Phases of the Anu Building Block

146.1 Phases of the Anu Building Block
Date: 05/02/04

My comments and excerpts in Bold.

Precession Phase Theory
of the Anu Building Block

While studying about phase, I had collected an animation of a line of spheres precessing in a phased array. Then I found a source document that explored atomic phase and wave analysis. I began to see that the text may as well have been describing the precession of the line of spheres, even without mentioning them. So I began comparing them myself. Here's an excerpt about the simple sinewave of Fig. 2-2, of the source document below, with its description:

"Our wave system allows the four-dimensional equivalent of 3-D plane waves; we'll call these hyperplane waves. (We can refer to such a geometric entity as a 3-D "space, like our "reference space, or a 4-D hyperplane, when we want to emphasize the analogy to a 3-D plane.) Two sets of hyperplane waves are depicted in Fig. 2-2."

The hyperplane waveform, of the source document, represents a partial oscillation of positive peak/negative peak/positive peak. I'm comparing the simple hyperplane wave of the source document and we are converting this hyperplane wave to a two octave, precessing Anu wave, below.

These Anu tori just precess,
spin and breaths in and out,
they don't move from their position,
due to the close-packing of Anu.
These are not particles, spheres or visible.
It is space and it does what space does. ¹

Sphere Animation Precession of space in 34 easy steps.
Since a picture is worth about 1000 words, here's 2,000 words worth:

plus

34 Anu Tori

This stylized, 34 tori depiction of the fabric of space, represents the real, but invisible entities, called Anu/anima/UPA-ultimate physical atom/superstring, that not only precess but "spin". ² The line of Anu tori, in reality, should follow a spiral path according to the laws of close-packing of spheres. Upon each surface of each 4th-0th dimension, electrostatic, spatial-point Anu tori, spirals 1st dimension magnetic lines from pole to pole and through its own center with 2nd dimension electricity spiraling around each magnetic line, repeating to at least 7 more levels. Gravity appears when 12+1-empty-center Anu tori aggregate, and can be considered either 4th dimensional or the 0th dimension again, depending upon how we count dimensions 1,2,3 and 4 or 0,1,2 and 3. Every geometric "solid" known, is constructed by connecting the centers of aggregates of these close-packed Anu tori. Every waveform known is a result of the precession and spin of aggregates of these Anu tori, including sine waves that thread through the n/s poles, of lines of Anu tori, which sine waves use each successive Anu like the signal boosting repeaters on a phone line. Every 4D scalar calculation known is derived from the in/out, expansion/compression of these overlapping, "breathing" Anu tori.

From left to right (total 18), sphere 1 is replicated in sphere 9, which is exactly 180 degrees opposite, in phase, to sphere 1 and 17. If sphere 1 is (+) then sphere 9 is (-) and sphere 17 is (+). This is more than an octave in music and is a full cycle shift from (+) to (+), but in reality, it is only half of a full rotation or dimension. The full, two cycles or intrinsic spin plus angular momentum spin, requires 34 spheres (17x2), in this scheme. Perhaps atomics is arranged as two octaves of 7, 8, 9 or 12 notes but here we are using the 9 position enneagram which has an interesting history. ⁴

You might also ask.....If sphere 1 is (+) and sphere 9 is (-) and sphere 17 is (+)......then what roles do all the other sphere's play? Do they just take up space as placeholders? The answer is this.....Any other sphere can also be the first (+) or (-) sphere and that sphere has its own opposite phase sphere, 9 spheres down the line and its own similar phase sphere, 17 spheres down the line, however, these second 3 will be precession-phase-shifted from the original, first 3, and the 2 groups cannot "see" each other, even if the 2 groups are right next to each other. It's like both are in a different frame, or world. Therefore, depending upon how many spheres (dimensions) really exist in the line, we can only "see" the frequency and spin-plane of 3 of them. The rest of universe is totally invisible to us because of these phase shifts.

Also from left to right, these 34 spheres do not show the unique alternating rotation and tilt, that keeps any two Anu attractive (+/-) or repulsive (+/+), (-/-) to its adjoining neighbor Anu. If two neighbors spin the exact same way, they grate and push the other away, as in (+/+), (-/-). If two neighbors spin the exact opposite way, they attract each other like two gears meshing (+/-)....strange and backward, but true.

(+/-) is simply opposite phase and charged particles (+/-) probably don't exist. In other words, in this theory, charge means phase, not so-called "charged particles". When we see "(+) protons" within a strong, spiral field of "(-) electrons" we should be looking at a 1/4 shift in a wave, by 90 degrees (1/4 x 8 = 2 rotations). In other words, divide 720 (two cycles) by 8 (8-90 degree quadrants).

