SECTION HOME        ALPHABETICAL INDEX
 The Society for the Diffusion of Knowledge
P.O. Box 964,
Kaunakakai, HI 96748
 
SIMPLE FIELD WAVES

    The surfaces comprising the Random Field are neither fixed nor at rest.  As a direct result, the field is filled with incessant activity, referred to as noise.  Much of this activity is translated by the lateral, non-inertial movement of surfaces and simple field waves.
Strictly on its theoretical behavior, a simple wave is thought to be analogous to electromagnetic quanta (light/photons/neutrinos).
    A simple wave is two dimensional shape, with a finite wave diameter and a finite speed, traveling through a three-dimensional field;  its overall rectilinear path is tunnel shaped, but of course, zig-zagged from surface to surface, as it follows an orthogonal re-direction from surface to surface.
    The wave may normally be thought of as a uniform distribution of motion, when such motion coincides to a surface.  In the absence of coincidence, such motion is unknown observationally.
    At the very center of the wave, this motion is maximum, uniformly diminishing at its edges, thus marking the perimeter of the wave, which may be thought of as circular, or nearly circular, in which case, the wave diameter would be the diameter of this circle, roughly speaking.
    The maximum speed of this wave is thought to approach some constant, where such a maximum occurs randomly, perhaps statistically following a standard bell shaped distribution.  This is based on centuries of scientific measurement of the speed of light in air and in vacuo, with some of the older observations falling closer to the mean than newer.
    These studies, for the most part, were performed long before Albert Einstein came upon the scene and no where reflect his opinion, without fundamental basis, the light must travel at a fixed and exact speed in any fixed medium.

    Such a behavior is entirely consistent with this study, simply because there is no established theoretical mechanism which might alter wave speed as each wave travels through the field of surfaces, but only its direction.
    One might say that of the two components of wave velocity, one remains fixed and the other is variable.
    When such motion manifest coincidentally to a surface, its approach, before impinging with that surface, may come from any angle, but, once associated with that surface, is motion is deemed properly perpendicular to that surface;  longitudinal directions along the surface being meaningless.
    In this accord, under different conditions of the field, in terms of its general surface orientation, will cause the wave to follow specific paths, such that in a field of purely random surfaces orientation, the wave will follow a zig-zagged path, appearing straight (rectilinear) to the observer, macroscopically.
    In the following illustration, the wave energy is frozen as it is ready to leave the tenth surface.  Note that the wave is redirected with each surface shown.  This is an idealized representation which assumes that the wave undergoes interchange with every surface shown, though statistically on average, it would undergo interchange with every other surface.
    It is estimated that the entire distance across this illustration (eleven somewhat parallel surfaces), is somewhere in the neighborhood of 10-35  centimeters. [READ]
    This sequence of individual processes is not subject to frictional losses, and may proceed unabated indefinitely.
 
 

    What we have is wave motion, which if occurring in other than free space, would be occurring within a field of surfaces;  each sufficiently close together so that waves may move from surface to surface without decay.
    We also have choices as to the shape of the wave, such as being either transcendental, damped or bell shaped.
    If you will then, imagine a vibrant field of surfaces, so close together that these waves  may readily pass through the field without convolution leading to decay;  though we know that at times, under certain circumstances of low field density, these waves will ultimately decay into many smaller waves of respective distributions of motion.
Imagine then within the Random Field one surface bulging out to meet another. Upon encounter, interchange may or may not happen, being that there is a fifty-fifty chance. In this example, let's say it does not, the first surface passing through the second, only to encounter another surface. Let's say that interchange fails again and again to happen, eventually causing the first surface to bulge outward to the extent that it begins to auto-convolute. 

    When this happens there is a simple rule. Since interchange happens only half the time; each encounter at a new point of non-definity has only a 0.5 probability of resulting in interchange. Thus the total probability for any given surface to undergo interchange within a group of N surfaces can be expressed as:

