James Maxwell's Physical Model

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James Maxwell's Physical Model

Unread postby pln2bz » Wed Mar 19, 2008 11:32 pm

I'll go ahead and post the text for this now. There is an important graphic involved with part 2 that shows the spinning cells (vortices). I've yet to scan it in, and it may be a few days before that happens. Those who have been learning about Tesla and Meyl will notice some interesting correspondences here. But more than that, this is a great way to learn Maxwell's Equations.

This will require three separate passages. All three excerpts come from Basil Mahon’s The Man Who Changed Everything: The Life of James Clerk Maxwell. The first excerpt concerns Maxwell’s fluid analogy and comes from Chapter 5: “Blue and Yellow Make Pink, Cambridge 1854 – 1856,” pages 59 – 65.

Everyone marveled at [Michael Faraday’s] experimental genius, but few placed equal value on his ability as a theoretician.

Maxwell was one who did. Reading through Faraday’s Experimental Researches, James was struck at first by Faraday’s openness and integrity:

Faraday … shows us his unsuccessful as well as his successful experiments, and his crude ideas as well as his developed ones, and the reader, however inferior to him in inductive power, feels sympathy even more than admiration, and is tempted to believe that, if he had the opportunity, he too would be a discoverer.

Reading further, James came more and more to recognize the power of Faraday’s thinking. The great man’s modest description of his task as ‘working, finishing, publishing’ gave no idea of the intellectual strength and subtlety which pervaded his work. Discoveries had not come easily: great leaps of imaginative thought had been needed, but these were always subjected to the most searching interrogation before Faraday would commit himself to an opinion. James could see that Faraday’s notion of lines of force was far from a vague flight of fancy; it was a serious theory.

Faraday had puzzled hard and long about the way magnets behave. He concluded that a magnet is not just a piece of iron with interesting properties but the center of a system of invisible curved tentacles, or lines of force, which spread through all space. In Faraday’s scheme, magnetic attraction between a north pole and a south pole arises because every tentacle runs from one pole to the other and exerts a pull along its length like a piece of elastic. On the other hand, magnetic repulsion, as between two north poles, comes about because the tentacles push sideways against each other like pieces of compressed rubber. Near the magnet’s poles the tentacles are packed closely together and the forces are great; far away the tentacles are sparse and the forces small. One can see why Sir George Airy called the idea ‘vague and varying’. But anyone who has seen the beautiful curved patterns made by iron filings sprinkled on a sheet of paper near a magnet can see exactly what Faraday had in mind. The filings become little magnets and are pulled into perfect alignment along the lines of force, each line of filings being kept separate from neighboring lines by the sideways repulsion.

To explain electrostatic forces between electrically charged bodies, Faraday postulated electric lines of force which behaved in a similar way. And he went further by suggesting that a magnet induces a kind of tension in any nearby loop of metal wire, which will make a current flow if either magnet or wire is moved. He called this the electrotonic state.

To James, Faraday’s ideas rang strong and true; all they lacked was numerical expression. If he could find a way to represent lines of force mathematically, he should be able to show that all the known formulae for static electrical and magnetic effects could be derived from them just as well as from the hypothesis of action at a distance. This would confound Faraday’s critics and, although it would not itself be a new theory, it might give James a base from which he could develop one.

The present task was to deal with stationary lines of force. This was a limited objective: a complete theory of electricity and magnetism would need to deal also with moving lines, but that could come later. The static problem was essentially geometrical, but it was a more complex geometry than that of Euclid. The curving lines of force filled all space and at every point a force acted with a particular strength along the line that passed through it. This was the geometry of vectors, quantities which vary continuously through space in both magnitude and direction. Although the formal mathematics of vectors was in its infancy some good work had already been done by others and James was able to make use of it. We shall come to that, but first James wanted to get as far as he could by simply following the steps in Faraday’s reasoning, giving the lines of force a rigorous quantitative interpretation but using as few mathematical symbols as possible.

But where could one start? Were there any other physical phenomena which behaved something like lines of force and were mathematically amenable? If so, perhaps an approach by analogy might work. Inspiration was at hand. It came from William Thomson, the Glasgow University colleague of cousin Jemima’s husband Hugh Blackburn, whom James had first met while still at school. Only 7 years older than James, Thomson was already an influential figure and well established as Professor of Natural Philosophy at Glasgow University. While still an undergraduate at Cambridge he had made a remarkable discovery – the equations for the strength and direction of electrostatic force had the same mathematical form as those describing the rate and direction of a steady flow of heat through a solid material. It seemed a bizarre association, static force and moving heat, but James saw a chink of light; surely this was an idea worth pursuing. He knew Thomson well by now and wrote announcing his wish to ‘poach on your electrical preserves’. Thomson enjoyed the role of mentor and was delighted to agree. Like James, he was more concerned with advancing human knowledge than with building his own reputation, and in any case was by now deeply engaged in other work, including the most exciting technology of the day – the telegraph.

William Thomson’s comparison of electrostatic force to heat flow was an inspired insight but did not quite fill the bill. James wanted an analogy that the mind could grasp more readily than the flow of heat. He was also keen, at this early stage, to avoid even the appearance of proposing any particular physical mechanism for lines of force. The analogy he chose was that of an imaginary weightless and incompressible fluid flowing through a porous medium: the streamlines of flow would represent lines of either electric or magnetic force and he could vary the porosity of the medium from place to place to account for the particular electrical or magnetic characteristics of different materials.

Faraday had thought of lines of force as discrete tentacles. James merged them into one continuous essence of tentacle called ‘flux’ – the higher the density of flux at a point, the stronger the electrical or magnetic force there. The direction of fluid flow at any point corresponded to the direction of the flux and the speed of flow to the flux density. As a device to track the motion of the whole body of swirling fluid, James constructed imaginary tubes for it to flow along. The fluid behaved as though the tubes had real walls, because the lines of flow never crossed one another and the whole system of tubes fitted together, leaving no gaps. The fluid traveled fast where the tubes were narrow and slower where they widened out. Electric and magnetic flux, although stationary, were similarly contained in tubes: and, by analogy, forces were strong where the tubes were narrow and the flux dense, and weak where the tubes were wide and the flux sparse.

What made the fluid move was pressure difference. Along each tube the fluid flowed from high pressure to low and the flow at any point was proportional to the pressure gradient there. Correspondingly, flux was caused by differences in electrical potential (voltage) or magnetic potential and the flux density at any point was proportional to the potential gradient, which he called the intensity of the field. Points of equal pressure or potential lay on imaginary surfaces which crossed the tubes everywhere at right angles, fitting together like a continuous set of onion skins.

James elaborated the analogy to account for every characteristic of static electricity and magnetism. Positive and negative electrical charges were represented by sources and sinks of fluid, and materials with different susceptibilities to electricity and magnetism by media with different porosity. Electrical conductors were represented by regions of uniform pressure where the fluid was still. And by a separate analogy he found that the flow of the same fluid could also represent an electric current flowing through a conducting material.

It all came together. The fluid analogy not only gave formulae identical to those from the action at a distance hypothesis, it accounted for some electric and magnetic effects which occurred at the boundary between different materials but could not be explained by action at a distance.

The key to it all was that the fluid was incompressible: every cubic centimeter of space always contained the same amount of fluid, no matter how fast the fluid was moving. This automatically led, for example, to the result that electric and magnetic forces between bodies varied inversely as the square of their distance apart – it was simply a matter of geometry.

James had vindicated Faraday and turned his ‘vague and varying’ lines of force into a new and mathematically impeccable concept, the field. So far, he had only dealt separately with static electric and magnetic fields. The difficult problem of working out how the fields interacted when they changed lay ahead, but there was more he could do, even now. It concerned the well-known effect that a moving magnet makes a current flow in any nearby loop of wire. As we have seen, Faraday thought this happened because the magnet, even when stationary, induced a mysterious ‘electrotonic state’ in the wire, which caused a current as soon as the magnet (or the wire) moved. Odd though it seemed, James felt in his bones that the idea was sound and he set out to find a way to express the electrotonic state mathematically.

For this he had to deviate from his plan to use only pictorial descriptions and simple equations. He needed some power tools and looked into what had already been done in the mathematics of vector quantities. It had been mainly the work of three men. The first was George Green, a Nottinghamshire miller who had taught himself mathematics and eventually managed to get to Cambridge University at the age of 40 but died in 1841, 2 years after gaining a fellowship. The second was none other than William Thomson, who in 1845 found a forgotten paper which Green had written 17 years earlier and saw at once that it was pure gold. He had the paper re-published and started to develop Green’s ideas. The third was George Gabriel Stokes, Lucasian Professor of Mathematics at Cambridge, who was a good friend to Thomson and, later, to Maxwell and a valued source of advice and encouragement to both.

