MAXWELL'S EQUATIONS

© Harold Aspden, 1998

Research Note: 4/98: June 6, 1998

I am writing this in conjunction with Gieskieng's Addendum in order to clarify my point of view concerning the relevance of the findings of Dave Gieskieng in his antenna experiments performed by propagating radio signals across canyons in USA. The question at issue is the validity of Maxwell's equations.

Now, very few scientists could ever dream that Maxwell's equations are open to challenge, but it is as well to ask if the majority of scientists familiar with electrical theory and the theory of radio transmission have answers to the following questions.

Firstly, given that we are taught in physics to recognize that, in fundamental terms, energy has three forms, namely electric, magnetic and kinetic, how do we explain the difference between magnetic energy and kinetic energy?

Well you might say that one has to do with how electric charges in motion interact with one another across empty space and the other is something far more familiar that is just the energy acquired by a something having mass owing to its motion. Now, in history, J J Thomson, the person who discovered the electron, derived a theoretical expression for the electromagnetic energy acquired by an electron of electric charge e, of radius a, and moving at a speed v, obtaining the result: E_k = (e²/3a)(v/c)² ...... (1), c being the speed of light, and he compared this with the formula for kinetic energy:
E_k = mv²/2 ......... (2) to deduce an 'electromagnetic mass' value m, which one can see satisfies the equation: m = (2/3)e²/3ac² ......... (3) This was based on the electric field energy E_s of the electron being assumed to be
E_s = e²/2a ......... (4) and so we can then see that E_s, which is applies at zero speed and so has something to say about rest mass is: E_s = (3/4)mc² ......... (5).

He pondered the question of whether this electromagnetic energy E_k was in fact nothing other than the kinetic energy of the electron. Indeed, he went so far as to show that, if it were, then the electron could never be accelerated to a speed exceeding that of light. This was many years before Einstein came along and, indeed, it was back in the 19th century that it had been shown experimentally that electrons got heavier and heavier as their speed converged on that of light.

In case you wonder about that factor 3/4, not being unity, as needed to satisfy E=Mc², take note that J J Thomson had assumed that the electron was a charged sphere with all its charge distributed around its surface, as if it were of conductive material. Had he assumed that the sphere was simply holding electric charge within it at uniform pressure and so uniform energy density, he would have obtained the E=Mc² formula.

So you have here two auxiliary questions to weigh in your minds. Did we really need Einstein and his Theory of Relativity to understand that E=Mc²? Is the kinetic energy of a fundamental electric particle wholly that of, and nothing other than, the magnetic energy set up in the surrounding field as that charge moves?

My answer to the first question is: "No" and my answer to the second question is revealed as we move on to the next primary question.

Secondly, why is it that Maxwell's equations contain no terms which represent mass? Here you may jump to the obvious conclusion. From what has just been said about J J Thomson, one can see that there is no need for mass terms at the fundamental level, if electric and magnetic field energy is all there is to consider.

That, however, is not my answer. I have an eye to the need to account for gravity and the problem of how energy travels at the speed of light. I spent a very long time trying to decipher the secrets underlying something called the 'Neumann Potential', on which electrodynamic interaction forces are founded. I also explored in various ways the notion that electric, magnetic and kinetic energies are distinct energy forms. The outcome depends upon experimental proof, something that is rather elusive, but I see a glimmer of such a proof in the antenna research findings of Dave Gieskieng.

Now you may think that, if I challenge the Einstein account for E=Mc² and accept the derivation founded in J J Thomson's method, I must identify kinetic and magnetic energy as one and the same. That is not so. The reason is that, fortunately, long ago and shortly after I began to raise these fundamental questions, I found a flaw in the Larmor derivation of the formula for energy radiation by the accelerated electron. The formula is used in physics and physicists will say that it works and so must be valid. They are wrong, because their experimental data only indicate that it works in respect of the collective action of charges sharing a common acceleration. The question I am concerned with is radiation by an individual electron, as opposed to how it may play the 'field' when part of a team.

I reasoned that Larmor had declared the electron to be accelerated without saying how it was accelerated and without allowing for its charge interaction with that essential accelerating field. Keep in mind here the advent of the 'quantum' and the need to explain why the single electron in its accelerated motion around the proton in the hydrogen atom did not radiate energy according to the Larmor formula. If atoms were to lose energy by radiation in that way, then all motion within atoms would have stopped long ago, but, as it is, they enjoy a life of perpetual motion!

