actions along the lines of force must be assumed as infinitely great! The
force between two bodies, according to Newton’s law, depends only on distance;
time does not enter the picture. The force has to pass from one body to another
in no time! But, as motion with infinite speed cannot mean much to any reasonable
person, an attempt to make our drawing something more than a model leads
nowhere.
The lines of force indicate the direction of the force. The
density of the lines of force in space shows how the force varies with the
distance. If this field carries motion with infinite speed (as per Newton’s
law) it cannot be taken as real.
We
do not intend, however, to discuss the gravitational problem just now It served
only as an introduction, simplifying the explanation of similar methods of reasoning
in the theory of electricity.
We
shall begin with a discussion of the experiment which created serious
difficulties in our mechanical interpretation. We had a current flowing through
a wire circuit in the form of a circle. In the middle of the circuit was a
magnetic needle. The moment the current began to flow a new force appeared,
acting on the magnetic pole, and perpendicular to any line connecting the wire
and the pole. This force, if caused by a circulating charge, depended, as shown
by Rowland’s experiment, on the velocity of the charge. These experimental facts
contradicted the philosophical view that all forces must act on the line
connecting the particles and can depend only upon distance.
The magnetic force does not act as postulated by the mechanical
view.
The
exact expression for the force of a current acting on a magnetic pole is quite
complicated, much more so, indeed, than the expression for gravitational forces.
We can, however, attempt to visualize the actions just as we did in the case of
a gravitational force. Our question is: with what force does the current act upon
a magnetic pole placed somewhere in its vicinity? It would be rather difficult
to describe this force in words. Even a mathematical formula would be complicated
and awkward. It is best to represent all we know about the acting forces by a
drawing, or rather by a spatial model, with lines of force. Some difficulty is
caused by the fact that a magnetic pole exists only in connection with another
magnetic pole, forming a dipole. We can, however, always imagine the magnetic
needle of such length that only the force acting upon the pole nearer the
current has to be taken into account. The other pole is far enough away for the
force acting upon it to be negligible. To avoid ambiguity we shall say that the
magnetic pole brought nearer to the wire is the positive one.
We postulate that the magnetic pole brought nearer to the wire
is the positive one.
The character of the force acting upon the positive magnetic pole can be read from our drawing.
First
we notice an arrow near the wire indicating the direction of the current, from
higher to lower potential. All other lines are just lines offeree belonging to
this current and lying on a certain plane. If drawn properly, they tell us the
direction of the force vector representing the action of the current on a given
positive magnetic pole as well as something about the length of this vector.
Force, as we know, is a vector, and to determine it we must know its direction
as well as its length. We are chiefly concerned with the problem of the
direction of the force acting upon a pole. Our question is: how can we find,
from the drawing, the direction of the force, at any point in space?
How can we find, from the drawing, the direction of the force, at any point in space?
The
rule for reading the direction of a force from such a model is not as simple as
in our previous example, where the lines of force were straight. In our next
diagram only one line of force is drawn in order to clarify the procedure. The
force vector lies on the tangent to the line of force, as indicated. The arrow
of the force vector and the arrows on the line of force point in the same
direction. Thus this is the direction in which the force acts on a magnetic
pole at this point. A good drawing, or rather a good model, also tells us
something about the length of the force vector at any point. This vector has to
be longer where the lines are denser, i.e., near the wire, shorter where the lines
are less dense, i.e., far from the wire.
This vector has to be longer where the lines are denser, i.e.,
near the wire, shorter where the lines are less dense, i.e., far from the wire.
In this way, the lines of force, or in other words, the field, enable us to determine the forces acting on a magnetic pole at any point in space. This, for the time being, is the only justification for our elaborate construction of the field. Knowing what the field expresses, we shall examine with a far deeper interest the lines of force corresponding to the current. These lines are circles surrounding the wire and lying on the plane perpendicular to that in which the wire is situated. Reading the character of the force from the drawing, we come once more to the conclusion that the force acts in a direction perpendicular to any line connecting the wire and the pole, for the tangent to a circle is always perpendicular to its radius. Our entire knowledge of the acting forces can be summarized in the construction of the field. We sandwich the concept of the field between that of the current and that of the magnetic pole in order to represent the acting forces in a simple way.
