Y-Bias and Angularity:©

The Dynamics of Self-Organizing Criticality

From the Zero Point to Infinity

David G. Yurth

Donald Ayres, A.E.

August 2005

Fifth Scale

This is the scale at which Quarks combine to create Hadrons of 26 types and Leptons of two known varieties. [[i]] It is at this scale that the phenomena referred to as gravitational field effects, electromagnetism and the nuclear forces are first evinced. Additionally, this is the scale at which the binding forces which combine Hadrons and Leptons to create atoms first become operative. These binding forces are measurable in the form of photons, energy quanta with distinct wave form attributes, physical particles with energy densities [mass] and non-local field effects. This is the scale at which the Standard Model first fails to provide reliable predictive indicators with respect to the physical attributes of L4.

Three issues become paramount at this scale.

* First, this is the first scale at which gravitational effects become evident. Why this is so, and what it means for any cosmology which seeks to explain how gravitational effects operate, can now be considered from a fundamentally different perspective when viewed through the lens of Y-Bias and Angularity Theory.

* Second, this is the first scale at which the property of mass referred to as the “permanent magnetic vector” is found in six members of one family of elements. In the absence of a cogent model which explains what magnetism is and how it works, it is not possible [for example] to understand why some materials are naturally magnetic while others are not. Neither is it possible to understand how permanent magnetic fields exert a definitive effect on non-magnetic materials. More importantly, without a cogent explanation for this phenomenon, it is not possible to understand many of the phenomena which are known to exist but are nevertheless prohibited by the Standard Model.

* Third, and perhaps most importantly, this is the first scale at which the physical attributes referred in the physics literature as ‘mass’ are observed. Again, it is possible to define what mass is in the context of Y-Bias and Angularity theory in a way which is not possible within the context of the Standard Model. This facilitates a more robust understanding of sub-atomic particle interactions and provides a sound basis for explaining how Nature works.

Accordingly, the authors provide a context for describing these phenomena by explaining what they are and how they operate in L4, as manifestations of SOC behaviors operating at quantum-defined scales of self-organized criticality. While this discussion is not intended to be exhaustive, it is hoped that the application of the Y-Bias/Angularity concepts to these ambiguous constructs will serve to better integrate our understanding. Further, it is hoped that this approach will stimulate further investigation and research into these avenues of inquiry.

Gravitational Fields, Magnetism and Mass

Gravitational Field Effects

In personal correspondence with scientist Gary Vesperman, noted Russian physicist Dimitriy Plotnikov has posited that the Law of Gravitational Effects can be stated in quantum mechanical terms as follows:

F.6

C(X,Y)=((2*B*COS((2*E0)/h)*EXP(-i*t*(E0-A)/h)*(COS(2*k*R*COS(Z))+COS(2*k*R*S IN (Z))))^2 ([1])

M1*M2*1/R2

As in Whittaker, Anastasovski and Frolov, we find two aspects of this equation worthy of further consideration. The first part of the equation corresponds to the proportionality of the masses, = M1*M2. This suggests, among other things, that until the organization of Quarks reaches a minimal level of complexity, the aggregated set of properties and attributes which constitute Mass are not yet found to exist. Before this scale of organization is achieved, gravitational field effects are not found to operate on constituent spinors.[[ii]] While Gell-Mann and his colleagues at MIT argue that this is not consistent with their findings, the evidence amassed since 1986 by many other teams of investigators clearly demonstrates that quarks do not exhibit any behaviors suggesting they are effected in any way by gravitational forces.

Second, and perhaps equally compelling, is the notion represented by the new factor ‘Z’. According to Plotnikov’s analysis, gravitational field effects correspond to the inverse proportionality of the square of the distance between masses, as a function of harmonic resonance(s) between them. Accordingly, a new value appears – the incidence angle ‘Z’ – which reflects the angularity quotient for the energy exchanged between the masses within a radius R.

If the gravitational interaction between the bodies depends on the distance separating them as a harmonic function, then at certain values of R the amplitude of the probability of the energy exchange between the two masses must become zero. That is, certain areas will be seen to emerge in the space between interacting masses where gravitational interaction between the masses is dissonant and therefore non-organized. On the other hand, certain areas will be seen to emerge where the resonance [Y-Bias/Angularity] of the interaction is maximal, which in some cases is evidenced by highly concentrated aggregations of matter.