So it was that I argued that an electric charge would respond to an accelerating field in just such a way as to conserve its energy against the prospect of radiation. When analysed mathematically, that gave me the formula E=Mc², without appeal to J J Thomson's method or the methods used by Einstein [1976b]. My derivation meant that the inertia and mass of an elementary particle are in no way dependent upon magnetic fields. Kinetic energy stands as an energy form in its own right. A full formal derivation of the E=Mc² formula by this method is to be found in my 1980 book 'Physics Unified' at pp. 80-84.

Just to put this in context, what it means is that all the elementary particles, such as protons, which have a core charge radius that is less than one thousandth that of the electron, have an intrinsic kinetic energy somehow stored as part of their moving system. The questions that then arise make one wonder if leptons, such as electrons and muons handle that kinetic energy storage in a manner different from hadrons, such as the proton. However, our immediate concern is Maxwell's Equations and where mass might feature in those equations.

Now here it is a question of where you want to begin. I submit that if you really want to understand Maxwell's Equations you have to think in terms of an aether containing charge that can be displaced. How else can waves sent between Sun and Earth make that transit through intervening space. If you think it is all done by photons then I ask you, where do you see photons in Maxwell's equations? Cast those equations aside and forget them, if the photon picture can satisfy your need for knowledge! You cannot back both horses and expect both to win.

I maintain that we must accept that the aether exists and contains electric charge in some form and so I say that it contains quons, electric charges of common polarity permeating a uniform continuum of opposite charge. That is the model of the aether which I find does give the right answers.

Now instead of bringing into play our empirical equations, such as that which expresses the law of induction, meaning something involving magnetic energy, let us first ask how those quons in the aether might oscillate as they transmit an undulating electric wave. They will, like the up-and-down wave motion of the sea, oscillate laterally with respect to the wave propagation direction and the potential energy stored by electric displacement will be exchanged with the kinetic energy of the up-and-down charge motion. In fact, the energy is that of a standing wave condition, meaning that energy does not have to flow at the propagation velocity of the wave.

If you study the mathematics of Maxwell's Equations you will see that they are reduced in form to two wave equations, one representing the electric field and the other the magnetic field. Both of those equations imply the transport of energy at the wave propagation velocity. Yet the equation for the electric oscillations is the same as that we can deduce if the electric potential is exchanged cyclically with the kinetic energy involved in those lateral oscillations, given that the quons must have a mass property. Is it then a problem that the aether has mass?

Before we consider that let us now look at that wave equation assigned to the magnetic field. Here it helps to have an idea as to what a magnetic field really is and how, and where, it involves energy storage. Never mind what the empirical formulations tell you, just think here about passing current through a long solenoid. There is a magnetic field set up along the axis of that solenoid and all of it is contained within the solenoid if that solenoid is infinitely long. That could be in a vacuum. How is energy stored in a vacuum?

Well I have already explained this elsewhere in these Web pages but I will describe the process once more. What we think of as empty space is not empty. It contains charge in motion. A component of that motion could be said to be a random vibration characteristic of heat. Apply a magnetic field and a proportion of those charges, just enough to set up an optimum reaction, as determined by maximum energy transfer, will react by assuming a helical kind of motion setting up a reaction magnetic field in opposition to the applied field. This works out as being precisely half that of the primary field. So, given that 2 minus 1 is 1, we know that the primary magnetic field set up by current in the solenoid is really double that we assume in our standard theory, because half of it, a half we do not 'see', is cancelled by the reaction. The analysis involved in that tells us also that the energy transferred from the primary field source to the secondary reacting field system is precisely that we formulate as 'magnetic energy'.

In other words, when we power a solenoid the magnetic energy we supply is transferred into that random thermal component of motion of the reacting charge in the aether. It heats that charge and that heat energy disperses through the aether. However, when we switch off the current supplying that solenoid, that 2 minus 1 reaction, becomes a primary action, equal but opposite to what we thought was the original primary input action, and it feeds energy back to the solenoid by cooling the aether within the solenoid.

That is what magnetic induction is all about. There is really no such thing as 'magnetic energy'. All one needs to consider is the kinetic energy of reacting charge in the aether.

