1. Introduction
This section introduces the postulates of SFT. It is an aether theory, but not one that assigns any physical properties to the aether other than the ability to support the existence of an electric and magnetic field. These fields are viewed strictly in the classical sense with intensities which are independent and proportionally consistent regardless of an observer's perspective.
Imagine a three dimensional space that is continuous. This space is governed by a flow of time that is uniform and constant for every point in the space. This space contains no matter and no particles of any kind. The space is at absolute rest, but more, it defines an absolute rest, since being devoid of matter, no concept of velocity for a body exists. This space allows for the existence of the electric and magnetic vector fields in the classical sense. The fields have continuity at all times and in all places. These two fields are quantitatively related by the two following equations:
(1)
(2)
where, as usual, E is the electric field, B is the magnetic field. c represents the speed of light.
Furthermore, two more equations define these fields:
(3)
(4)
where f(r) is a scalar function over 3d space which is yet to be defined. There is no charge density to establish this divergence, but we will allow for some artificial constructions for the purpose of experiment.
One will note the lack of a current density term in Eq.(2). This follows from the lack of charged particles to establish such a current. These equations and the static particle-less space constitute the postulates of what is to be called "stationary field theory"1.
Though this space has no particles and no velocity, it still has energy, which is bound within the electromagnetic fields themselves. The energy of these fields is expressed by the Poynting theorem (in free space)2:
(5)
Not only does this show the energy content and its conservation, but it also shows that energy can flow from one location to another in the space, even though the electromagnetic fields never move. This relates to the wave motion derived from the above equations which is3
(6)
If f(r)=0, then this represents normal electromagnetic propagation.
1. This is not actually a new theory at all. It is simply a strict interpretation of classical electromagnetism in empty space. When we say "stationary field theory" at this point, it only means that we are using this classical subset. These equations can be found in any basic textbook on the subject such as Griffiths1 or Jackson2.
2. This derivation can be found in Griffiths1 322 or Jackson2 236. It should be pointed out that normally this is derived from Newtonian concepts of energy and in this theory it must be a postulate, that the Poynting Theorem represents an energy in the fields. Since we will derive the Newtonian concepts from this, it actually covers the same ground.
3. This derivation can be found in Griffiths1 341 or Jackson2 270.
Contents
Next