Fractal Substitution

In the context of Y-Bias and Angularity Theory, the characteristics of this interaction can be further illuminated by the substitution of Mandelbrot’s primary operator defining harmonic resonance [Z D Z2 + C] for Plotnikov’s constant [Z]. This substitution is warranted because the universe is observed to be fractal at all scales. This substitution yields two operators not identified by Plotnikov or Anastasovski. First, the nature of harmonic resonances operating between two masses becomes a dynamic interaction, the strength and value of which is defined as a Y-Bias interaction operating at an angle of incidence between them. This interaction works to create harmonic effects ranging from minimal to optimal, depending on the magnitude of the Y-Bias function and the Angularity of the interaction, as illustrated [for example] by the structure of the galaxy known as M51 and billions of other similarly structured galaxies. Accordingly, gravitational field effects are shown to not be invariant at any scale. Rather, as Anastasovski rightly holds, excitation of the field between masses must be seen in terms of a standing wave function, whose attributes demonstrate amplitude, frequency, angular momentum, weighted waveform vector velocities, periodicity, phasing and so on, which interact harmonically in the context of a realtime fractal [SOC] feedback loop.[[iii]]

This paradigm can be applied with respect to an analysis of the distribution of mass in the solar system. As predicted by Plotnikov and Whittaker, the Fibonacci relationships demonstrated by the energy exchange between the mass of the Sun and those of the orbiting planets [for example] occur only in maximal areas of Y-Bias and Angularity. In the areas between the planetary orbits, the probability amplitude diminishes to values which approach zero. In these areas, we find little or no mass, as predicted. Consider the motion of planets, represented by the formulation

W= DC = (D) . C(Z), F.7([2])

Dt Dt

with the angular velocity responsible for the motion of planets shown as the component [Z]. This equation and the whirlpool structure of galaxies [for example] illustrate the range of conditions which operate across the range of Y-Bias interactions to create optimal and minimal gravitational field effects in space. This function operates to change the co-ordinates of these interactions over time as the complexity of such structures evolves. As Y-Bias and Angularity Theory predicts, the masses have nothing to do but roll down to the areas of maximum Y-Bias/Angularity effect in order to find stasis in stable orbits.

Fibonacci Relationships

The Fibonacci numbers have been known since ancient times. These are not random numbers but, rather, are members of the following sequence:

0 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 etc.

This sequence is known as the Fibonacci Series, and is well known in mathematics. Each number is the sum of the previous two. The ratio of successive pairs tends to the so-called golden section (GS) = 1.618033989, whose reciprocal is 0.618033989, so that we have a resultant product mathematically defined as:

1/GS = 1 + GS F.8

The following diagram represents the range of values from N = 0 to N = 1000, including the F numbers 377, 610 and 987, rescaled by dividing the vertical values by N, to show the multiple harmonics of the ‘Golden Mean’ more clearly. These are shown by blue horizontal lines. The short blue lines mark the two golden section (GS) points in each segment. If the length of a long blue line is taken as 1, then the three segments have lengths GS2, GS3 and GS respectively. GS2 and a GS3 add to GS.

In a vertically integrated view, the plot of these functions appears as follows:

Figure 9

The values represented by the resultant function are –

GS = 0.618033989

GS2 = 0.3819659

GS3 = 0.2360678

The bar-graph diagram derived from the same number set and values is rather like a one-dimensional fractal. Each element contains all the information contained in the entire expression, regardless of the smallness or largeness of the scale.

Figure 10

When plotted as an X-Y graph, the X-axis spiral intersects the Y-Bias at the values shown as 1 2 5 13 [etc.] on the positive axis, and 0 1 3 8 etc on the negative axis. The oscillatory part crosses at 0 1 1 2 3 5 8 13 [etc.] on the positive axis. The resulting curve is the analogue of SOC structures found at virtually all scales, the magnitude and strength of which vary as a function of the extent to which the intersections approach the optimal angulature defined by the Fibonacci Series. This is not surprising, since the spiral of the curve demonstrates its logarithmic nature as it expands.