Analysis of the Source Document

This analysis simply highlights all narrative of this PDF Document that applies to the Anu precession and spin, with added, necessary comments in bold type. The Anu is the basic building block of universe at scale 10^28 or smaller.
Ben Kristoffen's theory has doubts about what takes place in the "cores" of his waveforms but The Anu Building Block Theory ³ can explain the "core", with understanding that the Anu is the source of de Broglie waves (7x10^-24 meter) and biologic process. Non-linear "flow" waves are interpreted as Bearden/Tesla longitudinal sound waves of space, repeating in "one dimension" called phi, or spiraling space, the seat of phi-gravity, that golden ratio condition that allows phi-space to implode into its spiral F#/Bb dual centers and also to expand space from its "core" F#/Bb dual centers.
Ben uses "phase velocity" as limited by light velocity whereas in other papers it means superluminal velocity. Ben treats "time as an additional, unidirectional parameter" and I say universe really has no "time" at all because of universe's atomic "core" renewal velocity, which is almost instant, due to de Broglie wavelengths and the communicative abilities of the 10^28 scale Anu tori associated with bio-logic process.
Additionally, I regarded J.W.Keely's ¹⁶ comment that "time is gravity" and that the mysterious 4th dimension is our mysterious 0th dimension, again, after cycling through 1,2,3 and 4...or 0,1,2 and 3 dimensions, by whichever numbering system suits you. The conditions of no-time or space of the 4th and 0th dimensions are just as mysterious as gravity, so my conclusion has been that mysterious gravity is the same as the mysterious 4th or 0th dimension of time.lessness and space.lessness, after eliminating all other forces and dimensions, and in this context, universe has two kinds of gravity....an inward earth-center seeking gravity and a large-scale space expanding gravity, both gravities also having almost instant renewal velocities, because both gravities are simply "what space does".
And any system will be subject to relativistic shiftings. Ben's self-organizing "wavicles" which he calls "particles", are not particles at all. They are simply the result of total wave compression of phi-space. If the structure of space were to disappear, these "particles" would also disappear, instantly

There was no "Big Bang" and Ben's large-scale space-time curvature of 60 magnitudes greater than observed is also substantiated as the almost imperceptable-flat curve of the largest universal curve of space, itself, called The Toroidal Universe ⁵ In contrast to Ben's dilemma that universe's age is less than the oldest star age, my theory, 53 Evolution and Creation, ⁶ shows the universe's age to be far, far older than modern estimates of a mere 13.7 billion yrs.

A New View of Universe by Ben Kristoffen (PDF) ³ c/o K. Krogh,
Neuroscience Research Institute
University of California,
Santa Barbara, CA 93106
e-mail: krogh@psych.ucsb.edu

Abstract

A new, very different physical model of the universe is proposed. Its virtues include unifying relativity and quantum mechanics, and particles with de Broglie waves. It also appears to provide a truly unified physical basis for electromagnetic, gravitational and nuclear forces. The basic system is a four-dimensional Euclidian space, containing an array of nonlinear "flow" waves. These repeat in one dimension, called "phi". As in Newtonian mechanics, time is treated as an additional, unidirectional parameter describing the evolution of the system. Nevertheless, this wave system is shown be inherently relativistic. Further self-organizing patterns arise within the overall wave structure. Called "wavicles", these have intrinsic quantized fields, "spin", and rest energy, and represent elementary particles. Relativistic expressions are derived for particle behavior in scalar, vector and gravitational potentials. Proper representations of these potentials, based on the wave fields and associated flows of wavicles, are also obtained. As in the causal quantum mechanics of de Broglie and Bohm, wavicles exist continuously and follow definite, stochastic trajectories. Although experimentally equivalent to Einstein's special relativity, this theory differs fundamentally from his general relativity and the associated Big Bang model. According to Linde, the latter predict a large-scale space-time curvature roughly 60 orders of magnitude greater than observed values. Here a flat large-scale geometry is predicted, in agreement with the observed distribution of galaxies. This theory is also consistent with recent observations pertaining to the age of the universe.

Contents

1. Introduction 3 Nonlinear Waves. Wraparound Trapping. Coherent Structures. 2. A New Wave System 14 The Geometric Framework. The Wave Medium. Pro-particles and de Broglie Waves 3. Special Relativity 21 Moving Mirrors. Moving Mirrors in 4-D. Relativistic Velocity Transformation. 4. Flows and the Scalar Potential 42 5. Flow Waves and the Vector Potential 49 Wave Frequencies. Pro-particle and Particle Velocities. 6. Wavicles 65 Moiré Wavefronts. 4-D Wavefront Transformations. Flow Wave Effects and the Wavicle Core. 7. Future Additions 81 Quantum Mechanics. Gravitation and Cosmology. Nuclear Forces and Sub-particles. Computer Modeling. 8. The Course of Physics 89 Acknowledgments. References.

