Fields
A field in mathematics is something which exists throughout a region and which has a definite value at every point within that region.
In electricity and magnetism, we have, in a mathematical sense, two types of field. We have vector fields and scalar fields. We can produce two such fields quite simply with a small boy and a balloon. Take the balloon and rub it on the small boy's hair. (If you can find a small boy with recently washed hair, they work best) Now hold the balloon near the boy. If there are any dust particles in the air which are electrically charged, they will subjected to a force because we have generated a strong electric field between the boy and the balloon. This is a vector field because at every point, it has properties of strength and direction. There is another field present, that of the electric potential. This is a scalar field because it does not posses any directional properties. We can in theory measure potential with a voltmeter but in practice they are all too insensitive to use in this situation.
An experiment which demonstrates the reality of the electric potential field was performed by Reiss and latter far more accurately by Kohlrausch. In this two plates of metal, a small distance apart, form a capacitor which is charged with static electricity. When the plates are moved apart, the voltage between them increases. Modern voltmeters consume an electric current and allow the charge to drain away, so this experiment is hard to repeat, but it does demonstrate the reality of electric potential.
When we speak of an electric field, we refer to the one entity which can be mathematically described in terms of both a vector field and a scalar field. However, when we enquire more deeply into the workings of the universe, we find that the fundamental nature of reality is the presence of energy. The electric field is primarily an energy density field.
The electric field surrounding a charge stores energy in space. Electric potential does the pulling apart of the positive and negative layers of space and the pulled-apart-ness stores energy. The potential is not a force, but a doing of work, an amount of energy. The energy density and the potential are part of the fundermental nature of the electric field. The ability of the electric field of one charge to exert a force on another charge is a property of its energy density. It is not the fundermental nature of the electric field.
Classical physics does not pay too much attention to whether a field is a mathematical device or a real physical entity. My physics on the other hand places great emphasis on understanding the nature of things and the mechanisms by which nature works. There are some very significant differences between classical physics and my understanding of physics. This comes from the fact that I see energy as the primary reality and believe that we can only formulate fundamental laws of nature in terms of concepts based on this fact.
In classical physics, electric fields are measured in terms of electric intensity 
. This is sometimes assumed to be addative. The concept seems to be that fields exist both as mathematical artefacts, in which case they have separate existence, and also as a single physical entity which is the sum of the separate mathematical fields. It is the single entity which results in the polarisation of space. The process of polarisation results in energy being stored in space.
My view is that each charged particle has its own private electric field which is an integral part of the particle. These individual fields are able to coexist in space and it is their presence which exerts forces on other charges. I call this the principle of superimposition (as distinct from the principle of superposition) and regard it as the mechanism by which force is exerted at a distance. It also provide us with an explanation of the generation of magnetic fields. In my theories it is very important to distinguish between real phenomena and mathematical artefacts.
Perhaps the most alarming difference between my understanding of electric fields and the view of classical physics is the fact that the polarisation of space around a charge is in the opposite direction! When I first discovered this fact, I found it very alarming and spent several months coming to terms with it. In classical physics, I create an electron in a region of space, the surrounding space becomes polarised and a displacement current flows through the surface which bounds the region. The quantity of charge which flows into the region is equal and opposite to the charge of the electron which I created. There is therefore no change in the total charge within the region. If there is no net charge within the region, then why should an electric field extend beyond it? I do not think classical physics is able to answer that question. There is yet another paradox. If we polarise space, and then place another charge within that polarisation, it will feel a force exerted on it by the displaced charge of the polarisation. The force it feels is in the opposite direction to the force form the electron which caused the polarisation. Indeed, it should cause an equal and opposite force! Classical physics ignores this paradox.
In my model of an electric charge, the charge consists of a polarisation of space towards a point which terminates in a spherical surface. By assuming that the charge on this surface is unable to exert a force at a distance, we can can understand the ability of one charge to exert a force on the other as a property of the polarisation field of the charge. Such a model works very well in an otherwise empty universe which contains just one charged particle. As we create extra charges, the model will only continue to work if the polarisation fields of the individual charges can coexist in space.
The only interaction between the polarisation fields of charges comes from their relative motion. This is responsible for generating magnetic fields. It is at the surface of the charge that a raw edge of polarised space appears. It is this raw edge which is able to feel the presence of the polarisation fields of other charges.
Energy density fields
There are two types of energy density field: electric and magnetic energy density field. As the name implies both are typified by an energy density. We use the symbol Q for energy density and suffix it to denote a particular form of energy density. Thus Qe is electric energy density and Qm is magnetic energy density. An energy density field has the scalar property of the actual energy density, but may also have a directional property. Electric and magnetic fields have directional properties, but the energy density field which described energy stored in a compressed gas would have no directional property because pressure acts in all directions.
An energy density field cannot exist by itself, but needs some medium to exist in. This could be a fluid, a solid or even space as in the case of electric and magnetic energy density fields.
There is associated with every energy density field an internal "tension" like property. In the case of an electric field , this is the electric intensity which has both magnitude and direction, so we represent it as a vector. For a magnetic energy density field, it is the magnetic induction 
which describes the internal tension.
There is also associated with every energy density field a "stiffness" with which the medium resists the tension like property. We might consider the energy stored in a stretched piano wire. The stiffness is called Young's modulus (symbol Y). The internal tension must be expressed as a force per unit area of the cross section of the wire and this is called the "stress". When the wire is stretched, it increases in length. We have to work out the amount it stretches per unit length and we call this the "strain". Young came up with the formula
and claim that 
but such thinking is wrong because we are interested in the ability of electric and magnetic fields to exert forces on electrons and it is the magnetic induction 