Making good use of their work, James brought legitimate status to Faraday’s electrotonic state by deriving a mathematical expression for it. As usual, it was his intuition that pointed the way. There were two established laws connecting electricity and magnetism. One gave the total magnetic force round an imaginary loop surrounding a wire carrying a given current. The other said how much electric current would be generated in a loop of wire when the magnetic flux passing through the loop increased or decreased at a given rate. These laws appeared to be sound but James felt that they did not quite get to the nub of the matter, because they dealt only with accumulated quantities summed round or through the loop. The only way to get a proper understanding, he thought, would be to look at the intimate relationship between electricity and magnetism in a single small part of space, so he set about re-expressing the laws in what mathematicians call differential form – using vectors at a single point rather than accumulated quantities summed through or round the loop. When he did this he found that one of the vectors exactly fitted Faraday’s concept of the electrotonic state: it had no effect when at a uniform and steady value but when it varied over time or space it gave rise to electric or magnetic forces. A success, but to James’ mind only a partial one – he had given a mathematical definition but could not think how to interpret the symbols physically, even in terms of an analogy. So the electrotonic state still held on to some of its mystery – for the present.

This was as far as he could go for now. From Faraday’s notion of lines of force he had created the field, a concept that became the standard pattern for twentieth century physics but was startlingly new to scientists of the time, who were used to thinking of reality in terms of material bodies with passive empty space in between. His system of interlocking forces, fluxes and potentials is exactly what physicists and electrical engineers use today. Even so, he had added little to Faraday’s ideas beyond giving them mathematical expression, and the resulting equations, although satisfactory, accounted only for static electrical and magnetic effects. He still had to confront the task of extending the work to include changing fields. These appeared to interact in ways quite unlike any other physical phenomenon, and he must have felt he was facing a sheer rock-face. But the field concept gave him a solid base, and by expressing the electrotonic state mathematically he had at least made a toe-hold on the climb.

Our second excerpt explains Maxwell’s vortex theory and comes from Chapter 7: “Spinning Cells, London 1860 – 1862”, pages 95 – 110:

In his Cambridge paper On Faraday’s Lines of Force he had found a way of representing the lines of force mathematically as continuous fields, and had made a start towards forming a set of equations governing the way electrical and magnetic fields interact with one another. This was unfinished business and he now felt ready to make a serious attempt to settle it. He had made progress so far by using the analogy of a swirling body of incompressible fluid – the pressure in the fluid corresponding to electric or magnetic potential and the direction and speed of flow represented the direction and strength of either an electric or a magnetic field. By extending the imagery, so that, for example, sources and sinks of fluid represented electrically charged surfaces, he had been able to derive all the important formulae for static electricity and magnetism. He had also managed to bring steady electric currents and their effects into the scheme by using the fluid analogy in a different role to represent the flow of electricity.

The analogy had served well but could take him no further because it worked only when electrical and magnetic fields were static and electric currents steady. As soon as anything changed, the fields acted in a way that was nothing like the smooth flow of a fluid; in fact their behavior was completely different from that of any known physical process. So to go further he had to find a new approach.

Two courses seemed to be open. One was to desert Faraday and fields, and assume that all effects result from action at a distance between magnetic poles and electrical charges or currents. This was the approach taken by Simeon-Denis Poisson and Andre-Marie Ampere, who had derived the original formulae for static fields and steady currents which James had re-derived by the field approach. It was also the basis of an attempt at a complete theory by Wilhelm Weber, which was mathematically elegant and offered an explanation for most of the known effects. But Weber had made a critical assumption – that the force between two electrical charges depends not only on their distance apart but also on their relative velocity and acceleration along the straight line joining them. James respected Weber’s work but his intuition bridled at this assumption and, more generally, at the whole action at a distance concept.

He therefore chose the second route, which was to go beyond geometrical analogy and make an imaginary mechanical model of the combined electromagnetic field – a mechanism that would behave like the real field. If he could devise a suitable model, the equations governing its operation would also apply to the real field.

As we have seen, all the known experimental results in electricity and magnetism could be attributed to four types of effect; to gain the day, James’ model would have to account for all of them:

1. Forces between electrical charges: unlike charges attract; like charges repel, both with a force inversely proportional to the square of the distance between the charges.
2. Forces between magnetic poles: unlike poles attract; like poles repel, both with a force inversely proportional to the square of the distance between them; poles always occur in north/south pairs.
3. A current in a wire creates a circular magnetic field around the wire, its direction depending on that of the current.
4. A changing total magnetic field, or flux, through a loop of wire induces a current in the wire, its direction depending on whether the flux is increasing or decreasing.

And it would need to do so precisely, so that all the established formulae involving electric charge and current, magnetic pole strength, distances and so on could be derived from the model, together with any new formulae.

James began with effect 2, magnetic forces. For his model he needed to envisage a medium filling all space which would account for magnetic attraction and repulsion. To do this, it would need to develop tension along magnetic lines of force and exert pressure at right angles to them – the stronger the field, the greater the tension and the pressure. And to serve its purpose as a model the imaginary medium would have to be built from components which bore some resemblance to everyday objects.

It seemed an impossible task, but James’ idea was amazingly simple. Suppose all space were filled by tiny close-packed spherical cells of very low but finite density, and that these cells could rotate. When a cell rotated, centrifugal force would make it tend to expand around the middle and contract along the spin axis, just as the earth’s rotation causes it to expand at the equator and flatten at the poles. Each spinning cell would try to expand around the middle but its neighbors would press back, resisting the expansion. If all the cells in a neighborhood spun in the same direction, each would push outwards against the others; they would collectively exert a pressure at right angles to their axes of spin.

Along the axes of spin the opposite would happen. The cells would be trying to contract in this direction and there would be a tension. So if the spin axes were aligned along lines in space, these lines would behave like Faraday’s lines of force, exerting an attraction along their length and a repulsion sideways. The faster the cells spun, the greater would be the attractive force along the lines and the repulsive force at right angles to them – in other words, the stronger the magnetic field.

So the field would act along the spin axes of the cells. But which way? Magnetic force is conventionally defined as acting from north to south pole. James built an extra convention into his scheme: the sense of the field would depend on which way the cells were spinning – it would be in the direction a right-handed screw would move if it rotated the same way; if the cells reversed their spin, the field would reverse too.

But if the cells occupied all space, why were they not apparent? And how could they exist in the same space as ordinary matter? James was not put off by such awkward questions. It was, after all, only a model. The cells’ mass density could be so low as to offer no perceptible obstruction to ordinary matter. As long as they had some mass and rotated fast enough they would generate the necessary forces.

The scheme did not yet explain how different materials could have different magnetic characteristics. For example, iron and nickel had a high magnetic susceptibility – they could be readily magnetized – whereas other substances, like wood, seemed to be even less receptive to magnetism than empty space. James solved this problem with his customary sureness of touch. Where cells occupied the same space as an ordinary substance their behavior would be modified according to the magnetic susceptibility of the substance. The modification was equivalent, in mechanical terms, to a change in the mass density of the cells. In iron, for example, they would become much more dense than in air or empty space, thereby increasing the centrifugal forces, and hence the magnetic flux density, for a given rate of spin.

Here was the basis of a model. The spin axes of the cells gave the direction of the magnetic field at any point in space: their density and rate of spin determined its strength, and the model provided exactly the right equations for effect 2, magnetic forces in static situations.

So far so good. But there were two problems. First, what set the cells in motion? And second, the cells along one line would be spinning in the same direction as those in neighboring lines, so that where two surfaces made contact they would be moving in opposite directions, rubbing awkwardly against one another. Amazingly, James solved both problems with a single stroke.

To avoid the cells rubbing against one another, he tried putting even smaller spherical particles between the cells. They would act like ball bearings, or like the ‘idle wheels’ engineers put between two gear wheels which need to rotate in the same direction. The idea seemed crazy but James persevered and suddenly things began to fall into place. Suppose the little idle wheels were particles of electricity. In the presence of an electromotive force they would tend to move along the channels between the cells, constituting an electric current, and it would be this movement that set the cells spinning.

But everyone knew that currents could flow only in substances which were conductors, like metals. In insulators like glass or mica, or in empty space, there could be no currents. So James proposed a second way in which the behavior of the cells would be modified according to the type of substance which shared their space. In an insulator the cells, or perhaps local groups of cells, would hold on to their little particles so that they could rotate but not move bodily. But in a good conductor like a copper wire the particles could move bodily with very little restriction and a current would flow. In general, the lower the electrical resistance of the substance, the more freely the particles could move.

An essential feature of James’ little particles was that they had rolling contact with the cells – there was no sliding. Where the magnetic field was uniform the particles would just rotate, along with the cells. But if the particles in a conductor moved bodily without rotating, they would cause the cells on either side of the current to spin in opposite directions, exactly the condition to create a circular magnetic field around a current-carrying wire – effect 3. If the particles rotated and moved, the circular magnetic field due to their movement would be superimposed on the linear one due to their rotation.