Section: 1. Introduction p3 Contents

Chapter: Nonlinear Waves.

"Unlike the waves of standard quantum mechanics, the waves in this theory are nonlinear. Involved is a nonlinear effect, common in nature, whose importance is not widely appreciated. The waves are also highly organized, in what is sometimes called a coherent structure. Within this overall structure, additional self-organizing wave patterns arise: these correspond to both particles and their fields."

What causes nonlinearity in waves? The obvious answer is: nonlinearity in the wave media. However, even with a perfectly linear medium (if there were such) nonlinearity can still arise. Nonlinearity in waves has a second cause, equally as important as the characteristics of the medium: the waves themselves.

Ben sites a few slight untruths about waves:

...each particle of water itself merely oscillates about an equilibrium point . . . This is a general feature of waves: waves can move over large distances, but the medium itself has only limited movement . . . A wave consists of oscillations that move without carrying matter with them. - Douglas C. Giancoli Physics, 3rd Ed., 1991

Waves transport energy, but not matter, from one region to another. [Original italics.] - Hugh D. Young University Physics, 8th Ed., 1992

...here we see an essential feature of what is called wave motion. A condition of some kind is transmitted from one place to another by means of a medium, but the medium itself is not transported. - A. P. French Vibrations and Waves, M.I.T. Introductory Physics Series

By the time they reach graduate school, most continuing physics students probably learn that this picture of waves is wrong. However, although it becomes apparent in more advanced texts, the error of this wave picture is seldom pointed out explicitly.

* Real waves can transport their media.

Now we understand waves...or do we...there are far more kinds of waves.

Where the present theory is concerned, an important feature of flow waves is that, even in a "linear" medium, they do not superpose like linear waves. When interacting, in addition to displacing each other, flow waves can also refract and reflect one another.

In addition to its presence in many nonlinear wave phenomena, flow is also found at the heart of a great many chaotic systems. Some well-known examples are Edward Lorenz's air convection model, or the Lorenzian waterwheel (also known as the "turbulent fountain"), dripping water faucets, Taylor vortices, meandering rivers, the Brusselator (a chemical reactor with flowing reactants), piling streams of sand, stirred paint, and Jupiter's Great Red Spot.

Chapter: Wraparound Trapping.

It's not always so apparent where the phase of a coherent structure comes from. Starting with a large flat area of sand and a steady wind, sand ripples are observed to form. The question arises: how do they decide where to form initially? The answer must be that, while it may be unobservable, at some finer level, there is always some pre-existing structure with a predominant spatial phase.

Here's a clue: ..."a cloud of dust being affected by a repeated non-linear force will separate into rings with orbital periods which match the harmonics of the forcing period." R.Tomes ⁷

I'm glad he said the answer must be due to some unobservable, pre-existing structure with a predominant spatial phase.....this is exactly what the Anu tori is....logarithmic (musical), phase-space.

Chapter: Coherent Structures.

This finishes the informal introduction to nonlinear wave phenomena and coherent structures. Where the present theory is concerned, some relevant points are these:

Flow is an essential element of many self-organizing, chaotic nonlinear systems.
Commonly, waves transport their media, i.e., cause them to flow.
Flow waves are inherently nonlinear, regardless of the medium in which they are found.
Flow waves can refract and reflect each other.
It's not unusual for nonlinear wave systems to organize themselves into repetitive structures.
Repetitive wave structures may exhibit quantum mechanical behaviors.

Precession and spin relationships between any two Anu tori creates flow of information but the medium, the Anu, do not move from their place.

Section: 2. A New Wave System p14 Contents

Now I'd like to introduce a new kind of nonlinear wave system...Here we'll be using a higher-order Euclidian alternative to the non-Euclidian geometry of Einstein and Minkowski.

Chapter: The Geometric Framework.

The framework for this theory is a 4-dimensional Euclidian space and classical time. (So if time is counted as a dimension, this system has five.) We'll call the spatial dimensions x, y, z and (phi, phase symbol). Within this framework there is a repeating system of waves, redundant along the (phi symbol) dimension. Initially, we'll assume that the entire wave pattern repeats perfectly along in a sinusoidal fashion, with a spatial period which we'll call the structure interval or s. (In other words, at any given x, y, z location, along (phi, phase symbol) we would see a uniform sinusoidal variation in the wave amplitude with a spatial period s.)

