Copyright, Harold Aspden, 1996

In this Essay I suggest a suitable theme for the research student in search of a project worthy of a Ph.D.


One of the most fundamental problems confronting the physicist is the understanding of the forces that act on electrical charge in motion. If you think the answer is all wrapped up in something called the Lorentz force law, then you need to sort out your ideas! I will address this discussion to the professors of physics who have a special interest in the theories which relate to electrodynamics and the forces at work in the interaction of moving electric charges.

The specific issue that concerns me is not so much the electrodynamic forces which act on charge moving as a visible transporter of electric current, but rather the forces on the charges moving as if they are hidden in an electrically neutral, but ever-active, ionized medium. This medium is not necessarily one in which there are ionized atoms, but can be the subtle background medium of the multitude of conduction electrons in a block of copper, for example. It could even be the medium we call the 'vacuum', given some latitude in our perception of the physical world and remembering that Maxwell did introduce us to an arena of scientific interest that we have neglected and pushed aside as we 'bask' in the cool shadow cast by the Einstein monument.

If you think I am ignorant of the orthodox methods of explaining why there appears to be no overwhelming 'free electron diamagnetism' in copper, for example, then take note of the above reference to 'methods'. Years ago, when I surveyed this subject I counted some three quite different ways in which this anomalous phenomenon is explained in the scientific literature. They were all different and mutually inconsistent, which I saw as evidence that the subject was wide open and still in need of clarification. You see, the problem was that physicists knew something as an experimental fact but yet their theory, as confirmed by several other experimental facts did not fit with that absence of 'free electron diamagnetism'. It seemed that any odd-ball theory that could slide over the problem could be accepted, given that other more interesting problems attracted one's research interest. So, all I am saying is that it is time to put things in order.

I have already, in Lecture No. 17, hinted at the subject I now introduce. I declared towards the end of that Lecture that I had long wondered why it is that the magnetic field of a permanent magnet can penetrate through a block of copper without the numerous free electrons in motion within that copper reacting to screen such fields virtually in their entirety. I said that the answer I adopted long ago, is the following:
When an electron in motion reacts to a magnetic field it is a quantum event, meaning that maybe it will and maybe it won't, this being determined by whichever affords the optimum response from an energy equilibrium viewpoint.

This, therefore, is the subject I commend as a worthy research project for a budding Ph.D. student. It is a pursuit that offers enormous potential and one I would have welcomed as my indoctrination process in my younger years. There is a bridge that needs to be constructed as a link between the quantum world and what is of practical importance in electrical science. It would be foolish to think that no mistakes have been made in interpreting certain phenomena in electrodynamics, and one should not live in awe and be overwhelmed by the alleged power of quantum theory or the theory of relativity, given that, notwithstanding the contributions of Paul Dirac, there are so many mysteries that seek solution.

So, I will venture here to pursue, in outline, the topic that I raised in Lecture No. 17 and I hope that it will arouse interest and warrant being taken up by someone as a Ph.D. research project.

Force or Energy?

Which would you rather believe, (a) that there are laws which tell you the force which is exerted on an electric charge moving in a magnetic field or (b) that there are energy-dependent factors which govern how a charge moves in a magnetic field? Well, you can say that the choice is irrelevant if the answers are always the same and serve us well in their practical application. However, you will, I hope, have doubts if I can draw your attention to certain anomalies that our physics fraternity has chosen to 'sweep under the carpet', as it were.

When quantum physics took root in the early decades of the 20th century, we found that we had to break faith with the natural logic and experience of physics, as based on what we could see and denmonstrate in our hands-on bench-type testing of electrical apparatus using standard electrical measuring instruments. We were, in effect, asked to rely as much on certain abstract theoretical notions as upon measurement data and regard such notions as fact, if they seemed to work, notwithstanding the lack of sense and logic in the formulations involved.

What seems to me to be a curious circumstance is that physicists persist in declaring their belief in the validity of the Lorentz force law, notwithstanding their admission that their efforts to relate the force of gravitation and the electrodynamic force, their Holy Grail of a 'unified field theory', is still eluding their efforts. Force equations are surely not the way Nature goes about regulating its affairs. Energy is what counts! If, in Nature, the optimum energy deployment implies action of some kind, then that action is what one sees and it could well be something that contradicts the predictions based on man-made laws of physics.

What sense is there is studying the effects of a magnetic field on an electron moving as part of the electron beam in a cathode-ray tube and then applying that knowledge to determine the effects the magnetic field has on a neutral plasma of electric charge. Overall, there can be no net electrodynamic force on a neutral plasma, but yet there is action and deployment of energy in some way, especially if the strength of that magnetic field changes.