Figure 11

The form and shape of this plot is precisely what Prigogine/Stenger’s Dissipative Structures, Bak’s SOC rules and Y-Bias/Angularity Theory describe. The fact that the relationships and attributes demonstrated across the scales of the cosmos demonstrate adherence to this same set of simple, elegant rules, suggests that our view of ‘How Nature Works’ must be substantially modified if we are to really understand its mysteries.

Dark Matter

If this assessment is correct, current notions about gravitational field effects which have occasioned the search for all the ‘dark matter’ and ‘dark energy’ thought to be missing in the cosmos must be obviated. In the alternative, Y-Bias and Angularity Theory suggests that the matter you see is the matter you get. There is, in all likelihood, no such thing as Dark Matter or Dark Energy. What is needed, instead of a feckless search for something that is not there, which is little more than a desperate attempt to defend a set of questionable conclusions drawn from a severely crippled model, is to develop a wholesale modification of the assumptions which have heretofore been used to describe gravitational field effects in the first instance.

Astronomers are finally tracking down the whereabouts of most of the baryonic (‘normal’) matter that is postulated to have been created in the Big Bang but doesn’t show up as stars or gas in the galaxies. The Chandra X-ray Observatory has discovered two huge intergalactic clouds of diffuse hot gas: They are the best evidence yet that a vast cosmic web of hot gas contains the long-sought Dark Matter – about half of the atoms and ions in the universe. Computer simulations of the formation of galaxies and galaxy clusters had indicated for some time that the missing baryons might be contained in an extremely diffuse web-like system of gas clouds from which galaxies and clusters of galaxies formed.

These clouds have defied detection because of their predicted temperature range of a few hundred thousand to a million degrees Celsius, and their extremely low density. Evidence for this warm-to-hot intergalactic matter (WHIM) had been detected around our Galaxy, or in the Local Group of galaxies, but the lack of definitive evidence for WHIM outside our immediate cosmic neighborhood made any estimates of the universal mass-density of baryons unreliable. The discovery of much more distant clouds came when Chandra took advantage of the historic X-ray brightening of the quasar-like galaxy Mkn 421 that began in October of 2002. Two Chandra observations of Mkn 421 in October 2002 and July 2003, yielded excellent quality X-ray spectral data.

These data showed that two separate clouds of hot gas at distances from Earth of 150 and 370 million light years were absorbing X-rays from Mkn 421. The X-ray data show that ions of carbon, nitrogen, oxygen, and neon are present, and that the temperatures of the clouds are about 1 million degrees Celsius. Combining these data with observations at ultraviolet wavelengths made it possible to estimate the thickness (about 2 million light years) and mass density of the clouds. Assuming these clouds are representative of a universally dispersed phenomenon, the first reliable estimate of average mass density of baryons in such clouds throughout the universe was then possible: It is consistent with the mass density of the missing baryons.[[iv]]

Secondly, and by extension, when examined in terms of an interactive harmonic resonance operating between two masses, whose constituent building blocks are comprised of time and spin-polarized energy ensembles, the resultant force vectors described by Whittaker’s formulations must also apply. This means, by extension, that gravitational forces operate in precisely the same manner between masses as two intersecting beams of laser light [e.g., time-energized photons demonstrating standing wave attributes], which exchange information across the interference fringe [Hait’s Y-Bias/Angularity as a function of [Z D Z2 + C]] to create patterns of resonance and dissonance at the point of intersection in a hologram. The prime operator in this interaction is the fractal function ‘Z’, as used by Plotnikov and Bak.

Einstein’s Vector Magnetic Potential

Perhaps the final and most widely accepted authority on the matter should be allowed to inform this dialogue. Einstein posited that only the vector magnetic potential has a physical reality in electrodynamics. He believed [and his work amply demonstrates] that electric and magnetic fields are merely concepts we have developed to explain the reciprocity of field interactions. Most modern physicists still do not accept Einstein’s assertion, despite the fact that more recent experimental research [e.g., the Aharonov-Bohm experiment] shows that the A field [the N2L2 non-local/non-linear field described by Kafatos and Bohm, as demonstrated by Gisin] is quite real. Their seminal experiment shows that the A field can alter the quantum wave function [even] when all other EM effects have been completely shielded out.[[v]]

Figure 12

Schematic Diagram of the Bohm-Aharonov experimental protocol.

