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Einstein 1938: Field and Ether

Reference: Evolution of Physics

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.

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Field and Ether

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.

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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.

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Einstein 1938: The Reality of the Field

Reference: Evolution of Physics

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.

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The Reality of the Field

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.

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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).

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Einstein 1938: The Two Pillars of the Field Theory

Reference: Evolution of Physics

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.

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The Two Pillars of the Field Theory

“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.

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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”.

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Einstein 1938: The Field as Representation

Reference: Evolution of Physics

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.

.

The Field as Representation

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.

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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.

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Einstein 1938: Ether and the Mechanical View

Reference: Evolution of Physics

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.

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Ether and the Mechanical View

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.

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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.

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