So, by this extraordinary assemblage of tiny spinning cells interspersed with even smaller ‘idle wheel’ particles, James had succeeded in explaining two of the four main properties of electricity and magnetism. A highly satisfactory start, but there was much more to do. The next task was to explain effect 4: a changing magnetic flux through a loop of wire induces a current in the wire. James chose to explain an equivalent effect – that when a current is switched on in one circuit, it induces a pulse of current in a nearby but separate circuit by creating a magnetic field that links the two. He drew a diagram to illustrate his argument, giving the spherical cells a hexagonal cross-section ‘purely for artistic reasons’. We can see it, slightly adapted for our purpose, in Figures 2a-d.

The diagram shows a cross-section of a small region of space. The idle wheel particles along AB are in a wire which is part of a circuit with a battery and a switch, initially open. Those along PQ are in another wire which is part of a separate circuit having no battery or switch. The idle wheels along AB and PQ are free to move because they are in conductors, but others in the neighborhood are in a non-conducting material and can only rotate in their fixed positions. AB and PQ are, of course, impossibly thin wires and impossibly close together, but this is to just keep the diagram compact; the argument James produced would apply equally well to normal-sized and normally spaced wires containing many rows of idle wheels and cells. The argument runs like this.

Suppose the magnetic field is zero at first, and the switch open, so that all the cells and idle wheels are stationary (Figure 2a). When the battery is brought into the circuit by closing the switch, the idle wheels along AB move bodily from left to right without rotating. This causes the rows of cells on either side of AB to rotate in opposite directions, thus creating a circular magnetic field around the wire. The idle wheels in PQ are now pinched between rotating cells on the AB side and stationary ones on the other, so they start to rotate (clockwise) and also to move from right to left, the opposite direction from those in AB (Figure 2b).

But the circuit containing the wire along PQ has some resistance (all circuits do), so the idle wheels there, after their initial surge, will slow down, causing the cells above PQ to begin rotating anticlockwise. Soon, the sideways movement of the idle wheels will stop, although they will continue to rotate. By this time the cells above PQ will be rotating at the same rate as those in the row below PQ (Figure 2c).

When the switch is opened again, disconnecting the battery, the idle wheels along AB stop moving and the rows of cells on either side of AB stop rotating. The idle wheels in PQ are now pinched between stationary cells on the AB side and rotating ones on the other, so they start to move from left to right, the same direction as the original AB current (Figure 2d).

Once again the resistance of the circuit containing PQ causes the idle wheels there to slow down. This time, when their sideways movement stops they will not be rotating: we are back to the state represented in Figure 2a.

Thus, switching on a steady current in AB induces a pulse of current in PQ in the opposite direction and switching the current off induces another pulse in PQ, this time in the same direction as the original current. More generally, any change of current in the AB circuit induces a current in the separate PQ circuit through the changing magnetic field that links them. Equivalently, any change in the amount of magnetic flux passing through a loop of wire induces a current in the loop – effect 4 is explained. If the battery in the AB circuit were replaced by an a.c. generator, the alternating AB current would induce an alternating current in PQ. This is exactly the way transformers work in our electrical power supply systems.

And here, at last, was a mechanical analogy for Faraday’s electrotonic state. It was the effect at any point in the field of the angular momentum of the spinning cells. Like a flywheel, the cells would act as a store of energy, reacting with a counterforce to resist any change in their rotation; this took the form of an electromotive force which would drive a current if a conductor was present.

James had now explained three of the four effects. He had not yet found a way of using the model to account for effect 1, forces between electric charges, commonly called electrostatic forces. But he wrote up the results with full mathematical rigor in a paper called On Physical Lines of Force, which was published in the Philosophical Magazine in monthly installments: Part1 appeared in March 1861 and Part 2 was spread over April and May. Not wanting to be misunderstood, he was at pains to point out that his bizarre arrangement of whirling cells and idle wheels was merely a model:

The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. I do not bring it forward as a mode of connexion existing in nature, or even as that which I would willingly assent to as an electrical hypothesis. It is, however, a mode of connexion which is mechanically conceivable, and easily investigated, and it serves to bring out the actual mechanical connexions between the known electromagnetic phenomena; so that I venture to say that anyone who understands the provisional and temporary nature of this hypothesis, will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena.

He had failed to achieve a full theory and it was with a feeling of disappointment that he and Katherine left London to spend the summer vacation at Glenlair. But it was good to get back to the easy rhythm of country life, with its concerns over crops, plantations and farm animals, and to the fresh Galloway air. He had not planned to do any serious work on electricity and magnetism during the summer and took no reference books. But his thoughts ran on and an idea began to crystallize.

It seemed a small idea at first. The material making up his little cells had to transmit the twisting forces internally so that each cell would rotate as a body. To do this without dissipating energy the material needed to have a degree of springiness, or elasticity. The idea grew. Could this elasticity be the source of the forces between electric charges which he had so far been unable to explain?

In conductors currents could flow because the electrical particles, the idle wheels, were free to move bodily in response to an electromotive force. Continuous currents could not flow in insulators because the particles were bound to their neighboring cells. But elastic cells would distort, allowing the particles to move a short distance. The distortion in the cells would cause a restoring force, like a spring. The particles would move until the spring-back force balanced the electromotive force.

So, for example, if a battery were connected by metal wires across two metal plates separated by an insulating material, there would be a small displacement of the electrical particles in the insulator away from one plate and towards the other. This small movement was, in effect, a brief electric current. The movement of electricity would be the same all round the circuit so that in the wires, where particles were not bound to cells, the same brief current would flow. This would result in a surplus of particles on the surface of one plate and a shortage on the surface of the other, so one plate would become positively charged and the other negatively. The distorted cells in the insulating material between the charged metal plates would act like a wound-up spring, exerting a mechanical force of attraction between them. So the elasticity of the cells explained the force between the charged plates.

Even when the battery was disconnected the spring would stay wound up, storing energy. If the plates were then connected by a metal wire, the spring’s energy would be released: a brief current would flow in the wire, the charges on the plates would fall back to zero and the cells and idle wheels would return to their rest positions.

Following his earlier thinking, James proposed that the elasticity, or spring-stiffness, of the cells would be modified if they were sharing their space with ordinary matter, and that the degree of modification would depend on the type of matter. The higher the electrical susceptibility of the substance, the softer the spring and the greater the electrical displacement for a given electromotive force. For example, filling the space between the metal plates with mica rather than air would soften the spring and increase the amount of charge on the plates for a given voltage across them.

He wrote up the mathematics and everything fitted together. James had shown how the electrical and magnetic forces which we experience could have their seat not in physical objects like magnets and wires but in energy stored in the space between and around the bodies. Electrostatic energy was potential energy, like that of a spring: magnetic energy was rotational, like that in a flywheel, and both could exist in empty space. And these two forms of energy were immutably linked: a change in one was always accompanied by a change in the other. The model demonstrated how they acted together to produce all known electromagnetic phenomena.

A triumph. But there was more. The model predicted two extraordinary and entirely new physical phenomena which took physics into undreamt-of territory.

One was that there could be electric currents anywhere, even in perfect insulators or in empty space. According to the model, as we have seen, there would be a little twitch of current whenever an electromotive force was first applied to an insulator, because the electrical idle wheels would move slightly before being halted by the spring-back force of their parent cells. In the model all space is filled with cells, so these twitches of current would occur even in empty space.

This new type of current would arise whenever the electric field changed. Its value, at any point, would depend on the rate of change of the electric field at that point. In fact, it was simply the rate of displacement of electricity due to the small movement of the particles. James asserted that it was in every way equivalent to an ordinary current. He gave it the name ‘displacement current’.

The equations governing electrical and magnetic effects had hitherto just dealt with the ordinary conduction current. In James’ new theory, the displacement current had to be added in. When this was done the system of equations was transformed from a motley collection into a beautifully coherent set. This was not immediately evident, however, even to James; he had seen something even more interesting.

All materials that have elasticity transmit waves. James’ all-pervading collection of cells was elastic, so it must be capable of carrying waves. In an insulating material, or in empty space, a twitch in one row of idle wheels would be transmitted via their parent cells to the surrounding rows of idle wheels, then to the rows surrounding them, and so on. Because the cells have inertia they would not transmit the motion instantly but only after a short delay – the twitch would spread out as a ripple. So any change in the electric field would send a wave through all space.

What is more, any twitch in a row of idle wheels would make the neighboring cells turn a bit and so generate a twitch in the magnetic field along the cells’ axes of spin. All changes in the electric field would therefore be accompanied by corresponding changes in the magnetic field, and vice versa. The waves would transmit changes in both fields; they were electromagnetic waves.

What kind of waves were they? Waves in the sea or along a rope are called ‘transverse’ because the individual particles of a sea or rope move at right angles to the direction of the wave. Waves like sound are called ‘longitudinal’ or ‘compression’ waves because the particles move back and forth along the same line as the wave. James’ electromagnetic waves are clearly transverse because the changing electric and magnetic fields were both at right angles to the direction of the wave.