In classical mechanics, the motion of a charged particle is not affected by the presence of magnetic fields in regions from which the particle is excluded. The motion of classical particles emitted by the source S is not affected by the magnetic field B because the particles cannot enter the region of space where the magnetic field is present. For a quantum charged particle there can be an observable phase shift in the interference pattern recorded at the detector D. This phase shift results from the fact that although the magnetic field is zero in the space accessible to the particle, the associated vector potential is not. The phase shift depends on the flux enclosed by the two alternative sets of paths a and b. But the overall envelope of the diffraction pattern is not displaced, indicating that no classical magnetic force acts on the particles. The Aharonov-Bohm effect demonstrates that it is the electromagnetic potentials, rather than the electric and magnetic fields, which are [as Einstein correctly intuited] the fundamental quantities in quantum dynamics. [[vi]]

E. T. WHITTAKER – On the Differential Equations of Physics

In the famous paper published by Physics Letters in 1903-04, E.T. Whittaker provided a mathematical proof which demonstrates that gravitational field forces are not only ‘undulatory’ [which we interpret in a semantic context to mean harmonic and interactively resonant], but are also the result of field force interactions occurring between masses in the Y axis. The following summary taken from Whittaker’s work suggests that the Y-Bias model is perfectly on target in this regard.

Equation 5 – Gravitation and Electrostatic Attraction explained as modes of Wave-disturbance.

The result of [formula 1], namely that any solution of the equation([3])

*2V + *2V + *2V = k2 *2V F.9

*2×2 *2y2 *2z2 *2t2

can be analysed into simple plane waves, throws a new light on the nature of those forces, such as gravitation and electrostatic attraction, which vary as the inverse square of the distance. For if a system of forces of this character be considered, their potential (or their component in any given direction) satisfies the equation on the differential equations of physics. ([4])

*2V + *2V + *2V = 0 F.10

*2×2 *2y2 *2z2

and therefore a` fortiori it satisfies the equation

*2V + *2V + *2V = k2 *2V F.11

*2×2 *2y2 *2z2 *2t2

where k is any constant. It follows from [1] that this potential (or force-component) can be analysed into simple plane waves in various directions, each wave being propagated with constant velocity. These waves interfere with each other in such a way that, when the action has once been set up, the disturbance at any point does not vary with the time, and depends only on the coordinates (x, y, z) of the point.

It is not difficult to construct, synthetically, systems of coexistent simple waves, having the property that the total disturbance at any point (due to the sum of all the waves) varies from point to point, but does not vary with the time. A simple example of such a system is found in the following.([5])

Suppose that a particle is emitting spherical waves, such that the disturbance at a distance r from the origin, at time t, due to those waves whose wave-length lies between 2p/m and 2p/m+dm, , is represented by 2p and 2p, m

m+dm

is therefore represented by

2dm sin(mVt – mr) F.12

pm r

where V is the velocity of propagation of the waves. Then after the waves have reached the point r, so that (Vt – r) is positive, the total disturbance at the point (due to the sum of all the waves) is

*

*0 2dm sin(mVt – mr) . F.13

pm r

Take mVt – mr = y, where y is a new variable. Then this disturbance is

*

2 *0 sin y (dy) F.14

pr y

or, since

*

*0 sin y (dy) = p F.15

y 2

it is

1 F.16

r

Therefore, the total disturbance at any point, due to this system of waves, is independent of the time, and is everywhere proportional to the gravitational potential due to the particle at the point.

