17. Coherence
In view of electromagnetism, modern concepts of polarization do not make a lot of sense. If the field of a photon were in a single direction, it would have to spread as it propagated. Since the photon does not spread, its transport of a electric field vector in one direction contradicts electromagnetic theory. Thus polarization is simply some attribute of the photon that is unexplained. Here we have managed to keep the photon from spreading, but to do so requires electric field vectors in all directions transverse to the direction of propagation. The problem is then that this photon cannot be polarized.
This section explains what polarization has to be in this model. It was the realization of the dominance of stimulated radiation (from Einstein's A and B coefficients) that lead to this solution. The problem is it still does not explain all the observations, only the bulk observations.
We have found that photons have an extended field that apparently can influence atomic behavior up to a certain distance (stimulated emission). While it is true that photons can trigger the emission of other photons, the phase cannot match exactly because it would require instantaneous response at a finite distance. It is thus evident that the phase matching must occur 360° out of phase. In other words a stimulated photon leaves on the tail of the photon that has triggered it. We will call this relation between the photon and its triggered follower a coherence link. In the process of continued stimulated emission, a great number of these coherence links are created, each building a path to the initial triggering event. In this way a constant phase-to-distance relation is created resulting in a general longitudinal or depth coherence.
These coherence links are never perfectly in line, but some distance to the side of the triggering photon. In the process of continued stimulated emission, the area of linked photons becomes macroscopic and a transverse or breadth coherence is developed. So, even though the photons are individual entities, this grouping behavior gives them a plane wave appearance.
When travelling through a transparent substance, this coherence is not lost. However, all photons are actually absorbed for short periods of time. They are not absorbed at the same time, but some are absorbed while others that are not absorbed stimulate them to re-emit. this process continues until they all eventually traverse the material. Because of the time that they are absorbed, it takes longer for the light to pass through the substance than free space. The presence
of electric and magnetic fields in the material does not change the permittivity or permeability of the space itself1. The transparency of a substance is defined by the ability of currently unabsorbed photons in the material to stimulate absorbed photons to re-emit.
Note that a coherence link in respect to breadth coherence can correspond to a photon which is offset in any direction from the stimulated photon. Apparently, there can exist directionally
transparent materials which will allow the currently unabsorbed photon to stimulate the absorbed photon to re-emit only from one direction (or a limited range of directions). When the photons
pass through such a material, all photons manage to traverse the substance, but on leaving, the coherence links are all in the same direction. The loss of coherence in all directions makes
the photons susceptible to absorption if they pass through a material which has a different direction of transparency. If the new direction is perpendicular to the original direction, then
virtually all the photons are absorbed. If they pass through a material which has a direction which is 45° from the original, then 50% will be absorbed and the other 50% will exit with
coherence links in the new direction. This occurs because after the coherence is aligned, when coherence links are later lost, there is less help from other photons to cause the absorbed photons to re-emit. Apparently when the photons first enter a directionally transparent substance, since they have a normal distribution of direction of coherence links, the existence of interim angles of coherence aid in eventually being able to shift the coherence to the direction of transparency with few photons actually being absorbed. After alignment, these interim angles of coherence no longer exist and shifting the coherence becomes more difficult to the point that with a 90° shift it becomes impossible and all photons are absorbed.
The point of all this is that even though the photons have no intrinsic polarity (having only a cylindrically radial field) the coherence can have a polarity, which can be linear in any direction or circular, if the direction of coherence changes over time2. Since light is not a plane wave, field polarity must be ruled out. The photon cannot have an electric field in a single direction or it will propagate and spread. This is required by Maxwell's equations.
While single photons do not have polarity (directed fields), there are apparently two types of photons, one which leads with the negative field (transverse field vectors pointing inward) and one which leads with the positive field (transverse field vectors pointing outward). It could be that this would have some effect on absorption and re-emission as well.
1. There is no statement in classical electro-magnetic theory that intrinsic permittivity or permeability can ever be altered. As a practical matter of including the effects of polarization or magnetization of materials, a different permittivity and/or permeability can be used to calculate the resulting effects, but the intrinsic permittivity and permeability of space is not changed.
2. This has the same observational consequences as described in Griffiths1 350 and Jackson2 273 though they were referring to plane wave propagation.
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