Our entire knowledge of the acting forces can be summarized in
the construction of the field.
Every
current is associated with a magnetic field, i.e., a force always acts on a
magnetic pole brought near the wire through which a current flows. We may remark
in passing that this property enables us to construct sensitive apparatus for
detecting the existence of a current. Once having learned how to read the
character of the magnetic forces from the field model of a current, we shall
always draw the field surrounding the wire through which the current flows, in
order to represent the action of the magnetic forces at any point in space. Our
first example is the so-called solenoid. This is, in fact , a coil of wire as
shown in the drawing. Our aim is to learn, by experiment, all we can about the
magnetic field associated with the current flowing through a solenoid and to
incorporate this knowledge in the construction of a field. A drawing represents
our result. The curved lines of force are closed, and surround the solenoid in
a way characteristic of the magnetic field of a current.
The curved lines of force are closed, and surround the solenoid
in a way characteristic of the magnetic field of a current.
The field of a bar magnet can be represented in the same way as that of a current. Another drawing shows this. The lines of force are directed from the positive to the negative pole. The force vector always lies on^ the tangent to the line of force and is longest near the poles because the density of the lines is greatest at these points. The force vector represents the action of the magnet on a positive magnetic pole. In this case the magnet and not the current is the “source” of the field.
In this case the magnet and not the current is the “source”
of the field.
Our
last two drawings should be carefully compared. In the first, we have the
magnetic field of a current flowing through a solenoid; in the second, the
field of a bar magnet. Let us ignore both the solenoid and the bar and observe
only the two outside fields. We immediately notice that they are of exactly the
same character; in each case the lines of force lead from one end of the
solenoid or bar to the other.
The
field representation yields its first fruit! It would be rather difficult to
see any strong similarity between the current flowing through a solenoid and a bar
magnet if this were not revealed by our construction of the field.
The field representation reveals the clue that in each case the
lines of force lead from one end of the solenoid or bar to the other.
The
concept of field can now be put to a much more severe test. We shall soon see
whether it is anything more than a new representation of the acting forces. We
could reason: assume, for a moment, that the field characterizes all actions
determined by its sources in a unique way. This is only a guess. It would mean
that if a solenoid and a bar magnet have the same field, then all their
influences must also be the same. It would mean that two solenoids, carrying
electric currents, behave like two bar magnets, that they attract or repel each
other, depending exactly as in the case of bars, on their relative positions.
It would also mean that a solenoid and a bar attract or repel each other in the
same way as two bars. Briefly speaking, it would mean that all actions of a
solenoid through which a current flows and of a corresponding bar magnet are
the same, since the field alone is responsible for them, and the field in both
cases is of the same character. Experiment fully confirms our guess!
All actions of a solenoid through which a current flows and of a
corresponding bar magnet are the same, since the field alone is responsible for
them
How
difficult it would be to find those facts without the concept of field! The
expression for a force acting between a wire through which a current flows and
a magnetic pole is very complicated. In the case of two solenoids, we should
have to investigate the forces with which two currents act upon each other. But
if we do this, with the help of the field, we immediately notice the character
of all those actions at the moment when the similarity between the field of a
solenoid and that of a bar magnet is seen.
We
have the right to regard the field as something much more than we did at first.
The properties of the field alone appear to be essential for the description of
phenomena; the differences in source do not matter. The concept of field
reveals its importance by leading to new experimental facts.
The field presents the force pictorially, which, otherwise, is
very difficult to present mathematically.