It is clear from the foregoing that the field of force due to a gravitating body can be analysed, by a “spectrum analysis” as it were, into an infinite number of constituent fields; and although the whole field of force does not vary with the time, yet each of the constituent fields is of an undulatory character, consisting of a simple wave-disturbance propagated with uniform velocity. This analysis of the field into constituent fields can most easily be accomplished by analysing the potential 1/r of each attracting particle into terms of the type

sin (mVt – mr) F.17

r

as in the example already given. To each of these terms will correspond one of the constituent fields. In each of these constituent fields the potential will be constant along each wave-front, and consequently the gravitational force in each constituent field will be perpendicular to the wave-front, i.e. the waves will be longitudinal.

But these results assimilate the propagation of gravity to that of light: for the undulatory phenomena just described, in which the varying vector is a gravitational force perpendicular to the wave-front, may be compared with the undulatory phenomena made familiar by the electromagnetic theory of light, in which the varying vectors consist of electric and magnetic forces parallel to the wave-front. The waves are in other respects exactly similar, and it seems probable that an identical property of the medium ensures their transmission through space.

This undulatory theory of gravity would require that gravity should be propagated with a finite velocity, which however need not be the same as that of light, and may be enormously greater.

Of course, this investigation does not explain the cause of gravity; all that is done is to show that in order to account for the propagation across space of forces which vary as the inverse square of the distance, we have only to suppose that the medium is capable of transmitting, with a definite though large velocity, simple periodic undulatory disturbances, similar to those whose propagation by the medium constitutes, according to the electromagnetic theory, the transmission of light.

A New Gravitational Formulation

Therefore, as Whittaker conclusively demonstrates, gravitational field effects arising from Mass interactions are rigorously shown to conform to SOC-mandated 1/ƒ quantum thresholds operating in harmonic resonance between masses, in a way which corresponds to Mandelbrot’s fractal formula, as driven by the Fibonacci Series. The interaction between the masses operates as a self-referential live feedback loop between them, which is optimized as a function of the Y-Bias and Angularity values they exert on each other. Notwithstanding the commonly invoked arguments which suggest that this notion is invalidated by the aggregate values seen at larger scales [called ‘granularity’] [[vii]], it is nevertheless logical to suggest, therefore, that gravitational effects are a derivative expression of the Y-Bias/Angularity values exchanged between masses which exhibit properties referred to in the literature as ‘harmonic resonance’. The resultant effect is demonstrated across the scales of the cosmos as an analogue of the Fibonacci series.

The structure of M51, The Whirlpool Nebula, illustrates how Whittaker’s formulation actually appears in the heavens. The underlying set of interactive dynamics he described in 1903 operate across hundreds of thousands of light years to produce a typical self-organizing pattern of effects.

Figure 8

Whirlpool Nebula [Hubble/NASA]

M51 (also known as Arp~85 and VV~1) comprises the large spiral galaxy NGC5194 and its smaller, barred and more amorphous companion NGC5195. M51 was the first astronomical object in which spiral structure was discerned, discovered by the Third Earl of Rosse in 1845. The spiral arms are perhaps the most perfect `textbook’ example in any nearby galaxy of Y-Bias/Angularity SOC dynamics as expressed by the Whittaker and Plotnikov formulations. This archetypal architecture is found at all scales above the Quaternary Scale and is a clear example of the observable effects attributable to the harmonic resonance function [Z D Z2 + C] found in the Y-Bias derivative of Plotnikov’s formulation of gravitational effects.[[viii]]

Precessing Gyroscopes

The acid test of this conclusion can be established by investigating the extent to which gravitational field effects can be mitigated in any region or locale by deliberately varying the Y-Bias and Angularity values which operate between the masses. For example, consider the widely reported experimental results which demonstrate inertial mass reduction in the case of a free-falling gyroscope which is precessed at an optimal angle. Widely published experimental results reveal that gravitational force is not mitigated in free-fall by a stable, non-precessing gyroscope. However, so long as precession is present, gravitational field effects are rigorously shown to be diminished. Sir Eric Laithwaite, inventor of the Magnetic Levitation technologies currently in widespread use in Germany and Japan, understood this principle. His work is both illustrative and compelling.[[ix]]

According to Euler’s equations, the composite force vectors in the Y and Z axes are perpendicular to the X axis of the rotor’s rotation. The inertial value of the vertical component [ + on the Y axis] is always exactly identical to the downward force of gravity [minus on the Y axis] due to the weight of the gyroscope in the Earth’s gravity, which keeps it from falling. The forward component is the precession-causing component.