James felt he was on the verge of a great discovery. Light waves were known to be transverse. Could light consist of waves of the kind his model predicted? The speed of light was known with reasonable accuracy from experiments and astronomical observations. It was also well known that the speed of waves in any elastic medium is given by the square root of the ratio of the medium’s elasticity to its density. In the model, the elasticity of the cells controlled the electrostatic (spring-back) forces and their density the magnetic (centrifugal) forces. James’ calculations showed that the spring stiffness of his cells in empty space was not completely determined: it could vary over a factor of three. But if he set it at the lowest value in this range – equivalent to assuming that the cell material was a hypothetically perfect solid – a remarkable result would follow. The wave speed in empty space, or in air, would then be exactly equal to the ratio of the electromagnetic and electrostatic units of electric charge . It seemed impossible that such a simple and natural result could be wrong, so James confidently set the elasticity of his cells to fit it.

He now had a very simple formula for the speed of his waves. To check their speed against that of light he first needed to look up the result of an experiment by Wilhelm Weber and his colleague Rudolf Kohlrausch. They had measured the ratio of the electrodynamic and electrostatic units of charge; electrodynamic units are closely related to electromagnetic ones, so James would easily be able to convert their result to give the value for the ratio he needed. He also needed to look up the exact values for the experimentally measured speed of light. But he had brought no reference books; this would have to wait until he got back to London in October. The summer passed in a glow of anticipation.

He had left for Glenlair disappointed at having failed to produce a complete theory of electromagnetism. He returned to London not only with a complete theory but with two entirely new predictions, displacement current and waves. Moreover, the waves might turn out to include light. He eagerly looked up Weber and Kohlrausch’s experimental result and from it worked the speed of his predicted waves. In empty space or air they would travel at 310,740 kilometers per second. Armand-Hippolyte-Louis Fizeau had measured the speed of light in air as 314,850 kilometers per second.

The correspondence seemed too close for coincidence, even allowing for a possible error of a few percent in each of the experimental results. Light must consist of electromagnetic waves. Some of the greatest leaps in science have come when two sets of apparently different phenomena are explained by a single new theory. This was one such leap: at a stroke, he had united the old science of optics with the much newer one of electromagnetism.

James had not expected to extend his paper On Physical Lines of Force beyond Parts 1 and 2 but now he set about writing Part 3, which covered electrostatics, displacement current and waves, and Part 4, which used his model to explain why polarized light waves change their plane of vibration when they pass through a strong magnetic field – an effect discovered experimentally by Faraday. Even for one with the calmest of temperaments it must have been an exhilarating time. The two further parts of the paper were published early in 1862. In Part 3, James announced:

We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electrical and magnetic phenomena.

The idea of a medium, an ‘aether’ pervading all space, was far from new. Physicists of the day believed an aether of some kind was necessary to transmit light waves, so one might have expected ready acceptance of James’ application of the principle to electricity and magnetism. But there were misgivings; the reaction of his friend Cecil Monro was typical:

The coincidence between the observed velocity of light and your calculated velocity of a transverse vibration in your medium seems a brilliant result. But I must say I think a few such results are needed before you can get peple to think that every time an electric current is produced a little file of particles is squeezed along between two rows of wheels.

The difficulty lay deep in the scientific thinking of the time. People believed that all physical phenomena resulted from mechanical action and that all would be clear to us if, and only if, we could discover the true mechanisms. With a century and a half of hindsight we can see the spinning cell model as a crucial bridge between old and new ideas – built from old materials but paving the way for a completely new type of theory, one which admits that we may never understand the detailed workings of nature. One cannot blame James’ contemporaries for seeing things differently. To many of them the model was simply an ingenious but flawed attempt to portray the true mechanism, for which the search would continue.

James himself was not entirely content with the model, but for different reasons. He wanted to free the theory if possible from all speculative assumptions about the actual mechanism by which electromagnetism works. He was to achieve this wish 2 years later by taking an entirely new approach. Scientific historians now look upon his spinning cells paper as one of the most remarkable ever written but hold the one that followed to be greater still.
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Re: James Maxwell's Physical Model

Unread postby pln2bz » Wed Mar 19, 2008 11:32 pm

Part 3 ...

Our final excerpt regarding Maxwell’s Equations deals with the popular final mathematical form that is considered standard by scientists today. From Chapter 8: “The Beautiful Equations, London 1862 – 1865”, pages 114 – 127:

James was becoming heavily involved in an entirely different kind of work, not in the least glamorous but nonetheless demanding and crucially important – the development of a coherent set of units of measurement for electricity and magnetism. The new science was bedeviled by a chaotic rag-bag of units and this was already beginning to hamper the progress of technology. Someone had to sort out the mess. The British Association for the Advancement of Science had asked James to lead a small team to make a start in bringing things to order. His colleagues were two other Scotsmen: Fleeming Jenkin, who was also an old boy of the Edinburgh Academy, and Balfour Stewart.

The seeds of the problem were historical. Magnetism and static electricity had been known for centuries but were regarded as separate phenomena. Some enlightened scientists had suspected a link but it was only in the nineteenth century that proof came.

There were three key events. In 1799 the Italian Count Alessandro Volta invented the voltaic pile, or battery, which provided a continuous electric current: previously it had only been possible to store electricity in such devices as the Leyden jar, which released all its charge in one burst. Volta had not set out to produce currents; he merely wanted to show that his friend Luigi Glvani was wrong. Galvani believed that the electricity by which he had made dead frogs’ legs twitch came from animal tissue but Volta thought it was generated by chemical action between different metals in the circuit. His first pile, or battery, built from repeated layers of silver, damp pasteboard and zinc, was intended simply to prove he was right. It did indeed prove the point but the battery soon took on a life of its own and people started to use currents for such things as electro-plating. Curiously, the name they first gave to the phenomenon of continuous electric currents was not ‘voltism’ but ‘galvanism’.

Now that scientists had electric currents, the link between electricity and magnetism was waiting to be found. It only needed someone to put a magnetic compass near a current-carrying wire and notice that the needle was deflected. Amazingly, 21 years passed before Hans-Christian Oersted switched on a current while lecturing to a class and happened to glance at a compass lying on the bench. He was astonished to see the needle jerk; the link was proved. News of Oersted’s discovery spread fast. Within a few months Ampere had worked out how to use magnetism to measure currents, and by the following year Faraday had made a primitive electric motor.

If electric currents produce magnetism, surely magnetism should produce electric currents. Scientists tried many experiments but found no currents. It was a further 11 years before Faraday discovered that to make a current flow in a wire loop you needed to change the amount of magnetic flux passing through it: the faster the change, the bigger the current – the same principle is used today to generate the electrical power we use in our homes, offices and factories.

So magnetism, static electricity and current electricity were inextricably bound together. But because of the way the science had grown up, they were measured in different ways. The task of setting up a coherent set of units was formidable. The very connectedness of electricity and magnetism meant that quite a lot of units were needed and that some were fairly complex. An example is the unit of self-inductance. Any loop of wire carrying a current generates a magnetic field which acts through the loop, and whenever the current changes the consequent change in magnetic flux induces an electromotive force in the wire which is proportional to the rate of change of current, and opposes the change. The number of units of electromotive force generated in the loop when the current changes at a rate of one unit per second is called the self-inductance of the loop; our unit for it is the henry, named after Faraday’s American contemporary Joseph Henry, who designed the world’s first powerful electromagnet and invented the electromagnetic relay, which made long-distance telegraphy practical.

No-one had yet made a systematic review of all the various quantities in electricity and magnetism, and how they should be measured. James took on the task and, with Fleeming Jenkin’s help, wrote a paper for the British Association which included recommendations for a complete system of units. These were later adopted almost unchanged as the first internationally accepted system of units, which became known, misleadingly, as the Gaussian system (Gauss’s contribution was certainly less than Maxwell’s and probably less than those of Thomson and Weber).

In fact, confusion over units was not confined to electricity and magnetism. When two people spoke of a quantity like ‘force’ or ‘power’ you could not be sure that they meant the same thing. James saw a prime opportunity to straighten out the muddle. He went beyond his brief for the paper and proposed a systematic way of defining all physical quantities in terms of mass, length and time, symbolized by the letters M, L and T. For example, velocity was defined as L/T, acceleration L/T2, and force ML/T2, since, by Newton’s second law, force = mass x acceleration. His method is used in exactly this form today. Called dimensional analysis, it seems to us so simple and so natural a part of all physical science that almost nobody wonders who first thought of it.


It was at this time, busy as he was with experiments and College business, that Maxwell produced a paper which will remain forever one of the finest of all man’s scientific accomplishments, A Dynamical Theory of the Electromagnetic Field. It’s boldness, originality and vision are breathtaking.