P = (1 - 0.5N )
Thus the probability of interchange occurring within say ten surfaces (N - 10), would be .9999. On the average though, as a surface bulges through the field, it will undergo interchange with every other surface encountered, leading to this following convention.
    In all following illustrations diagramming surface behavior, particularly where a wave moves through the field, the effects of interchange will not be shown for every surface, but rather every other surface; it being understood that the surfaces lying in-between, which upon interchange does not occur, are invisible. This is merely a convention which reduces by one half the number of surfaces drawn, as well as possible confusion by showing a clutter of surfaces in high density fields.
    Another convention is that because three-dimensional field illustrations are both difficult to draw as well as interpret, in virtually all illustrations, surfaces will be shown only as lines; being understood that these lines represent the location of a given surface as it intercepts a flat plane, called a K-plane, common to all surfaces within that particular illustration. The K-plane is purely imaginary, aiding the manner of illustration. When one sees these lines, they should always regard them as being surfaces.
    In our first example, the initial surface bulged outward, passing through several surfaces before it began to auto-convolute. In this next example, the same surface undergoes interchange at uniform and regular intervals. Accordingly, by our first convention, it is shown undergoing interchange with each line; being redirected orthogonal as it does so. This is the beginning of a simple field wave. As a point of order, a field wave is not the surface moving through the field, nor the essence of surfaces, nor energy (such as changing curvature), but simply motion. In short, a field wave is motion only, not something moving. Because of IDDI, as the initial surface moves towards the second surface, it will advance more than normal, and the second surface, given to be at rest, will be displaced backwards in the direction of the first; both always meeting mid-way.
    Progressively, as interchange continues between these two surfaces, the initial surface will acquire the rest motion of the second surface which acquires the forward motion of the first surface, leaving the first surface at rest mid-way between their original positions and sending the second surface on to meet the third surface, with much of its exterior portions set backwards. The process then repeats itself, leaving the maxima of each wave set forward and at rest in the position of the old position of each successive
surface lying ahead. The maxima (the fastest point of the wave, normally corresponding to the wave center) moves through the field orthonormal from surface to surface, leaving each spent surface displaced forward of its original position by the distance between surfaces. On the average, this displacement will be twice the mean distance between field surfaces, since interchange skips on the average every other surface.
    Upon departure from this condition, the first wave remains ahead by only one-half h, and the second wave falls back this same distance, resulting in an IDDI of one-half of what might be otherwise expected.
As mentioned, if the field is isotropic; not favoring any particular orientation of surfaces, such as a radial orientation, the simple wave will move through the field orthonormal from surface to surface;  describing a microscopically zig-zagged path.
    As a matter of random chance concerning the waves deflection, its path would be macroscopically straight. 
    In a radial field, a simple wave will follow an outward spiraling path around and around the radial center; its outward rate inversely proportional to the radial field density as shown following.

      Geometrically self evident, if a wave approaches a whole series of surfaces whose curvatures are concave to its approach, its wave size will swell, increasing its wave diameter.  Conversely, if it approaches a whole series of surfaces which are convex to its approach, its wave size will diminish.
 
 

    The following illustration shows the typical motion of a field wave as it grows larger and smaller during its propagation through the field.
    As a simple wave bulges outward to meet and undergo interchange with the next surface, it can only travel a limited distance before it tends to undergo auto-convolution and interchange with itself.  When this happens, some of the motion is redirected in different directions away from the original. Since this would normally commence on the outer fringes of the wave, the wave size representing its more or less cohesive motion, becomes smaller. It is a negative feedback condition. Smaller waves cannot travel as far as larger waves without undergoing auto-convolution. (Auto convolution results in the production of smaller and smaller waves.) As the final result, a wave can simply no longer continue on, essentially decaying into a localized set of smaller waves.
   Roughly speaking, being based solely on graphical analysis, a wave generally will undergo the first stages of auto-convolution after traveling upon a given surface three times its wave diameter before undergoing interchange. Statistically speaking, waves are nearly assured interchange within a distance embracing ten surfaces. If this distance is always slightly less than three wave diameters, then waves of this size will most likely make it through the field. What is this distance?
    Since we already know that the mean distance between surfaces is 6.6 x 10-36 centimeters (very roughly speaking), a wave can travel ten times this distance, or about 6.6 x 10-35 centimeters without decaying; a distance representing three wave diameters. Therefore, waves whose diameters are no less than 2 x 10 -34 centimeters can propagate through the field; anything smaller, providing the field has the same mean, universal density, will most likely decay. Of course very large waves are unaffected by all this, being well beyond this threshold.

        A simple wave (l) moving through the field will become redirected by each new surface it undergoes interchange.   Here we see a simple wave shown as a red arrow moving about a section of the field consisting of a radial array of surfaces.  These surfaces are radial because they all pass through each other at a common axis.  One surface is shown in blue, because it is canted to the group.  When the simple wave encounters this surface, it will be redirected orthonormally to this surfaces, as illustrated by the blue arrows.  The circle defines the path of such a simple wave in a field of a much higher density of surfaces than shown here.  If we were to trace the path of this wave as shown, it would follow an outward spiral away from the axis.
    Noteworthy to say, there will be other surfaces canted in the opposite direction, offsetting each other overall, such that the circular path as shown, tends not to drift along the radial axis.  The precision of radial alignment is not such that all surfaces will pass through a common axis, but only near it.  Remember, this is a random order of surfaces  with specialized alignment taking place, such as polarization, or as in this last example, the surfaces accidentally being ushered into a radial array by conditions present at the moment.

Go here if you would like to see animation of a simple wave moving through the field.

SECTION HOME          ALPHABETICAL INDEX