Read about this in your textbooks and you will perhaps find the kind of comment that says, there is no energy transfer if the magnetic field is changed very slowly. To a practically-minded person this almost suggests that the author of such an idea does not know the difference between 'energy' and 'power'. Einstein is one of the culprits on this account. He once declared that there could be no radiation of energy if an electron was accelerated slowly and used this to justify how electron mass increased with speed according to his relativistic formula, the point being that energy had to be conserved to get the right answer. Do you believe that an electron has a mass that can vary, not just according to its speed, but according to the history of its acceleration? This is the sort of thing that has been 'brushed under the carpet' and it is no wonder there are so many unanswered questions in fundamental electrodynamics.

Consider, for example, the Neumann Potential. Is this something historic or is it of importance in modern electrodynamic teaching? Well, I could go on, but I am not going to develop this into that thesis I hope some student will undertake. So, I will move rapidly now and plot the research path that I would recommend.

The theme is to concentrate on energy, not force. Then one does need to explore the physical basis of the Neumann Potential. It is the subject of Tutorial Note No. 4 in these Web pages. It concerns energy potential and leads to an inverse-square law of attraction force as between moving electric charges that share mutually parallel motion.

From there one needs to move on to the formulation of a generic force law that includes the Lorentz force as a special case, one avoided by gravitation, which is a special case of a different kind, still embraced by the generic force law. That leads the student to what I described in my paper in the Journal of the Franklin Institute 1969a. Then, to jump directly into the problem at hand, the next scientific paper to inspect is one entitled 'Instantaneous Electrodynamic Potential with Retarded Energy Transfer', Hadronic Journal, v. 11, pp. 307-313 (1988). This paper is also to be found in the book 'Aether Science Papers', published in 1996,and is of record in these web pages as [1988a].

The derivation of the Neumann potential from first principle analysis is presented on p. 310 of the paper as equation (5). As an energy expression it is:
W = (ee')(v.v')[r]/2r2
and it corresponds to a force:
F = -(ee')(v.v')[r]/r3
where v and v' are the velocities of electromagnetic charges e, e', respectively, r is their distance of separation and [r] their vector distance of separation.

This is an inverse square of attraction force for interaction of charges of the same polarity moving mutually parallel. It is the basis of the gravitational force and the electrodynamic force, but in the latter case we have the complications which arise from the presence of numerous other charge interactions, ever present in the scenario of what we call the 'magnetic field'. The experience on which we formulate the laws of electrodynamics stem from an observation that an electric charge subjected to a magnetic field will move in a helical path so as to have a component of motion in a reacting circular orbit. The reaction opposes the 'action' of the magnetic field, but extracts no energy from that field, given that the field is not varying in strength.

Now, what this really means, as is fully explained in those background references just mentioned, is that, in addition to that force F just formulated, there are two separate force components acting on the charge that are induced by a kind of inertial response which ensures no net transfer of energy between the Neumann potential and the kinetic energy of the interacting charges, meaning the charge in question and those that are the source of the magnetic field. The three force components feature in Maxwell's famous treatise on Electricity and Magnetism but you do not see this explained in modern textbooks, which develop the Lorentz force law by adoption of Einstein's ideas. In fact, the Lorentz force law drops one of the three force components and is really an abbreviated vector-product version of what is, in reality, an expression including the current element vectors as two scalar-products. By dropping that third term, possible if the problem at hand is restricted to interactions involving current flow around a closed circuit, the scope for developing the link with gravity vanishes and takes with it all prospect of field theory unification. It further destroys the basis for energy transfer as between the field medium and real matter. Therefore, it is not surprising that physicists have lost their way and cannot make sense of the efforts of those of us who talk about gaining access to the sea of energy that pervades the field medium which they call 'space-time'.

The point at issue concerning those two additional force components, which I labelled [A] and [B] on p. 310 of that Hadronic Journal paper, is that these two forces can assume the directions v and v', respectively, if they are to set up the inertial effects that result in the electrodynamic actions we observe. However, that is an optional reaction and it is this prospect that I am now saying warrants special research. The key words that apply here are those at the bottom of p. 310 where I wrote:
"There is nothing to be gained by writing [A] as -[B], as that denies the induction process that we know exists, so we now look at the alternative. ... This is where I developed the argument that led to the full formulation of the electrodynamic law generic to the force of gravity and the Lorentz force."

Now, clearly, seeing this in retrospect, I erred in saying 'there was nothing to be gained' by pursuing that alternative case. Indeed, the argument now developed turns on this very point. If the deployment of energy involved in the electrodynamic actions between charges in motion can optimize by taking advantage of the option as between bringing those force components [A] and [B] to bear or by not invoking the inertial reactions implicit in those forces, then the action will be so determined. That, plus a condition that no system of electric charge can develop rotation solely by virtue of its internal electrodynamic self-interaction, is the basis of a comprehensive understanding of electrodynamic phenomena.