The following set of relationships is proposed to describe this interaction:

F.18

forward component gravitationally caused downward moment M ([6])

_________________ = _____________________________________ = ________

upward component angular momentum of gyroscope I * omega

Again, experimental evidence bears this out. According to Y-Bias Theory, gravitational field effects are locally mitigated as a function of and in proportion to the Y-Bias angle exerted by the gyroscope on the inertial plane created by its angular momentum. This effect is the product of an interruption of the harmonic resonance which operates between the meta-dynamic system represented by the gyroscope and the planet. Because the interaction between masses operates in conformity with the fractally-deterministic SOC dynamics, the precession of the gyroscope exerts a perturbation on the Y-Bias which results in a discontinuity in the standing wave coherence between them. The effect of this interaction is to diminish the gravitational field effect, which is measured in terms of latency in the acceleration rate, demonstrated as reduced acceleration by the falling gyroscope.

As Laithwaite demonstrated, a precessing gyroscope can move appreciable mass through space. In his writings, he says

‘The spinning top showed us that all the time, but we couldn’t see it. If the gyroscope does not produce the full amount of centrifugal force on its pivot in the centre then indeed you have produced mass transfer.’

‘It became more exciting than ever now because I could explain the unexplainable. Gyroscopes became absolutely in accordance with Newton’s laws. We were now not challenging any sacred laws at all. We were sticking strictly to the rules that everyone would approve of, but getting the same result — a force through space without a rocket.'[[x]]

Laithwaite demonstrated that as the angular momentum of the gyroscope diminishes below the 1/ƒ threshold point, this variable becomes so low as to require an extremely high precession rate to maintain this relationship. At that point, the rotational energy exhibited by the gyroscope is no longer capable of counteracting the force of gravity, and the gyroscope suddenly falls. Notice that the experimental results show that the gyroscope does not fall at a greater gradual velocity as its angular momentum dissipates. Rather, as the angular momentum falls below the 1/ƒ threshold, the gyroscope falls at a velocity which is fully accelerated by the gravitational field. This is consistent with the SOC-mandated behavior referred to in the literature as ‘Punctuated Equilibrium,’ which is always in compliance with the 1/ƒ quantum threshold requirements.

A rigorously conducted experimental verification of this interaction between masses suggests, among other things, that inertia, as a measure of the relative values resulting from the interaction between two masses, can be deliberately mitigated by the application of a suitably engineered device which employs Y-Bias and Angularity vectors to interdict the harmonic resonances [i.e., gravitational field effects] which operate between them. This is a profound insight because if it is correct, it suggests that anti-gravitational effects can be deliberately engineered in the context of Y-Bias and Angularity dynamics.

Inertial Mass Reduction: Electro-Gravitic Devices

It has long been held that gravitational field effects cannot be mitigated because the phenomenon known as Gravity is a primary field effect. The fact that gravitational field effects can be consistently, repeatedly mitigated in a defined locale by exercising more than a dozen experimentally validated protocols, suggests that something is fundamentally amiss with the Standard Model. Such effects are specifically prohibited by the model and not accepted for publication in mainstream scientific journals, despite the fact that in the United States, the DOD has been employing electro-gravitic effects to enhance the flight performance of the B-2 Stealth Bomber for more than a decade.

Nevertheless, the phenomenon of locally mitigated gravitational field effects is now so ubiquitously recognized [even if unofficially] in mainstream scientific circles that it is time for science as a community to supply a cogent model which both explains what gravitational field effects are and demonstrates how they work. With such a model in hand, it will then become possible to not only understand how gravitational field effects operate, but to design-engineer applications which act to exert correctly structured Y-Bias vectors, at optimal angles, to produce the anti-gravitational or hyper-gravitational effects. In order to accomplish this, we must first understand what Mass is.

