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RADIAL CONFIGURATION AND FIELD DENSITY
    In dynamic geometry, in a field of one or more surfaces, points and lines excluded in this discussion, auto-convolution will cause an apparent increase in the number of surface sections passing through a finite region of the field, as apparant to the observer.
    Then the question to be asked, from the observer's point of inquiry, how many surface sections might one expect inside a specific and fixed finite region of the field at this moment?  The answer of course, must relate to common standards in scientific investigation, in this case, a one centimeter unit standard, seving as a unit volume of the finite region of study, and the second as the unit time.
    Hypothetically, we know that the slow outward spiraling of the counter rotating waves of the radial configuration can provide a consistent rate of decay providing that all waves within the field, which at some time or another might cause the generation of a radial configuration, share a more or less constant and equivalent speed.RELATE TO QUARK
    The average rate of decay of all radial configurations would directly correspond to the average speed of all waves within the field which are associated with the structure of radial configurations.
    It is also essential that the field density overall is uniform and relatively constant.
    If these two conditions are met: a relatively constant and universal field density as well as a constant and universal wave speed, the rate of decay of all radial configurations should be nearly equivalent.
    Give and take minor perturbations and variations, such as variable entry conditions of the two counter rotating waves into the radial field at the beginning of each generation cycle; technically the beginning of each radial configuration's life cycle, the lifetimes of all radial configurations should then be nearly equivalent.
    As a wave moves around a radial configuration, it essentially follows a segmented spiral path as it moves from surface to surface, where each time it encounters a surface and undergoes interchange, it is re-directed orthogonal to that surface. After one complete revolution in orbit, it will always be slightly further out from center, an amount which depends on the angular density of the radial configuration. The angular density of course depends on the field density and the ability of radial configurations to capture and hold surfaces. This is of course dependent in turn on wave speed.
    All things being equal, all radial configurations should fall within the same range of capturing and holding, thus all radial configurations should contain the same number of radials. This means that their angular densities should nearly be the same, that the change (DR) in orbital radius should be the same. This relationship can be expressed as:

Eq. 1           DR = R x (1/cos(1/W) - 1)        (Refer to 2.2 following.)
 

The variable R is the present radius. Since each wave will begin its orbital spiral very close to the radial array's center, where R is small, DR will also be small, but as the waves move outward, both R and DR will increase in value to some maximum, at which point, the waves dissociate.