By admitting that an excess of energy seeking transfer to the reacting system of charge in the field medium will set those [A] and [B] force components in a mutually cancelling mode, we have introduced that quantum scenario into the electrodynamic interaction.

To explain this, imagine you hold a magnet and it produces a magnetic field in a region of vacuum, or near vacuum, as inside an evacuated thermionic tube. Ignoring the 'matter' aspect of the problem, suppose I say that there are electric charges inside the space within that tube, all dashing around as a kind of neutral-overall gas. You see that as something in the 'aether' if you wish or you can give it meaning by thinking of the charge which accounts for Maxwell dispacement current. The question is whether those charges react or not to the presence of that magnet.

Well, I am sure they will react and do so to the precise extent that they half-cancel the applied magnetic field, in the manner already explained above. (The half-cancellation theme is my discovery that 2 minus 1 is 1, meaning that if all magnetic fields are twice as strong as we think they are based on their known source but are alyways half-cancelled by an unknown reaction then 1 suffices as an answer until we confront the gryomagnetic ratio factor of 2, when 2 minus 1 has to become the right answer!) However, what precludes them from all reacting together so as to swamp the applied field and virtually kill it completely?

The answer to this lies in that Neumann potential, because the sum of all the Neumann potential terms applicable to those reacting charges that exist unseen and undetected inside the space within that vacuum tube will be zero, once they have adjusted to the presence of the magnet. Therefore, there is no action able to induce reactions that demand a transfer of energy from the source of that magnetic field. Those [A] and [B] force components must all then cancel one another, meaning that there are no forces acting to speed up or slow down the vacuum charges and no corresponding reaction forces on the charges within the magnet. In short our quantum hypothesis is vindicated and explained by formal electrodynamic analysis as developed from that Hadronic Journal paper.


The scope for onward study of the theme suggested here is enormous as it opens an unexplored avenue in orthodox physics. The standard theory of quantum-electrodynamics, with its Feynmann diagrams and assumptions that are melded into a mathematical framework with little relevance to energy as such, deals with certain abstruse phenomena. Yet it cannot account for gravitation. Nor can it explain the process of electriomagnetic induction discovered by Michael Faraday. How is energy fed into a solenoid by a current stored in the space within that solenoid so as to be returned on demand when the current is switched off?

The answer lies in what I have described above. So I am saying that a magnetic field acting on what you see as empty space is really governing the reaction of charges moving around unseen in that space. I am saying that a magnetic field need not act on electrons moving though it, meaning that they need not be deflected at all, if the reaction energy in that field is already sufficient to feed the return of the field energy when the field is switched off. That is a breakthrough in our way of thinking about electrodynamic phenomena.

If I were a Ph.D. student interested in this theme I would research it in two ways, initially. I would ask if there are instances where an electron can be affected by a magnetic field when moving in near proximity with the field but not through it, which seems just as unorthodox as saying that there are instances when, moving though the field, it is not affected by it. Also, I would ask how the reaction might be affected when reacting charges of different properties are present.

The first of these topics would cause me to consider the Aharanov-Bohm effect. The second topic would cause me to consider the Nernst Effect, as introduced in Lecture No. 17. However, I would also study the whole background history of what is called 'free electron diamagnetism', which is surely a chapter of errors, given what is here proposed. Last, but not least, the argument must converge on the energy of the field medium and that challenging question of whether we can harness it for useful purposes.

The theme here, given that the case is made for the presence of the half-field reaction condition, is whether one can do anything to take that energy from the field environment and apply it to useful ends, before needing to restore the field equilibrium. Look at this with a lump of iron in mind. The quantum underworld keeps the iron fully magnetized in its internal system of magnetic domains. If I apply a magnetizing field I will augment that state of magnetism but the effort in storing energy in the reacting charge moving as free conduction electrons in the iron or in the space underworld will be shared by that quantum activity. Therefore, something must happen to the energy involved. The iron must get hotter or cooler and whatever I do is augmented by action of the 'free energy' world.

What all this means is that more research needs to be directed into 'magnetocaloric phenomena', with an eye to something that might be practical on the energy front.

That, in summary, is the pursuit which I commend to someone looking for a worthy project for investigation in an academic environment. My hope is that there will be those who engage in such research. If your professor thinks that what I am suggesting is wrong, then ask him to tell me why. Where does my analysis fail? If your professor says that he, or she, is unaware of my writings on this subject and is far too busy to spend time studying such writings, then you must weigh that response for what it is worth.

My onward efforts to take this theme forward will be recorded in these Web pages as I proceed. The following links will take you to: Main Index, Essays Index, and Lectures Index.

Harold Aspden