The work had been many years in gestation. Most creative scientists, even the most prolific and versatile, produce one theory per subject. When that theory has run its course they move on to another topic, or stop inventing. Maxwell was unique in the way he could return to a topic and imbue it with new life by taking an entirely fresh approach. To the end of his life there was not one subject in which his well of inventiveness showed signs of exhaustion. With each new insight he would strengthen the foundations of the subject and trim away any expendable superstructure. In his first paper on electromagnetism he had used the analogy of fluid flow to describe static electric and magnetic effects. In the second he had invented a mechanical model of rotating cells and idle wheels to explain all known electromagnetic effects and to predict two new ones, displacement current and waves. Even the most enlightened of his contemporaries thought that the next step should be to refine the model, to try to find the true mechanism. But perhaps he was already sensing that the ultimate mechanisms of nature may be beyond our powers of comprehension. He decided to put the model on one side and build the theory afresh, using only the principles of dynamics: the mathematical laws which govern matter and motion.

Much of the mathematics he had developed in earlier papers was still applicable, in particular the way of representing electric and magnetic fields at any point in space at any time. But to derive the equations of the combined electromagnetic field independently of his spinning cell model he needed something else.

It sometimes happens that mathematical methods conceived in the abstract turn out later to be so well suited to a particular application that they might have been written especially for it. When he was wrestling with the problems of general relativity, Albert Einstein came across the tensor calculus, invented 50 years earlier by Curbastro Gregorio Ricci and Tullio Levi-Civita, and saw that it was exactly what he needed. James enlisted a method that had been created in the mid-eighteenth century by Joseph-Louis Lagrange.

Lagrange was a consummate mathematician with a penchant for analysis and for the orderly assembly and solution of equations. Unlike James, he distrusted geometry – his masterpiece on dynamics, the Mecanique analytique, did not contain a single diagram. He had devised a way of reducing the equations of motion of any mechanical system to the minimum number and lining them up in standard form like soldiers on parade. For each ‘degree of freedom’ – each independent component of motion – a differential equation gave the rate of that motion in terms of its momentum and its influence on the kinetic energy of the whole system.

For James, the keynote of Lagrange’s method was that it treated the system being analyzed like a ‘black box’ – if you knew the inputs and could specify the system’s general characteristics you could calculate the outputs without knowledge of the internal mechanism. He put it more picturesquely:

In an ordinary belfry, each bell has one rope which comes down through a hole in the floor to the bellringer’s room. But suppose that each rope, instead of acting on one bell, contributes to the motion of many pieces of machinery, and that the motion of each piece is determined not by the motion of one rope alone, but by that of several, and suppose, further, that all this machinery is silent and utterly unknown to the men at the ropes, who can only see as far as the holes above them.

This was just what he needed. Nature’s detailed mechanism could remain secret, like the machinery in the belfry. As long as it obeyed the laws of dynamics, he should be able to derive the equations of the electromagnetic field without the need for any kind of model.

The task was formidable; James had to extend Lagrange’s method from mechanical to electromagnetic systems. This was new and hazardous ground, but he was well prepared. From study of Faraday and from his own work he had built up a strong intuition for the way electricity and magnetism were bound together and how their processes were, in some ways, similar to mechanical ones.

His cardinal principle was that electromagnetic fields, even in empty space, hold energy which is in every way equivalent to mechanical energy. Electric currents and the magnetic fields associated with them carry kinetic energy, like the moving parts in a mechanical system. Electric fields hold potential energy, like mechanical springs. Faraday’s electrotonic state is a form of momentum. Electromotive and manetomotive forces are not forces in the mechanical sense but behave somewhat similarly. For example, an electromotive force acts on an insulating material (or empty space) like a mechanical force acts on a spring, putting it under stress and storing energy. When it tries to do this to a conductor the material gives way, so the force does not build up stress but instead drives a current. With these and similar insights, James tried applying Lagrange’s method.

In some ways electromagnetic systems were nothing like mechanical ones; for example, linear electrical forces tended to produce circular magnetic effects and vice versa. James hoped to show that such behavior followed naturally from the normal laws of dynamics when they were applied to an electromagnetic field. He represented the properties of the whole field mathematically as a set of inter-related quantities which could vary in time and space. To solve the problem he needed to find the mathematical relationship between the quantities at a single arbitrary point, which could be in any kind of material or in empty space. The resulting equations would need to describe how the various quantities interacted with one another in the space immediately surrounding the point, and with time.

Most of these quantities were vectors, having a direction as well as a numerical value. The five main vectors were the electric and magnetic field intensities, which resembled forces, the electric and magnetic flux densities, which resembled strains, and the electric current density, which was a kind of flow. One important quantity, electric charge density, was a scalar, having only a numerical value. These six quantities were like the ropes and bells connected by the invisible machinery inside the belfry. If one could find the equations connecting them one would know everything about how electromagnetic systems behaved. One would be able to ring a tune on the bells without knowing anything about the machinery inside.

Everything came together beautifully. James showed that all aspects of the behavior of electromagnetic systems, including the propagation of light, could, in his interpretation, be derived from the laws of dynamics. Disinclined as he was to crow about his achievements, he could not entirely contain his elation. Towards the end of a long letter to his cousin Charles Hope Cay he wrote:

I also have a paper afloat, with an electromagnetic theory of light, which, till I am convinced to the contrary, I hold to be great guns.

Great guns indeed. The essence of the theory is embodied in four equations which connect the six main quantities. They are known to every physicist and electrical engineer as Maxwell’s equations. They are majestic mathematical statements, deep and subtle yet startlingly simple. So eloquent are they that one can get a sense of their beauty and power even without advanced mathematical training.

When the equations are applied to a point in empty space, the terms which represent the effects of electric charges and conduction currents are not needed. The equations then become even simpler and take on a wonderful, stark symmetry; here they are:

div E = 0 (equation 1)

div H = 0 (equation 2)

curl E = -(1/c) ∂H/∂t (equation 3)

curl H = (1/c) ∂E/∂t (equation 4)

E is the electric force and H the magnetic force at our arbitrary point. The bold lettering shows that they are vectors, having both strength and direction. ∂E/∂t and ∂H/∂t, also vectors, are the rates of change of E and H with time. The constant c acts a kind of grear ratio between electric and magnetic forces – it is the ratio of the electromagnetic and electrostatic units of charge.

Leaving aside mathematical niceties, the equations can readily be interpreted in everyday terms. The terms ‘div’ (short for divergence) and ‘curl’ are ways of representing how the forces E and H vary in the space immediately surrounding the point. Div is a measure of the tendency of the force to be directed more outwards than inwards (div greater than zero), or more inwards than outwards (div less than zero). Curl, on the other hand, measures the tendency of the force to curl, or loop, around the point and gives the direction of the axis about which it curls.

• Equation (1) says that the electric force in a small region around our point has, on average, no inward or outward tendency. This implies that no electric charge is present.
• Equation (2) says the same for the magnetic force, implying that no single magnetic poles are present: they always come in north/south pairs in any case.
• The first two equations also imply the familiar laws for static fields: that the forces between electric charges and between magnetic poles vary inversely with the square of the distance separating them.
• Equation (3) says that when the magnetic force changes it wraps a circular electric force around itself. The minus sign means that the sense of the electric force is anticlockwise when viewed in the direction of the rate of change of the magnetic force.
• Equation (4) says that when the electric force changes it wraps a circular magnetic force around itself. The sense of the magnetic force is clockwise when viewed in the direction of the rate of change of the electric force.
• In Equations (3) and (4) the constant c links the space variation (curl) of the magnetic force to the time variation (∂/∂t) of the electric force, and vice versa. It has the dimensions of a velocity and, as Maxwell rightly concluded, is the speed at which electromagnetic waves, including light, travel.

Equations (3) and (4) work together to give us these waves. We can get an idea of what happens simply by looking at the equations. A changing electric force wraps itself with a magnetic force; as that changes it wraps itself in a further layer of electric force and so on. Thus the changes in the combined field of electrical and magnetic forces spread out in a kind of continuous leapfrogging action.

In mathematical terms, equations (3) and (4) are two simultaneous differential equations with two unknowns. It is a simple matter to eliminate E and H in turn, giving one equation containing only H and another containing only E. In each case the solution turns out to be a form of equation known to represent a transverse wave traveling with speed c. The E and H waves always travel together: neither can exist alone. They vibrate at right angles to each other and are always in phase.

Thus any change in either the electrical or magnetic fields sends a combined transverse electromagnetic wave through space at a speed equal to the ratio of the electromagnetic and electrostatic units of charge. As we have seen, this ratio had been experimentally measured and, when put in the right units, was close to experimental measurements of the speed of light. James’ electromagnetic theory of light now no longer rested on a speculative model but was founded on the well-established principles of dynamics.