The
field proved a very helpful concept. It began as something placed between the
source and the magnetic needle in order to describe the acting force. It was thought
of as an “agent” of the current, through which all action of the
current was performed. But now the agent also acts as an interpreter, one who
translates the laws into a simple, clear language, easily understood.
The field provides the connection between source and its effect
as intended by Faraday.
The first success of the field description suggests that it may be convenient to consider all actions of currents, magnets and charges indirectly, i.e., with the help of the field as an interpreter. A field may be regarded as something always associated with a current. It is there even in the absence of a magnetic pole to test its existence. Let us try to follow this new clue consistently.
The field of a charged conductor can be introduced in much the same way as the gravitational field, or the field of a current or magnet. Again only the simplest example! To design the field of a positively charged sphere, we must ask what kind of forces are acting on a small positively charged test body brought near the source of the field, the charged sphere. The fact that we use a positively and not a negatively charged test body is merely a convention, indicating in which direction the arrows on the line of force should be drawn. The model is analogous to that of a gravitational field (p. 130) because of the similarity between Coulomb’s law and Newton’s. The only difference between the two models is that the arrows point in opposite directions. Indeed, we have repulsion of two positive charges and attraction of two masses. However, the field of a sphere with a negative charge will be identical with a gravitational field since the small positive testing charge will be attracted by the source of the field.
If
both electric and magnetic poles are at rest, there is no action between them,
neither attraction nor repulsion. Expressing the same fact in the field
language, we can say: an electrostatic field does not influence a magnetostatic
one and vice versa. The words “static field” mean a field that does
not change with time. The magnets and charges would rest near one another for
an eternity if no external forces disturbed them. Electrostatic, magnetostatic
and gravitational fields are all of different character. They do not mix; each
preserves its individuality regardless of the others.
Electrostatic, magnetostatic and gravitational fields are all of
different character. They do not mix; each preserves its individuality
regardless of the others.
Let us return to the electric sphere which was, until now, at rest, and assume that it begins to move owing to the action of some external force. The charged sphere moves. In the field language this sentence reads: the field of the electric charge changes with time. But the motion of this charged sphere is, as we already know from Rowland’s experiment, equivalent to a current. Further, every current is accompanied by a magnetic field. Thus the chain of our argument is:
We,
therefore, conclude: The change of an
electric field produced by the motion of a charge is always accompanied by a
magnetic fold.
The change of an electric field produced by the motion of a
charge is always accompanied by a magnetic fold.
Our
conclusion is based on Oersted’s experiment, but it covers much more. It
contains the recognition that the association of an electric field, changing in
time, with a magnetic field is essential for our further argument.
As
long as a charge is at rest there is only an electrostatic field. But a
magnetic field appears as soon as the charge begins to move. We can say more.
The magnetic field created by the motion of the charge will be stronger if the
charge is greater and if it moves faster. This also is a consequence of
Rowland’s experiment. Once again using the field language, we can say: the faster
the electric field changes, the stronger the accompanying magnetic field.
The faster the electric field changes, the stronger the
accompanying magnetic field.
We
have tried here to translate familiar facts from the language of fluids,
constructed according to the old mechanical view, into the new language of
fields. We shall see later how clear, instructive, and far-reaching our new
language is.
We have progressed from the language of fluids to the language
of field.
.
FINAL COMMENTS
Field represents continuous force filling the space. Force is
the core property of substance. From this we may conclude that field is the
flimsiest form of substance. This is what Faraday envisioned will replace
aether. In my view, the field is the best representation of aether.
The direction and density of force may vary in the field, but it
maintains continuity. The field provides the connection between source and its
effect as intended by Faraday. It explains the mystery of “action at a distance”.
Our entire knowledge of the acting forces can be summarized in
the construction of the field. The field presents the force pictorially, which,
otherwise, is very difficult to present mathematically. Electrostatic, electromagnetic
and gravitational fields are all of different character. They do not mix; each
preserves its individuality regardless of the others.
