and 
. Conventional theory says that we can calculate the electric intensity at a point by summing the individual electric fields of individual charges. There is a neat assertion that when we consider two charges, the sum of the energy contained in their combined electric field is equal to the the sum of the energy which their fields would contain if they were far apart plus the work which is done in bringing the two charges to within their current distance of each other. What I have not seen is a working through of the mathematics to prove this. When I try to do this for myself, I can not do the integration and neither can either of my two maths programs. A much simpler interpretation would be that the two electric fields do not combine, but that they each continue to exist in their own right. The potential energy would then be possessed by virtue of relative position, rather than being actually present in the electric field.
This leads to some interesting areas of speculation. The idea that each electric field could have a separate existence and that they might be superimposed on one another came to me when I was looking for an explanation of the force of gravity. If the fields did not combine but remained separate, then the space near the earth would be pervaded by the overlapping fields of all of the constituent charge particles of the earth's mass. There would be a very real presence in space and might produce gravity. I latter discounted such a model because it would make gravity dependent on the sum of the moduli of the charges and not on mass, but the seed was sown for the principle of superimposition.
Consider an electric current flowing in a wire. It produces a magnetic field in space beyond the wire. There have been many attempts to explain how this works. The modern trend is to say that magnetic fields are just a manifestation of moving electric fields. I would not go along all the way with this interpretation, but I do see moving electric fields as the prime generators of magnetic field. If the magnetic field extends beyond the wire, then the moving electric field must extend beyond the wire. We are unable to measure an electric field extending beyond the wire because the effects of the electric fields of all the positive and negative charges within the wire tend to cancel each other out. If we place a test charge near the wire, it shows no signs of experiencing any force from any electric field. There are two possible reasons for this: the fields might cancel each other out so that no electric field exists in the region of the test charge; or the test charge might experience the individual forces form the fields of all the individual electrons and quarks of the wire and these forces sum to zero. The experience of a magnetic field in the region surrounding the wire would suggest that the latter is the true case.
Another line of thought is to wonder how an electric field is propagated through space. I do not believe in action at a distance, for me, the nature of space has to be modified in a continuous point to point action. I can see that an individual charge might do this very simply by polarising space in a spherically symmetric fashion. Such a process has an immediate and obvious inverse square law. With two or more charges, it should be possible to envisage the same process provided that we can everywhere construct infinitesimally small pill boxes with their curved side parallel to the electric field and their ends perpendicular to it. This process is that used in finding the divergence of a vector field and it turns out that the process will work if the divergence of the resulting electric field is everywhere zero. There is a mathematical identity which says that the divergence of the sum of two vector fields is equal to the sum of the divergences of the two individual fields. This is not true. Our understanding of divergence requires us to be able to construct the pill boxes. The problem comes from the fact that regions exist where the vector sum of the two vector fields is very near zero. In such regions, the direction of the vector sum varies wildly and it is impossible to construct our parallel sided pill boxes. The identity breaks down in the region of a point where the vector sum is zero. I am forced to the conclusion that a group of charges could not transmit their combined electric field into all of the surrounding space in a continuous point to point process.
It seems obvious to me then that electric and magnetic phenomena are best explained by assuming that every charged particle in the universe has its own electric field extending to infinity, and that they all coexist.
The next question to ask ourselves is "What is the fundamental nature of the electric field of a charge". This is where we start to widen the gap between this new understanding and the accepted laws of Physics. I assert that energy is the primary reality of the universe. To me the electric intensity E which produces a force on a test charge is simply the by-product of the presence of an electric energy density field. The proof of this way of thinking lies a long way ahead, but we will eventually reach a point where the concept of inertia and the proof of Newton's laws of motion pop straight out of electromagnetic theory with mathematics which anyone with A level maths could understand and reproduce for themselves. Along the way, we have to rethink a lot of physics and sacrifice a few sacred cows, but a theory which can explain electromagnetic phenomena in such a way that Newton's laws pop out as a direct consequence has to have some merit.
It is impossible to think directly about space and time and the existence of matter and the laws of nature; we need to put together a whole set of analogies which lead us to the internalisation of the concepts. I like to think that space is like the beaker of two liquids used in the production of polymer fibres. The polymer is produced at the surface where the two liquids meet. There is no limit to the amount of fibre which can be produced and once created the fibres each exist quite separately. This meeting of the two liquids is like the interface between the positiveness and the negativeness of space. We can polarise space to form a charge and because we have to do work to stretch the two apart, the energy density field which is created exists in its own right and the positive and negative layered-ness of space remains waiting for the next electric energy density field to be created.
We meet the first sacred cow almost immediately. Maxwell's displacement current flows in the wrong direction. Under the classical theory, we create the charge by magic and the presence of the charge then causes a polarisation of space. The problem with this is twofold. The first is that if we create our charge within a given region, Maxwell's displacement current causes an equal and opposite quantity of charge to flow into the region. That means that the net charge in the region should remain zero. The second is that any test charge will find itself acted upon by both the electric field of the charge, and by the internal field of the polarisation which is equal and opposite. Thus, the test charge should not experience any net force. It is not easy to accept the idea that the displacement current needs to move in the opposite direction, but it is the simplest way of explaining how polarised space is able to exert a force on a test charge. When we latter come to consider how an alternating current in a circuit containing a capacitor produces a magnetic field, we will see that the continuity of the magnetic field depends not on our being able to perform a surface integral over a surface passing between the plates of the capacitor, but upon the fact that each electron has a spherically symmetric polarisation field extending into the surrounding region which moves as the electron moves.
The electric fields which surround objects which are electrically charged result purely from a rearrangement of the positions of the electrons. Consider a capacitor consisting of two plates in a vacuum. A deficit of electrons on one plate and a surplus of them on the other results in the sum of the electric fields pervading the region between the plates producing a sum equal to the theoretical electric field. The distinction between the mathematical artefact and the real mechanism comes when we consider the energy densities. The electric polarisation energy density field of each electron and of each quark remains unaltered. The only thing that changes is their positions. This change in positions creates a measurable effect on a test charge placed in the region of the electric field. The test charge experienced a separate force from every one of the superimposed electric energy density fields of the surrounding charges. These forces sum vectorially to produce a resultant force which is what we measure. Our mistake is to think that the resultant electric field, which is the sum of all the electric fields of the individual charges, has a real existence. It does not, it is only a mathematical artifact.
There are two types of electrical energy density field. Those which belong to individual electric charges and those which are generated by the movement of magnetic energy density fields.
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© Copyright Bruce Harvey 1997.