Trinary Relativity has 2 time dimensions going in 2 opposite directions.

Fig. 2-1 shows a simple wavefront pattern in the x, (phi, phase symbol) plane. (In a more realistic case, the waves would form interference patterns, without such distinct fronts.) Dividing space into parallel regions of thickness s along the (phi, phase symbol) axis, you can see that any wave or wave component exiting one side of a region is matched by an identical wave entering from the opposite side. As in the one-dimensional wave system of Zabusky, Kruskal and Tappert, the waves in each periodic section are effectively trapped there by the wraparound effect, and the periodicity of the overall structure is conserved. (So, if you start with a system of repeating waves with period s, and the waves don't dissipate, any wave patterns which develop will always have this period.)

Trinary Relativity also accounts for waves exiting from one side of a region and is matched by an identical wave entering from the opposite side....an added parameter is the neutral wave in the middle which is what we can call, gravity.

Chapter: The Wave Medium.

The wave medium in this theory is an elastic fluid; consequently, its waves are acoustic (i.e. sound-like). Except for its four-dimensional aspect, in many other respects it resembles an ordinary fluid, such as air. For example, a box of air is inhomogeneous and chaotic at the scale of molecules, but relatively uniform at the macroscopic level. Similarly, the properties of this wave medium will be taken to vary at different scales. In its scale-dependant nature, this medium differs from the historical ether, which was generally considered "ideal."

I agree the wave medium should be an elastic fluid. Spinning Anu vortexes of space have to be fluid and elastic. They also must transmit longitudinal sound waves as Bearden and Tesla pointed out. The Anu medium is the Aether which is scale-invariant, meaning at any scale, we will see the very same spinning Anu.

There are several other differences: In theories such as Lorentz's "Theory of the Electron, the ether was assumed to be an elastic solid, to accommodate transverse electromagnetic waves. Of course it had one less spatial dimension. Also, the ether was generally taken to be distinct from ponderable matter, and extremely tenuous, so the latter could pass through it unimpeded. On the other hand, the wave medium in this theory is substantive. Further, elementary particles here are wave-based phenomena, where both they and their medium are constituted of essentially the same stuff. So I'd like to call this four-dimensional fluid wave medium simply "stuff".

The Anu vortexes can be considered as extremely tenuous and ethereal or substantive, it can bump into anything, even another Anu and never slows down. It has a form, yet it is totally a wave, spiraling. It cannot be divided because the whole universe is packed with them, so the Anu space can be considered as One and Undivided. And everything made is made of them so we should call it something other than just "stuff".

Like sound in air at a given temperature, the acoustic waves in stuff have a characteristic velocity -- in this case, the speed of light, c.

True. There are also super-luminal phase waves and waves that travel backwards in the Anu space.

Since such waves are essentially longitudinal, of course they can't represent light per se, although they travel at more or less the same speed. (How can electromagnetic waves be accounted for then? As we'll see later, in repetitive nonlinear wave structures, transverse secondary waves can arise. These are waves of interaction within the waves, or wave waves if you like!

That's logarithmic space. Waves upon larger waves upon larger waves, ad infinitum.

In this "4-D Wave Theory", acoustic waves are responsible not only for particles, but also their fields. Before describing how, I need to introduce various basic features of the wave system. However, to introduce this system, it seems that something resembling particles is needed. So, initially, I'd like to make use of a very incomplete particle model proposed by Schrödinger.

Chapter: Pro-particles and de Broglie Waves.

One of these Schrödinger "particles" can be seen as a point moving with a wave, along a normal (Schrödinger's ray) to the wavefront, keeping the same phase position on the wave. (As though it were somehow possible to mark a point on a wave itself, instead of marking the wave medium.) The trajectory or velocity vector of this wave-point corresponds then to a ray.

What is a pro-particle? I think it's a hypothetical point to facilitate Schrödinger mathematics.

In Fig. 2-1, the bold arrow at x ,0 depicts the 4-D velocity vector of a Schrödinger "particle" A in our new wave system. Notice that, from the repetitive nature of this system, we necessarily have identical "particles" and vectors at (phi, phase symbol) = s, (phi, phase symbol) = 2s, etc., shown here as dotted arrows. Also, between these are others, which, although differing in phase, have exactly the same velocity vector. Since all these "particles, a continuous line of them at a given x, y, z position, move together, we can treat them as a single unit. This is depicted by the line, A, in the figure, which parallels the (phi, phase symbol) axis.