The electrostatic field exists only at the surface of the body because it extends from the interface between particle and void. The electromagnetic field extends from the interstices among nuclei inside the body where current of electrons flows. The gravitational field extends from the nuclei of the body where the lines of force originate and terminate.
This paper presents Chapter
II, section 10 from the book THE EVOLUTION
OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original
publication of this book by Simon and Schuster, New York (1942).
The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.
The heading below is linked to
the original materials.
The
discussion of all the various attempts to understand the mechanical nature of
the ether as a medium for transmitting light would make a long story. A
mechanical construction means, as we know, that the substance is built up of
particles with forces acting along lines connecting them and depending only on
the distance. In order to construct the ether as a jelly-like mechanical
substance physicists had to make some highly artificial and unnatural
assumptions. We shall not quote them here; they belong to the almost forgotten past.
But the result was significant and important. The artificial character of all
these assumptions, the necessity for introducing so many of them all quite independent
of each other, was enough to shatter the belief in the mechanical point of
view.
The idea of aether was used in an effort to make the mechanical
view apply universally. But it has been impossible to do so consistently.
But
there are other and simpler objections to ether than the difficulty of
constructing it. Ether must be assumed to exist everywhere, if we wish to
explain optical phenomena mechanically. There can be no empty space if light
travels only in a medium.
Yet
we know from mechanics that interstellar space does not resist the motion of
material bodies. The planets, for example, travel through the ether-jelly without
encountering any resistance such as a material medium would offer to their
motion. If ether does not disturb matter in its motion, there can be no
interaction between particles of ether and particles of matter. Light passes
through ether and also through glass and water, but its velocity is changed in
the latter substances. How can this fact be explained mechanically? Apparently only
by assuming some interaction between ether particles and matter particles. We
have just seen that in the case of freely moving bodies such interactions must
be assumed not to exist. In other words, there is interaction between ether and
matter in optical phenomena, but none in mechanical phenomena! This is certainly
a very paradoxical conclusion!
There is interaction between aether and matter in optical
phenomena, but none in mechanical phenomena! This is certainly a very
paradoxical conclusion!
There
seems to be only one way out of all these difficulties. In the attempt to
understand the phenomena of nature from the mechanical point of view, throughout
the whole development of science up to the twentieth century, it was necessary
to introduce artificial substances like electric and magnetic fluids, light
corpuscles, or ether. The result was merely the concentration of all the
difficulties in a few essential points, such as ether in the case of optical
phenomena. Here all the fruitless attempts to construct an ether in some simple
way, as well as the other objections, seem to indicate that the fault lies in
the fundamental assumption that it is possible to explain all events in nature
from a mechanical point of view. Science did not succeed in carrying out the
mechanical programme convincingly, and today no physicist believes in the
possibility of its fulfilment.
The inconsistencies seem to indicate that the fault lies in the
fundamental assumption that it is possible to explain all events in nature from
a mechanical point of view.
In
our short review of the principal physical ideas we have met some unsolved
problems, have come upon difficulties and obstacles which discouraged the attempts
to formulate a uniform and consistent view of all the phenomena of the external
world. There was the unnoticed clue in classical mechanics of the equality of
gravitational and inertial mass. There was the artificial character of the
electric and magnetic fluids. There was, in the interaction between electric
current and magnetic needle, an unsolved difficulty. It will be remembered that
this force did not act in the line connecting the wire and the magnetic pole,
and depended on the velocity of the moving charge. The law expressing its
direction and magnitude was extremely complicated. And finally, there was the
great difficulty with the ether.
The mechanical view could not explain the consistency between
the effect of a push (inertial mass) and that of continuously acting force
(gravitational mass). It could not explain the consistency between the
directions of electric current and magnetic force.
Modern
physics has attacked all these problems and solved them. But in the struggle
for these solutions new and deeper problems have been created. Our knowledge is
now wider and more profound than that of the physicist of the nineteenth
century, but so are our doubts and difficulties.