    The anticipated smallest value for R directly relates to the wave size of the smallest waves which are most commonly involved in the generation of a radial configuration, where presumably, they make their initial orbital entrance; striking an orbit so that the innermost edge of their wave motion does not overlap the radial center.  In the event the dual-wave radial results from the axial approach of opposite ISSs, the smallest value for R would be the lessor of the wave size of the two waves joining together.
    The maximum value for R probably corresponds to the effective limit of the radial field. At any greater radius, the orbiting wave would be engaging surfaces which are not radial, as it moves more so into the random ambient field around.
    Being that there is no expression nor known value for this radial limit, it can only be assumed to closely match the actual size of a neutral mass particles, such as a neutron; perhaps a diameter of about 10-13 centimeters.
    In order to evaluate equation one, in the attempt to quantify the decay rate, several other assumptions must be made. First, it is assumed that decay proper occurs when both waves dissociate from each other. It is further assumed that this occurs when one of the waves spirals outwards to a distance corresponding to more than the neutron's radius, about 5 x 10-14 centimeters. It is assumed that the innermost starting position for each wave corresponds to a distance of one half their wave diameters, at the least. Also, it is assumed that both waves, though most likely dissimilar in wave size, closely correspond in size to the most probable field waves which cause spontaneous generation or ISS association. It is lastly assumed that the speed of these waves most likely corresponds to the most commonly clocked speed in the electromagnetic spectrum, that of the speed of light (c).
    When a radial configuration decays into one inside-shelled and one outside-shelled spiral, each spiral comprises one each of the original waves. In the case of the outside-shelled spiral, the wave is inside this shell, locked in position as a standing wave, presumably with its innermost wave motion just outside the spiral center. In the least, its shell radius cannot be less than a full wave diameter. In the case of the inside-shelled spiral, the wave sits just outside the shell, a shell whose radius has some finite value. Of these two configurations, the outside-shelled spiral should be smaller, which means that it is most likely comparable to the electron.
    This choice is somewhat reinforced by cursory study of the motion of configurations within the field, which in the case of the inside-shelled spiral, there is no tendency for it to move in the field, whereas the outside-shelled spiral may display intrinsic motion (as do electrons). Also, the inside-shelled spiral can be shown to demonstrate a behavior similar to inertia, whereas the outside-shelled cannot demonstrate this. In short, of these two decay products, one is smaller, tends to move through the field and does not demonstrate inertia, whereas the other should be bigger, have a tendency to remain at rest, and demonstrates inertia. All of this suggests that of these two decay products, the outside-shelled spiral is most likely the electron or positron counterpart.
    As mentioned earlier, mass equivalency most likely corresponds to the number of surfaces captured and held cohesively together by a given configuration. In terms of mass vs. gravitational force, this relationship corresponds to how many impulses are produced by IDDI, which in turn is dependent on the number of radials held by a configuration. Mass also relates to inertial characteristic, which in this hypothesis would be akin to the characteristics of a configuration in terms of its movement through the field, particularly its acceleration. In both cases, whether it is mass due to force or mass due to inertia, it is the number of surfaces which plays a direct role. This implies that surfaces have mass, which is incorrect. The correct implication is that surfaces which comprise certain types of field configurations demonstrate the phenomenal and collective behavior, we call mass. In this case, when surfaces act collectively, they may be assigned apparent mass, as merely a matter of mathematical necessity. Simply put, if a collection of 10,000 surfaces demonstrate 10,000 units of mass, one surface would therefor be demonstrating 1/10,000 of the total mass, or a mass of one, though individually its mass would be zero.
    Presently, there is no derived expression for mass in these terms, leaving one with the option of making an educated guess.
    Under these conditions, the simplest and most expedient choice would be to equate mass equivalency to particle cross-sectional area. This is basically the same as equating mass to volume, where area is proportional to volume, and vice versa.
    Assuming a volumetric similarity between a electron and a neutron, if there is any relationship between mass and volume, given that the mass of both an electron and neutron are known, as well as the neutron's size, then the size of an electron might be determined. Given that the neutron has a volume of 4/3 p (5 x 10-14 cm)3 and a mass of 939.553, and that an electron has a mass of 0.511, then the electron's radius can be determined as 4 X 10-15 centimeters. This means that its component simple wave cannot exceed this radius. It also means that its wave size cannot be greater than this.
    This means that the most common and likely waves involved in the spontaneous generation of radial configurations do not exceed this size, and that since smaller waves cannot persist within the field, this becomes the most likely wave size.
    If two such waves participate in the formation of a radial configuration, then the nearest they can approach each other (what would be the start of their initial, innermost orbit) cannot be less than one half this wave size, or about 2 x 10-15 centimeters.  This would also be true for independent, newly formed ISSs which have not yet associated.
    Knowing this initial orbital radius and the outermost radius at decay, gives us an operable range in which to apply equation one, allowing for the determination of DR; the progression of outward increments as each wave circles the radial center.
    Rather than integrating this expression in its solution, I have chosen to simply take the average value for R lying between its closest and furthest values, where,

                                     (5 x 10-14) + (2 x 10-15)
                R (average) = ----------------------------- = 26 x 10-15.
                                                        2

    I believe that under these circumstances: many assumptions, rough approximations, a degree of expediency, that this is acceptable. Hopefully some young student of mathematics will devise more exacting results. In any event, Equation 1 now becomes:

Eq. 2                   DR = (26 x 10-15) x (1/cos(1/W) - 1).

What this means is that for every orbital passage taken by the orbiting wave as it circles the radial center, it will move outward by an average increment DR, starting at its innermost position 2 x 10-15 and ending at its outermost position 5 x 10-14.
    What does this all mean? Buried near the opening of this chapter is this statement: If these two conditions are met: a relatively constant and universal field density as well as a constant and universal wave speed, the rate of decay of all radial configurations should be nearly equivalent. Imbedded in this statement are three variables: (1) the universal field density, (2) the universal wave speed and (3) the rate of decay. Of these, assuming that simple waves are equivalent to photons, the universal wave speed would therefor be the same as the speed of light (c). And, if indeed a dual-wave radial is analogous to the neutron decay, we then know its rate of decay in terms of half-life, roughly 103 seconds. This of course leaves us with one unknown variable of the group: universal field density. It would seem then, that our objective is not so much the unearthing of neutron fine structure, but instead the utilization of what this hypothesis already knows about the structure of field configurations in conjunction with already established physical knowledge in the determination of the characteristics of the invisible: the field density.
    Since all field elements are invisible, immeasurable and undetectable, one must utilize alternative means of measurement, which is exactly what is being attempted. Thus it seems that the thrust here is not so much the mensuration and analysis of the dual wave configuration analogue, but instead, the determination of field density.
    By knowing the average orbital radius, and the assumed speed of these waves at and around the speed of light (c), one may determine the average orbital period, where,