His system of equations worked with jeweled precision. Its construction had been an immense feat of sustained creative effort in three stages spread over 9 years. The whole route was paved with inspired innovations but from a historical perspective one crucial step stands out – the idea that electric currents exist in empty space. It is these displacement currents that give the equations their symmetry and make the waves possible. Without them the term ∂E/∂t in equation (4) becomes zero and the whole edifice crumbles.

Some accounts of the theory’s origin make no mention of the spinning cell model, or dismiss it as a makeshift contrivance which became irrelevant as soon as the dynamical theory appeared. In doing so they wrongly present Maxwell as a coldly cerebral mathematical genius. One can hardly dispute the epithet ‘genius’, but his thoughts were firmly rooted in the everyday physical world that all of us experience. The keystone of his beautiful theory, the displacement current, had its origin in the idea that the spinning cells in his construction-kit model could be springy.

James published A Dynamical Theory of the Electromagnetic Field in seven parts and introduced it at a presentation to the Royal Society in December 1864. Most of his contemporaries were bemused. It was almost as if Einstein had popped out of a time machine to tell them about general relativity; they simply did not know what to make of it. Some thought that abandoning the mechanical model was a backward step; among these was William Thomson, who, for all his brilliance, never came close to understanding Maxwell’s theory.

One can understand these reactions. Not only was the theory ahead of its time but James was no evangelist and hedged his presentation with philosophical caution. He thought that his theory was probably right but could not be sure. No-one could until Heinrich Hertz produced and detected electromagnetic waves over 20 years later. The ‘great guns’ had been paraded but it would be a long while before they sounded.

It is almost impossible to overstate the importance of James’ achievement. The fact that its significance was but dimly recognized at the time makes it all the more remarkable. The theory encapsulated some of the most fundamental characteristics of the universe. Not only did it explain all known electromagnetic phenomena, it explained light and pointed to the existence of kinds of radiation not then dreamt of. Professor R. V. Jones was doing no more than representing the common opinion of later scientists when he described the theory as one of the greatest leaps ever achieved in human thought.
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Re: James Maxwell's Physical Model

Unread postby StefanR » Thu Mar 20, 2008 5:40 pm


Well if you like that and the Meyl bit, these pdf's are somewhat on those lines from some different inroads but
in way coming to the same sort of conclusions.

Intuitive Notes on Mathematical Physics
Jack Sarfatti
Einstein: “Physics should be as simple as possible, but not simpler than is possible.”
Table of Contents
1. Maxwell’s Classical Electromagnetic Field Equations................................................... 1
Faraday’s law of electric induction by changing magnetic flux. .................................... 2
Gauss’s law of electric flux from electric point monopole............................................ 2
Ampere’s law of magnetic induction by real electric current plus Maxwell’s timechanging
electric field (“displacement current”). ........................................................... 2
Lorentz force law ............................................................................................................ 2
Radiation Reaction (self-force) from the self-field of an electric point charge.............. 2
Classical vacuum electromagnetic duality...................................................................... 3
Hodge star duality operator formalism ........................................................................... 3
Einstein and the crackpots. ............................................................................................. 4
2. Relevant mathematical concepts applied to physics....................................................... 4
Topological spaces, manifolds, Einstein’s EEP & hyperspace ..................................... 4
Vector fields of arrows.................................................................................................... 6
Flows and Lie bracket commutator of vector fields ....................................................... 7
Cartan’s differential forms.............................................................................................. 8
The map is not the territory............................................................................................. 9
Physical meaning of the local tetrad LIF frames. ......................................................... 10
Cartan forms again........................................................................................................ 15
p-forms.......................................................................................................................... 15
The exterior derivative d generalized ∇
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.
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Re: James Maxwell's Physical Model

Unread postby StefanR » Thu Mar 20, 2008 5:41 pm


The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.
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Re: James Maxwell's Physical Model

Unread postby StefanR » Fri Mar 21, 2008 9:06 am

Some just cannot let go of gravity of course and will try to work around it.

Gyrotation, defined as the transmitted angular movement by gravitation fields in motion, is a plausible solution for
a whole set of unexplained problems of the universe. It forms a whole with gravitation, in the shape of a vector
field wave theory, that becomes extremely simple by its close similarity to the electromagnetism. And in this
gyrotation, the time retardation of light is locked in.
An advantage of the theory is also that it is Euclidian, and that predictions are deductible of laws analogous to
those of Maxwell

The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.
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Re: James Maxwell's Physical Model

Unread postby Solar » Sat Mar 22, 2008 6:35 am

I finally got the chance to read this thread. Thank for the most excellent information Pln2bz.
"Our laws of force tend to be applied in the Newtonian sense in that for every action there is an equal reaction, and yet, in the real world, where many-body gravitational effects or electrodynamic actions prevail, we do not have every action paired with an equal reaction." — Harold Aspden
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Re: James Maxwell's Physical Model

Unread postby pln2bz » Sat Mar 22, 2008 1:36 pm

I've yet to get to the fun part though. Check this out ... From The Electric Life of Michael Faraday by Alan Hirshfeld, page 190:

Inspired by Faraday's geometrical musings, Maxwell created an electromagnetic universe that cannot be effectively reduced to mental images. All self-imagined analogs to visualize the field are in some way deficient. Yet the mathematical rendering of the field is complete and accurate. Maxwell likened the situation to that of a bell ringer who tugs ropes that dangle through holes in the ceiling of the belfry; the bells themselves and their actuating mechanism remain a mystery. Maxwell's contemporary, Heinrich Hertz, put it more bluntly: "Maxwell's theory is Maxwell's equations." Or in the words of Nobel prize-winning physicist Richard Feynman, nearly a century later,

"Today we understand better that what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false. This is answered by doing experiments, and untold numbers of experiments have confirmed Maxwell's equations. If we take away the scaffolding he used to build it, we find that Maxwell's beautiful edifice stands on its own. He brought together all of the laws of electricity and magnetism and made one complete and beautiful theory."

I find this quote, within the context of what we know of the aether, Konstantin Meyl and everything presented in this thread regarding Maxwell's Equations, to strike at the fundamental core of what's wrong with physics today. There is in fact no more direct manner of demonstrating the point. Yes, they are right that Maxwell's Equations are conceptually or visually deficient, but we know from Meyl that there is a reason for this (the anti-vortex's absence), and it is Feynman's choice -- conscious or not -- to consider Maxwell's Equations to be "beautiful" in spite of this problem. We'd be wise to ask Feynman: Upon what do you base your claim that the Equations are beautiful? From what I can tell, they are only beautiful because they are not considered to be responsible for the noise associated with the near-field of antenna. They are certainly not beautiful in their ability to explain the technology of RFID. They are certainly not beautiful in their ability to explain Nikola Tesla's experimentation.

In calling the equations beautiful, Feynman appears to alter the very basis upon which we evaluate Maxwell's Equations, for we should be evaluating them on the basis of how accurate and complete they are. If they can be demonstrated to be incomplete, for instance, then Maxwell's Equations are in fact pseudo-pedagogical (they superficially appear to help, but in fact cause great harm) and possibly even ugly.

This idea that we've essentially proven Maxwell's Equations on the basis of the equations' experimental confirmations ignores the fact that the equations may be incomplete. We can see from Meyl that the statement is absolutely devoid of rigor. In conversations between Warren Siegel and David Thomson about quantum mechanics and aether structure, we see the exact same reasoning:

SIEGEL: (1) The concept of ether is in direct conflict with General Relativity.

THOMSON: There are two distinctly different Aether theories. One is the rigid Aether proposed by Albert Michelson, the other is the fluid Aether, first proposed by Rene Descartes and generally agreed upon by Clerk Maxwell, Augustin Fresnel, Albert Einstein, Dayton Miller, Charles Lorentz, and even recently by Renaud Parentani.

SIEGEL: Those are exactly the same. Both experimentally refuted, long after Maxwell died.

THOMSON: Do you have a reference for the fluid Aether being refuted? I have Whittaker's Classical and Modern Theories of the Aether. From what I have read, the fluid Aether theory was not refuted, but simply dismissed.

SIEGEL: Just look for any prediction of the ether theory that differs from relativity. Then find any reference on recent tests of relativity. Relativity so far has stood the test of all experiments.

THOMSON: Why are you defending relativity theory? Did I claim SR [Special Relativity] is wrong? As I told you, my theory neither confirms nor denies other theories. My theory is a parallel theory. It is based upon a completely different paradigm, which is based upon the same empirical constants and data as other theories. Does it seem impossible to you that there could be more than one way to interpret the data?

SIEGEL: Interpretation is irrelevant. It is only prediction that matters.

Siegel ignores the danger of the inferential step and asserts that there can only be one way to interpret the data. Feynman ignores the complex problem of establishing that a set of equations is complete. But the underlying cause for both errors is the same: They both fail to observe caution in their claim that experimentation generates proof. They both fail to be rigorous. They both stray from a core philosophy of science to make their claims.