So one can understand how Maxwell's Equations operate. Maxwell did not factor into his analysis the kinetic energy of the quons in the aether. Instead he incorporated the notion of the 'magnetic field' and assigned that an energy density. However, the problem with that was that he derived two wave equations which supposedly move waves together in step at the wave velocity, each carrying energy forward in the propagation direction. In fact, the energy of a single wave oscillation, that of the electric field, remains in situ as it oscillates between kinetic and electric forms. In free space remote from matter and a radiating source, electromagnetic waves therefore travel without conveying energy and they really would be better termed as 'electric waves', given that no magnetic field energy is involved.

You see, if the aether charge sets up the 'reaction', how can it at the same time sustain the 'action'? Where is the source of a magnetic field out there, well into space? If you say charge in motion must set up a magnetic field, I say where is the separate charge that can absorb the energy and store that magnetic field. In other words, I say that there is no such thing as a magnetic field out there in free space and that what we call electromagnetic waves are merely electrical oscillations exchanging electric potential energy and kinetic energy.

Now, of course, I cannot say that radio antenna do not radiate energy. They shed energy in setting up the disturbance which is that electric wave and, so long as there is undispersed surplus energy forced into the radiation field energy, there is an associated but rapidly attenuating wave that could be identified as a magnetic field wave. As with the wave on water analogy if something sets up a tidal wave, forcing water to move as a wave, then one distorts the natural equilibrium of the wave oscillations of the system.

You will then see why the antenna experiments of Dave Gieskieng are relevant to this question. If that antenna used by Gieskieng is specifically adapted to set up pure electric wave oscillations then it will ripple the ocean of space with a minimum of power input, because so little of the power needs to be dispersed by that thermal activity of the reacting aether charge.

On the fundamental scientific front, given my case that magnetic fields involve reacting charge, how can the J J Thomson formula hold up for the calculation of electromagnetic mass if those reacting charges are of far greater physical size than the primary charge? To satisfy that equation they must be minute in relation to the primary charge. Yet if they then have the unitary charge e common to all fundamental charged particles, they in turn must have an enormous mass compared with the primary particle. That is an escalating argument which takes one into the realm of absurdity and so one has to conclude that the electromagnetic mass notion of J J Thomson is erroneous.

I hold firm to my interpretation of inertia and mass as being the unwillingness of a charge to radiate its self-energy (as opposed to energy shared by mutual field effects) when accelerated. That 'unwillingness' or 'sluggishness' is what we call 'inertia' and the mass property that expresses that is given by the electric energy intrinsic to the particle as divided by the square of the speed of propagation of disturbances within the body of that energy E_s of the particle, invariably the parameter c.

There is then the question of how the aether can have all those quons with a significant measure of mass, given that the energy involved in those wave oscillations is by no means negligible.

The answer to this is that the quon system does have mass. Indeed, I calculated this long ago and found that it was very nearly 144 gm/cc, meaning that the aether has a mass density well exceeding that of Earthly matter. That is, however, no problem. Indeed, it is essential and was deemed so by our forebears in the 19th century who tried to explain the finite speed of light in terms of an analogy with propagation properties in solid matter. All one has to do is to explain the evident lack of aether momentum by accepting there is scope for motion of free quon charges in counterflow through moving aether [1976a] or an analogous activity by a leptonic activity involving muons The Ether - An Assessment, and it all begins to make sense, taking Michelson-Morley's experiment along with it.

To conclude, I can but say that it would be a pity if the copious experimental evidence provided by the researches of Dave Gieskieng were not investigated further and, indeed, repeated to secure full verification. If they do prove that we can set up waves in the aether with a minimum of energy input and support the suggestion that there is very little actual energy transport from transmitter to receiver, as opposed to an energy exchange with the thermal aether background, then one can see scope for a technology that is reminiscent of the efforts of Tesla. At the very least the experiments should establish the reality of the aether and dispose of the notion that photons, as particles, transport energy. That would be a very significant breakthrough in the onward march of science. There is so much wrong with the state of the art in pure physics that technology must be suffering as a consequence and it is due time that we faced up to the issues involved and began to see the 'aether' as a future workplace for the energy technologist.

Harold Aspden
June 6, 1998