                                                 2p x 26 x 10-15cm
       T (period) = C/c = 2pR/c = ------------------------ = 5.4 x 10-24 seconds.
                                                    3 x 1010 cm/sec

C is the circumference or distance a wave must travel to complete one average orbit.

    Given that the mean life of this configuration is equated to the mean life of a neutron, the average number of orbits can now be calculated:

                                  mean life          103 sec
                 Norbits = --------------- = ------------------- = 1.85 x 1026.
                                         T           5.4 x 1024 sec

    Since we know both the entrance radius and exit radius of the orbiting waves, a range of 52 x 10-15. centimeters, the average change in radius between orbits is then,

                        total range          52 x 10-15 cm
                 DR = ------------------- = ---------------------- = 2.8 x 10-40 cm.
                          Norbits                 1.85 x 1026

By re-arranging terms and substituting this value for DR into equation 2 the angular density (W) may be determined:

                                1                                          1
                W = ----------------------- = -------------------------------------------
                   cos-1(1/(DR/R+1)     cos-1(1/ (2.8 x 10-40/26 x 10-15+1)

                                                       1
                                              W = ----------------------- .
                                            cos-1(1/ (1026+1)

                                               W = 1.2 x 1011 +/- 102.

The angular density is an indirect measure of the number of surfaces encountered along the full circumference of any imaginary circle concentric to a radial center.
    The number of surfaces then cutting through a dual-wave configuration is,

Number of Surfaces = 0.5 x (1.2 x 1011) = 6 x 1010.

The cross-sectional area of a dual-wave configuration is roughly 7.8 x 10-27 centimeters. If 6 x 1010 surfaces pass through it, the two dimensional field density inside the dual-wave configuration would be:

                          6 x 1010 surfaces
                         r = ---------------------- = 7.7 x 1036 surfaces/cm2
                          7.8 x 10-27 cm2

    This value for field density represents a general density inside the radial configuration without regard to density gradients. It is the density basedupon two-dimensional area, representative of surfaces essentially parallel to the orbital axis, rather than those cutting through which are otherwise not parallel to this axis.

    It should be pointed out that those surfaces which are not parallel to the axis are not really participating in radial behavior, especially rate of decay; in essence not be being part of the radial configuration, but merely cutting through it. Nevertheless, they are there, and as field surfaces they must be counted.
To do so, one must consider the full volumetric density, rather than only the two-dimensional density, which is first converted to the path density; the number of surfaces within a field cutting a unit path at any angle, even extremely shallow (surfaces which are nearly parallel to the unit path) angles. Loosely speaking, without regard to field gradients inside the configuration nor the general radial order, the path density and the two-dimensional field density are virtually the same. Rough correlation between path density and three-dimensional field density suggest a nearly consistent ratio of:

Field Density = 3.3 x Path Density = Cross-sectional Density.

Since we have determined the two-dimensional cross-sectional density, the field density may be determined as:

density = 3.3 x 7.7 x 1036 = 2.54 x 1037 surfaces/cm3.