The allegation that Maxwell's physical model is nothing more than scaffolding begs the question: What is the cause for Maxwell's Equations? We hear all the time from establishment science about how their gravity-based models are so good at predicting our observations of space, but Maxwell's ability to model electromagnetism based upon a vortex or spinning cell aether-based physical model appears to not suggest to Feynman that an aether exists. This is a major problem.

Establishment science's "Aether Model Exception" is both inherently contradictory and hypocritical. All that Feynman has done is created a puff of smoke to distract us in order to deflect from the glaring fact that Maxwell's physical model probably works for a reason. Sure, this isn't enough by itself to conclude that the aether exists (we have much other evidence to point to for that). But, by itself, the degree to which Maxwell's Equations work should inspire honest investigation into the aether. The fact that the model works surely means that establishment science has no basis whatsoever to ridicule investigations of the aether.
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Re: James Maxwell's Physical Model

Unread postby Plasmatic » Sun Mar 23, 2008 2:34 pm

Good reading Chris ,thanks for the text!
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Re: James Maxwell's Physical Model

Unread postby junglelord » Sun Mar 23, 2008 8:01 pm

Which only brings us back to three dimensions of space and three primary fields that permeate that space. Aether, Electric, Magnetic. Gravity again being a subproduct of the scalar field (aether) + electric field which expresses itself as a closed longitudinal field line. This brings us back to the fact that gravity is therefore not a primary field. These six dimensions are the two fabrics of reality. Right angle rule of thumb applies to all six dimensions, three of space, three of fields. This is a workable model and more coherent then the current four field model.
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Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
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Re: James Maxwell's Physical Model

Unread postby Solar » Mon Mar 24, 2008 1:54 pm

pln2bz wrote:Establishment science's "Aether Model Exception" is both inherently contradictory and hypocritical. All that Feynman has done is created a puff of smoke to distract us in order to deflect from the glaring fact that Maxwell's physical model probably works for a reason. Sure, this isn't enough by itself to conclude that the aether exists (we have much other evidence to point to for that). But, by itself, the degree to which Maxwell's Equations work should inspire honest investigation into the aether. The fact that the model works surely means that establishment science has no basis whatsoever to ridicule investigations of the aether.

One of the first things I thought after reading this thread was how much of a 'contradiction' it seems to persistently deny the aether since the "beautiful equations" are derived from assuming it's existence.

According to the Masters thesis Longitudinal electrodynamic forces and their possible technological applications, longitudinal forces *can* be derived from Maxwell's equations. Not only that but it cites numerous experiments, including Ampere and de la Rive's"hairpin" experiment, wire explosion, the railgun recoil problem, and longitudinal forces in liquid metals just to mention a few.

"During the debate in the 80s it has been tacitly assumed that longitudinal forces and stress cannot be predicted from classical electrodynamics. The arguments have been based on the fact that the Lorentz equation only predicts a transverse magnetic force. By focusing on the eld properties rather than the charge carriers, I intend to show that Maxwell stresses, and thus classical electrodynamics, indeed can beinterpreted to predict longitudinal stress."

I think the biggest problem causing this false denial is that no one wants to see relativity as a 'special case'. Lets face it, with regard to longitudinal forces the speed limit imposed upon c is *not* of "universal" order.
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Re: James Maxwell's Physical Model

Unread postby StefanR » Sun May 10, 2009 8:13 am

As I was reading this next bit about the elephant trunks, there was the description of the use of an mechanical analogy model that struck me.
From there it seems quite logical to make out the core issue.

4 A mechanical analogy model

In CGK02 we described a mechanical analogy model which may shed some light on the physical background of the double helix mechanism being so vital to our theory. In the following we shall develop the analogy model a little bit further and give an account of some experiments performed. Since long it has been well-known that magnetic field lines can, in many respects, be compared to elastic strings (Faraday 1839-1855; Alfvén 1950). On this basis we have constructed an analogy model to illuminate some of the properties of our trunk model. In this model a bundle of elastic strings is stretched between two fixed positions, A and C, situated at the same horizontal level. The bundle represents the magnetic flux tube in the trunk model, while the separate strings imitate the magnetic field lines. Straight strings are thus equivalent to straight magnetic field lines implying that there is no axial electric current present. If we twist the bundle of strings at one of its ends, say A, the strings become helically shaped. This is equivalent to helically shaped magnetic field lines, and to a finite axial electric current in the flux tube. The bundle of strings studied thus constitutes a mechanical analogue of a magnetic flux tube.
link to paper

Historical origin & differences in field theories

Lines of force originated with Michael Faraday, whose theory holds that all of reality is made up of force itself. His theory predicts that electricity, light, and gravity have finite propagation delays. The theories and experimental data of later scientific figures such as Maxwell, Hertz, Einstein, and others are in agreement with the ramifications of Faraday's theory. Nevertheless, Faraday's theory remains distinct. Unlike Faraday, Maxwell and others (e.g., J.J. Thomson) thought that light and electricity must propagate through an ether. In Einstein's relativity, there is no ether, yet the physical reality of force is much weaker than in the theories of Faraday.[3][4]

Historian Nancy J. Nersessian in her paper "Faraday's Field Concept" distinguishes between the ideas of Maxwell and Faraday[5]:

The specific features of Faraday's field concept, in its 'favourite' and most complete form, are that force is a substance, that it is the only substance and that all forces are interconvertible through various motions of the lines of force. These features of Faraday's 'favourite notion' were not carried on. Maxwell, in his approach to the problem of finding a mathematical representation for the continuous transmission of electric and magnetic forces, considered these to be states of stress and strain in a mechanical aether. This was part of the quite different network of beliefs and problems with which Maxwell was working.

Views of Faraday

At first Faraday considered the physical reality of the lines of force as a possibility, yet several scholars agree that for Faraday their physical reality became a conviction. One scholar dates this change in the year 1838.[6] Another scholar dates this final strengthening of his belief in 1852.[7] Faraday experimentally studied lines of magnetic force and lines of electrostatic force, showing them not to fit action at a distance models. In 1852 Faraday wrote "On the physical character of the lines of magnetic force" which examined gravity, radiation, and electricity, and their possible relationships with the
transmission medium, transmission propagation, and the receiving entity.

Maxwell reports that he read Faraday's Experimental Researches with delight, extracting from them several ideas to aid his own growing conception of electromagnetism.(9) Among these was the notion of lines of force- a semi-physical, geometric arrangement of lines around charges which, just like iron filings around a magnet, indicated the direction in which a point charge would move if it were to be introduced at any location.(10) This idea was of great significance in drawing attention to the space around charges, and so introducing the idea of a potential field, rather than simply considering charges as sources of action-at-a-distance, or as elements of a material substance which flowed only through conductors.(11)

Another idea which Maxwell 'appropriated' was an analogy between charge distribution and heat flow which Kelvin had published in 1842.(12) It was through a combination of this and the line of force that Maxwell attempted his first discourse on electricity - his 1855 essay On Faraday's Lines of Force.(13) In essence, this paper took Kelvin's 1842 analogy between electric charge and heat flow, but in place of heat assumed 'an imaginary fluid' whose properties could be described with standard hydrodynamic equations, following Stokes. Assuming positive and negative charges as sources and sinks of the fluid, Maxwell argued that the fluid would flow from source to sink along precisely the same lines as Faraday's 'lines of force'. In fact, the lines of force (or rather, the space between lines) could be considered exactly as thin tubes of steadily-flowing, continuous, incompressible fluid.(14)

In terms of the history of field theory, this paper was a very significant step, since it brought Faraday's physical, geometrical conceptions under the control of powerful analytical mathematics.(15) In terms of our understanding of Maxwell's methodology, the paper is also highly significant, since it displays a characteristic and conscious use of what Maxwell called physical analogy: a compromise between physical hypothesis, which he felt restricted and channel one's thinking, and pure mathematics, which sometimes lacked sufficient connection with the phenomenon under discussion.

The use of mechanical models and analogies within Victorian physics is a substantial subject it itself, and also features heavily in the work of such figures as William Thomson and Oliver Lodge. It was also a fundamental part of Maxwell's next foray into electromagnetism, through his paper On Physical Lines of Force. This paper sought to turn the physical analogy of Faraday's Lines of Force towards physical explanation. As the title suggests, it was Maxwell's attempt to construct a physical basis for the previously imaginary lines of force, and to use this to account for other electromagnetic phenomena. Moreover, he was by now quite convinced of the value of Faraday's electrotonic state, and sought to find some way of mechanically describing this change in media.(16) As he noted, the behaviour of magnetised iron filings in forming filaments around a magnet 'naturally tends to make us think of the lines of force as something real...and we cannot help thinking that in every place where we find these lines of force, some physical state or action must exist in sufficient energy to produce the actual phenomena'.(17)

These are of course not real scientific sources but it's just to indicate the idea a bit.
Now I think this is the main issue and already adressed in this thread.
There are several people proposing new ideas that adress the percieved problems arising from "mainstream" physics and cosmology, EU does it but so do APM, TT, RST and as Meyl talks about Faraday and Maxwell and Einstein (see for PLN2BZ's version with improved English here).
And so as well Aetherometry says "So there's your direct connection.".