The effort to solve these inconsistencies has led to new
difficulties.
WE
SUMMARIZE:
In the old theories of electric
fluids, in the corpuscular and wave theories of light, we witness the further
attempts to apply the mechanical view. But in the realm of electric and optical
phenomena we meet grave difficulties in this application.
A moving charge acts upon a
magnetic needle. But the force, instead of depending only upon distance,
depends also upon the velocity of the charge. The force neither repels not
attracts but acts perpendicular to the line connecting the needle and the charge.
In optics we have to decide in
favour of the wave theory against the corpuscular theory of light. Waves
spreading in a medium consisting of particles, with mechanical forces acting
between them, are certainly a mechanical concept. But what is the medium through
which light spreads and what are its mechanical properties? There is no hope of
reducing the optical phenomena to the mechanical ones before this question is
answered. But the difficulties in solving this problem are so great that we
have to give it up and thus give up the mechanical views as well.
.
FINAL COMMENTS
We hear of aether in the context of light but not so much in the
context of electromagnetism. Faraday didn’t find any use for the mechanical
aether. He found the concept of “lines of force” more useful because it
provided flexibility. Maxwell followed the mechanical point of view and based
his electromagnetic theory on aether. Maxwell’s aether filled the empty space with
particles that acted as dielectrics. This made the electromagnetic theory quite
inflexible. Einstein’s later discovery of quanta then brought about some
flexibility.
Electric current has a direction of motion. This is the
direction of electrical lines of force. Perpendicular to it, are the magnetic
lines of force. The existence of a force perpendicular to the line of motion contradicts
the mechanical view. This limitation of the mechanical view came to the
forefront.
Light also has a direction of motion. It parallels the idea of electric
current, but the two have little in common. Perpendicular to the direction of
motion there are two planes of polarization. They parallel the idea of magnetic
lines of force, but, again, the two have little in common. Light is considered
to be electromagnetic simply because its speed matches the speed of the electrical
disturbance predicted by the electromagnetic theory. This is like saying that
planet-A matches planet-B in speed, so they are similar in construction.
Electromagnetism is a phenomenon confined to the interface
between particle and void. Light is a phenomenon of the void. These two
phenomena are very different, and light should not be placed under the category
of electromagnetism. Light is simply a radiating substance.
Aether has been considered as the medium in which light travels
as a wave. Once again, this is a mechanical viewpoint that distinguishes
between the movements of the substance and a disturbance traveling through that
substance. In case of light it is the light particle itself moving at the speed
of light, so no medium is required. A fast moving massless particle happens to
appear as a wave.
Mechanical properties seem to accompany substance with solid particles.
The properties are less mechanical in electricity because its particles
(electrons) have a less solid structure. The light particles (photons) have no
solid structure at all and they hardly display mechanical properties. For still
lighter particles we may postulate the following.
The lighter is the particle; the greater shall be its speed and
wave length. It would appear like a long, thin string. If aether is the lightest
and flimsiest substance that there is, then it would be farthest from being
fixed in space. Its speed would be infinite. The aether current is much lighter
than even light. In the direction perpendicular to its motion it may have
infinite number of “polarization planes”. This may tell us something not only about
the true form of aether, but about the line of force.
WE SUMMARIZE:
We postulate that
aether is made of lines of force that are massless. A line of force forms the “particle”
of aether, which appears as a long, thin string. This “particle” is moving in a
circle of infinite radius at infinite velocity. These particles (lines of force)
have a direction of propagation, perpendicular to which there are infinite polarization
planes.
A line of force
becomes more substantial (thickens up) as its wavelength shortens and the
frequency increases. The directions of its polarization also shrink in numbers.
It may become slightly slower in its speed as a result.
By the time the
lines of force thickens up as light it is left with only two polarization
planes and a finite speed. And, by the time the lines of force thicken up to
become electromagnetic current, it has no polarization planes but a single
magnetic field, which is perpendicular to its direction of propagation.