For this expression to be valid, the field must be perfectly isotropic, which is not the case inside the dual-wave radial. Because both orbiting waves capture and hold ambient field surfaces more so along the orbital plane, than at the poles, the density at the poles should be less than along the orbital plane. There is also the question of capture and hold, causing this configuration to have and maintain a higher field density inside than the surrounding ambient field.
To better evaluate these conditions, draw in pencil a two-dimensional field of surfaces (shown as lines) uniformly spaced, thus representing a field of fairly uniform density. Without adding or deleting surfaces, one-by-one, erase those surfaces which have been captured by the dual wave radial; essentially redrawing by bending these surfaces in towards the radial core. Don't make the core too big, nor have the surfaces pass through a common point when you bend them in. Don't try to draw all 6 x 1010 surfaces, because your paper will look black. What you will end up with will be a low density representative cross-section of a dual-wave configuration. When you are satisfied, try making a good xerox copy; you may have to retrace some lines in ink. Then make several extra copies to have on hand. This of course is a polar view of the dual-wave configuration.
    What you should end up with is four distinct zones: (1) a central core of surfaces randomly organized and passing through at all sorts of angles, (2) a zone just outside this core where all surfaces are radially organized, passing between the core and surrounding random field, (3) a threshold zone of moderate density, of radials and a few ambient surfaces, and (4) the random field of ambient surfaces mixed with the emerging radials.
    After doing all this, you might ask, where's the dual-wave configuration? After all, there seems no distinct boundaries.
    This of course is quite appropriate, being that in conventional physical studies, particles are detected, or at least surmised, to be fuzzy sort of blobs, without any clear-cut line of demarcation between themselves and nothing.
    Often when scientists describe the size of elementary particles, such information is derived from rather gross and inexact techniques, such as bombardment, in which case, a specific nucleus is targeted with high speed particles or quanta, such as electrons or X-rays, producing a scattering pattern, which is then interpreted, revealing the general dimensions the nucleus.
    Taking your drawing, you can do the same thing by tracing the orthogonal movement from surface to surface of a whole shower of "high speed particles". Also, to help establish the size of the dual-wave configuration, trace the orbital passage of one of its waves, starting it at the innermost edge of the radial zone just outside the central core, until eventually it encroaches upon the ambient field.
The following illustration shows these things: the shower of bombardment particles coming from the top of the page, the central core (dashed circle), and the orbiting wave, which finally breaks out of its spiral orbit and wanders into the ambient field. Notice that none of the bombardment particles seem to be able to make it into the central core; being deflected by the geometry of the array, which is very much what happens in the real.
    Though there is no defined line of demarcation between the configuration and the field, its apparent size is noted as being a diameter where (1) the orbiting waves no longer follow a spiral and (2) bombardment particles pass by without significant deflection.

    Also shown is a relative surface count (RSC) profile based upon the actual number of surfaces you can see and count, passing through a unit square. Notice that one side of the innermost unit square is twice the radius of the central core, which has already been stated as being most likely one half the wave diameter of the most prevalent field waves which cause the spontaneous generation of neutron dual-wave configurations. In conventional physical units, a unit square is equivalent to 4 x 10-15 centimeters. The relative surface count in your drawing will depend upon how many surfaces you draw; the relative surface count (RSC) therefor being arbitrary.
    As mentioned, the central core measures about one half s-units in radius. From this distance, 0.5 s-units, to the outer fringes, about 4.5 s-units, marking the outer boundaries of the dual-wave configuration, the average relative surface count is about 9.8. Again, this is an abstract number which corresponds to the dual-wave configuration's average density of 7.7 x 1036 surfaces/cm2. Based upon this RSC profile, the density of the central core (RSC=20) is 1.57 x 1037 surfaces/cm2, whereas at the outer ambient field (RSC=6) the density is 4.7 x 1036 surfaces/cm2. The exceptionally low RSC of four at about six unit distances, is explained as being the consequence of surface deficiency caused by the orbiting waves which have the ability to sweep surfaces out of this region, more so than anyplace else.
Since the outer ambient field is isotropic both in terms of surface orientation as well as density, a general value for field density (Fr) may now be given. This variable constant should be used in all computations.

        Fr = 3.3 x 4.7 x 1036 = 1.51 x 1037 surfaces/cm3. (Rev. 2/10/96)

    The absolute outer boundaries of this configuration appear to be about 6 s-units. Each s-unit is thought to be equivalent to 4 x 10-15 centimeters. This means that the hypothetical diameter of the dual-wave configuration is 0.24 x 10-13 centimeters, which is not too far off from what it should be.  Of course, that's where we started in the first place, so maybe we've just experienced some sort of circumlocution!  Nevertheless, we've got to set camp stakes somewhere, so this will be it for now.
    Another constant, actually a variable constant since the field density is forever changing would be its reciprocal, denoted as h, where h = 1/Fr.
    This value h is very important because it directly relates to the wavelength (l) of simple waves, where waves whose wavelengths are less than 3h are unlikely to propagate through the field, whereas waves whose wavelengths are greater than 3h, may.

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