Aside from the theory the following link gives a very nice historical review,
I think if one reads the six sections, one could get a very good idea where the diversion originates, it also will give a good idea of what Faraday was exactly after, his ideas about an aether or not, his idea of force, where Maxwell is different and seems to miss the fact that he is only describing a special case where the velocity of light is constant and that Einstein is following through on them, although this does't make them invalid, but limits their use for only that special case.

This idea of Faraday is what connects all the above stated theories at least in their roots.
The word mechanical is what typifies the adherence to classical science, the main link for Newton to Maxwell to Einstein, and that is also were they are limiting and obstructing themselves in their ideas, the mindset of the industrialisation is still used in the analogies used for modelling today.
From what I see is that all or almost all theories above accord more with Faraday,although there is an difference in departure from there, as did Tesla, and there is another name that connects Faraday and Tesla, it inspired them both and Tesla was keen to be photographed reading his book, how much of a wink does one need?
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.
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Re: James Maxwell's Physical Model

Unread postby Solar » Sun May 10, 2009 1:46 pm

Delighted to see that someone else has looked into "50 Years after Albert Einstein:The Failure of the Unified Field"

StefanR wrote:From what I see is that all or almost all theories above accord more with Faraday,although there is an difference in departure from there, as did Tesla, and there is another name that connects Faraday and Tesla, it inspired them both and Tesla was keen to be photographed reading his book, how much of a wink does one need?

Rudjer Boskovic (Boscovich, 1711-1787)
"Our laws of force tend to be applied in the Newtonian sense in that for every action there is an equal reaction, and yet, in the real world, where many-body gravitational effects or electrodynamic actions prevail, we do not have every action paired with an equal reaction." — Harold Aspden
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Re: James Maxwell's Physical Model

Unread postby StefanR » Sun May 10, 2009 4:18 pm

Solar wrote:Delighted to see that someone else has looked into "50 Years after Albert Einstein:The Failure of the Unified Field"

StefanR wrote:From what I see is that all or almost all theories above accord more with Faraday,although there is an difference in departure from there, as did Tesla, and there is another name that connects Faraday and Tesla, it inspired them both and Tesla was keen to be photographed reading his book, how much of a wink does one need?

Rudjer Boskovic (Boscovich, 1711-1787)

Yes, but perhaps it was not such a good choice to make to put in the shoes of the Correas, although they associate in a certain way with it.
The historial information of Aetherometry, I personally find not so satisfying, but still they make some good points. But connecting Faraday in the way they describe here with Maxwell et all. is not accurate I think.

And indeed Boskovic is the name, I find his book very hard to read, but there is something in there wherein he criticizes Newton and other things, that attracted the likes of Faraday and Tesla.
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.
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Re: James Maxwell's Physical Model

Unread postby Solar » Sun May 10, 2009 8:00 pm

I think you were correct to include Rudjer Boskovic in the picture. A suggestion. There are areas wherein Boskovic speaks to what has become known as longitudinal forces. When you read it consider this aspect of force also.

Pg 45 sec 17 & 17 is he speaking of longitudinal forces here via “velocity” and the “precussion” of particles?

“I say I had derived everything directly & solely from the velocity generated by the forces of those influences, which, according to the generally accepted view taken by all Mechanicians, either generate, or in some way induce, velocities that are proportional to themselves & the intervals of time during which they act; take, for instance, gravity, elasticity, & other forces of the same kind. I then began to investigate somewhat more carefully that production of velocity which is thought to arise through impulsive action, in which the whole of the velocity is credited with being produced in an instant of time by those, who think, because of that, that the force of percussion is infinitely greater than all forces which merely exercise pressure for single instants. It immediately forced itself upon me that, for percussions of this kind, which really induce a finite velocity in an instant of time, laws for their actions must be obtained different from the rest.

17. However, when I considered the matter more thoroughly, it struck me that, if we employ a straightforward method of argument, such a mode of action must be with drawn from Nature...”

More conjecture. On pg 45 sec 16 & 17 after mentioning “gravity“, and “elasticity” he centers on “the production of velocity” resulting in or causing “percussion” (collisions) as being “infinitely greater than all forces".

That sounds like longitudinal forces. The ‘axis’ of his drawings; either side of which he discovers all the other forces as being compounds of the initial force. Just as Steve O mentions with RST.

Pg 51 sec 29: “Local motion, & the velocity of that motion are what I am dealing with, & these are here broken off suddenly. These, it is perfectly evident, were something definite before contact, & after contact in an instant of time in this case they are broken off. Not that they are nothing ; although purely imaginary space is nothing. They are real conditions of the movable thing depending on its modes of extension as regards position ; & these modes induce relations between the distances that are certainly real. To account for the fact that two bodies stand at a greater distance from one another, or at a less ; or for the fact that they are moved in position more quickly, or more slowly ; to account for this there must be something that is not altogether imaginary, but real & diverse. In this something there would be induced, in the question under consideration, a sudden change through immediate contact.”

Now, he gets into discussing the nature of ‘particles’ having a line (surface) and a gravitational center, and layers having “pores” etc as proposed by those he calls the “Mechanicians”. Much of that was in reference to trying to understand how “velocity” as a pre-existing “impulse” is suddenly changed when ‘particles’ collide (“precussion”).

Look at the page 52. The axis of the geometrical relations he graphs appears to represent to him the nature of that pre-existing ‘velocity impulse‘ with line A-B. Consider what he says about either side of that zero axis AB and the sine wave-like “law of variation” represented by C-D-E. His comment at the top of page 55 continuing sec 37:

“…moreover, if the line CDE, which represents the law of variation, cuts the straight AB, which is the axis of time, in any point, then the magnitude can vanish at that point … In Geometry too we have this passage from positive to negative, & also in algebraical formulae, the passage being made not only through nothing, but also through infinity ; such I have discussed, the one in a dissertation added to my Conic Sections, the other in my Algebra ( 14), & both of them together in my essay De Lege Continuitatis ; but in Physics, where no quantity ever increases to an infinite extent, the second case has no place ; hence, unless the passage is made through the value nothing, there is no passage from positive to negative, or vice versa. Although, as I point out below, this nothing is not really nothing in itself, but a certain real state ; & it may be considered as nothing only in a certain sense. In the same sense, too, negatives, which are true states, are positive in themselves, although, as they belong to the first set in a certain negative way, they are called negative.”

Has this zero axis no become "Zero-Point Energy"? The same continuous "zero point" later developed by Einstein and Otto Stern? Note also how he further tries to asses this existent velocity producing component using water flowing. Top of page 63 continuing sec 47:

“Hence also in the case of water flowing from a vessel it reduces to the same example : so that the velocity is generated, not in a single instant, but in some continuous interval of time, and passes through all intermediate magnitudes; and indeed all the most noted physicists assert that this is what really happens. Also in this matter, should anyone assert in opposition to me that the whole of the speed is produced in an instant of time, then he must use a petitio principii, as they call it. For the water can-not flow out, unless the hole is opened, & the lid removed ; & the removal of the lid, whether done by hand or by a blow, cannot be effected in an instant of time, but must acquire its own velocity by degrees; unless we suppose that the matter under investigation is already decided, that is to say, whether in collision of bodies communication of motion takes place in an instant of time or through all intermediate degrees and magnitudes. But even if that is left out of account, & if also we assume that the barrier is removed in an instant of time, none the more on that account would the whole of the velocity also be produced in an instant of time ; for it is impossible that such velocity can arise, not from some blow, but from a pressure arising from the superincumbent water, except by continuous additions in a very short interval of time, which is however not absolutely nothing ; for pressure requires time to produce velocity, according to the general opinion of everybody.

I only made it to page 63. Perhaps this aspect of force is what Tesla either picked up on, and/or realized upon finding it; that this is what he had discovered, or this is what he thought might be the case through reading Boskovich. Aetherometry works directly with Tesla radiation (both massfree ambipolar electric and massbound electric). I think you're spot on here.
"Our laws of force tend to be applied in the Newtonian sense in that for every action there is an equal reaction, and yet, in the real world, where many-body gravitational effects or electrodynamic actions prevail, we do not have every action paired with an equal reaction." — Harold Aspden
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Re: James Maxwell's Physical Model

Unread postby Plasmatic » Mon May 11, 2009 1:27 am

Alton and I were recently discussing supraluminal causation. I suggested this analogy of a pipe filled with water 100 miles long. As soon as more water on one end enters the same instant water leaves the other end.That is not to say the causative process is instantaneous particularly though.
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