_____

[1] The Plotnikov formula of gravitational effects contains three expressions which are of interest here. The first, which is preceded by the expression [C(X,Y)] means that the interaction between the two masses X and Y, operate instantaneously. The second, the letter Z, connotes an angle of incidence between the field effects exerted by the masses X and Y on each other. The third, shown as [M1*M2*1/R2] suggests that the strength of the interaction between the masses decreases by a value expressed as the square of the radius which separates them.

[2] F.7: In this formula, the field strength exerted by two rotating planets on each other is expressed in terms of their relative rate of spin, which is referred to in physics as their angular momentum. The expression Z occurs again, as an expression of the way in which the gravitational field effects are effected by the angle of incidence between the two masses.

[3] This equation identifies four dimensional constructs, which are identified in terms of the X axis, Y axis, Z axis and t, time. It says that the sum of the square of the first three dimensions, expressed as a function of their relative wavefront velocities, is equal to the wavefront velocity of time, when time is multiplied by some constant K.

[4] This derivative substitutes zero for the equivalent function of the differential integral represented by the right hand set of values. What this implies is that the interaction of the three physical dimensions when viewed as interactions between masses occurs in zero time, or instantaneously.

[5] The formulas which follow contain a number of discrete elements which are expressions of the various properties of the waves which are being propagated between two masses. Whittaker’s formula is intended to portray in mathematical terms “…the total disturbance at any point (due to the sum of all the waves) varies from point to point, but does not vary with the time.” The use of the differential integral symbol [∫] suggests that the range of interactions extends from 0 to Infinity [*], suggesting in turn that while the velocity [V] of the waves extends across this range, the value for time [t] does not vary. This provides the basis for describing simultaneous, interactive wave propagation which is both infinite in expanse, instantaneous at all distances, and which ‘undulates’ to create addresses along the intersecting points where the wave interact, amplify and nullify each other as a function of their interference patterns.

[6] For the purpose of clarity and simplicity, we have substituted the linguistic description of the dynamics of gyroscopic precession for the more complex differential expressions. For mathematicians and scientists, these formulas are ubiquitously available. For non-scientists, the point to be made by this section is that a precessing gyroscope provides us with a way to examine and analyze all the dynamics associated with gravitational effects in a small, controlled, easily observable phenomenon.

_____

[i] The Pauli exclusion principle is a quantum mechanical <www.eurofreehost.com/qu/Quantum_mechanics.html> principle which states that no two identical <www.eurofreehost.com/id/Identical_particles.html> Fermions <www.eurofreehost.com/fe/Fermion.html> may occupy the same quantum state. Formulated by Wolfgang Pauli <www.eurofreehost.com/wo/Wolfgang_Ernst_Pauli.html> in 1925 <www.eurofreehost.com/19/1925.html> , it is also referred to as the “exclusion principle” or “Pauli principle.”

The Pauli principle only applies to Fermions, particles which form antisymmetric quantum states and have half-integer spin <www.eurofreehost.com/sp/Spin_(physics).html> . Fermions include Protons <www.eurofreehost.com/pr/Proton.html> , Neutrons <www.eurofreehost.com/ne/Neutron.html> , and Electrons <www.eurofreehost.com/el/Electron.html> , the three types of elementary particles which constitute ordinary matter <www.eurofreehost.com/ma/Matter.html> . The Pauli exclusion principle governs many of the distinctive characteristics of matter. Particles like the photon <www.eurofreehost.com/ph/Photon.html> and graviton <www.eurofreehost.com/gr/Graviton.html> do not obey the Pauli exclusion principle, because they are bosons <www.eurofreehost.com/bo/Boson.html> (i.e. they form symmetric quantum states and have integer spin) rather than Fermions.

[ii] Santilli, R., Il Grande Grido – A Cry in the Wildnerness, Ref.

[iii] Anastasovski, Ref

[iv] www.astro.uni-bonn.de/~dfischer/mirror/286.html

[v] www.enterprisemission.com/moon6.htm

[vi] rugth30.phys.rug.nl/quantummechanics/ab.htm

[vii] Jagnow, A., ref [gary vesperman]

[viii] www.noao.edu/image_gallery/html/im0063.html

[ix] Laithwaite, E., www.alternativescience.com/eric-laithwaite.htm

[x] Laithwaite, ibid.