Ben is extending the point to a line of points with different phase and the same velocity vectors. This is exactly what a line of Anu vortexes are.

We'll call these vertical, line-shaped ensembles "pro-particles, short for "provisional particles. (We'll be working with pro-particles until we get to the realistic particle mode l introduced in a later section.) While it corresponds to a line in four dimensions, a pro-particle appears as a single point in our 3-D reference space (having an associated phase value). Note that a pro-particle's position in the reference space is unchanged by its motion in the (phi, phase symbol) dimension. So, with waves moving parallel to the (phi, phase symbol) axis, the observed velocity of an associated pro-particle is zero. On the other hand, if the waves are moving almost perpendicularly to (phi, phase symbol), the pro-particle velocity seen in the reference space approaches its 4-D velocity, c.

So we learn that these vertical, line-shaped ensembles are called pro-particles...or as I call them....precessing Anu. We cant see what a point looks like but with my Anu tori, we can, since they are highly magnified 4D points.

Our wave system allows the four-dimensional equivalent of 3-D plane waves; we'll call these hyperplane waves. (We can refer to such a geometric entity as a 3-D "space, like our "reference space, or a 4-D hyperplane, when we want to emphasize the analogy to a 3-D plane.) Two sets of hyperplane waves are depicted in Fig. 2-2. Above are the wavefronts in the x, (phi, phase symbol) plane and below are the corresponding wave amplitudes seen in the reference space, (phi, phase symbol) = 0. Although the wavelengths are different, both sets of waves necessarily have the same spatial period, s, along the dimension. Arbitrary waveforms, including the curving wavefronts depicted in Fig. 2-1, can be constructed from multidimensional Fourier series' of sinusoidal hyperplane wave components such as these.

This is the Figure 2-2 referred to in the beginning.

Section: 3. Special Relativity p21 Contents

Having noted some appealing features of preferred frames, now we'll take up relativity in the context of our new wave system. As shown earlier, when this 4-D system is viewed from the perspective of a 3-D reference space, the waves associated with pro-particles resemble de Broglie waves. De Broglie based the equations for his waves on Einstein's relativity; consequently, they are inherently relativistic with respect to both space and time. The waves in this new system will be seen to behave in the same relativistic fashion. Also, we'll find that this automatically brings relativistic behavior to our provisional particles (as well as to the realistic particles introduced later).

Well...that's what you get by viewing a 4D system from 3D. You get de Broglie basing his equations upon relativity and preferred frames.

Recall that a pro-particle corresponds to a line in Euclidian 4-space, paralleling the (phi, phase symbol) axis, and represents points of varying phase on redundant waves. (Or a single point in our 3-D reference space.) The fronts of the associated waves all make the same angle with respect to the line of the pro-particle. And the points making up the 4-D pro-particle line all have the same velocity vector, so they move together. As we've seen, for a pro-particle to move in the 3-D reference space, its associated wavefronts must be tilted with respect to (phi, phase symbol) . Here we'll look at some hyperplane wavefronts and assume that they are tilted by some process which leaves the length of a given section of wavefront unchanged. (A mechanism which tilts waves in this fashion will be described later.) What effect would such tilting have on an arrangement of our pro-particles?

Let's make some analogies and replace pro-particle with "Anu": Ben's pro-particle (PP) is one Anu. A line of PP is many Anu. A PP or one "Anu" corresponds to a line in Euclidian 4-space, paralleling the (phi, phase symbol) axis, and represents points of varying phase on redundant waves. (Or a single point in our 3-D reference space.) The fronts of the associated waves all make the same angle with respect to the line of the "Anu". And the points making up the 4-D "Anu" line all have the same velocity vector, so they move together. For a "Anu" to move in the 3-D reference space, its associated wavefronts must be tilted with respect to (phi, phase symbol). Here we'll look at some hyperplane wavefronts and assume that they are tilted by some process which leaves the length of a given section of wavefront unchanged.......precession is a natural method of tilting.

Figs. 3-1(a) and (b) show a pair of pro-particles, A and B, associated with the same hyperplane waves. (As before, vectors on the right represent the pro-particle motions.) In (a) the wavefronts are perpendicular to (phi, phase symbol), and A and B are stationary in three dimensions. Fig. 3-1(b) shows the same wavefronts, tilted, with the pro-particles moving at velocity v. The length of wavefront separating A and B in four dimensions (invariant by our assumption) is d, while d is the apparent distance seen in the reference space, (phi, phase symbol) = 0.

This is relativity's torsion at light velocity, tipping mass from its dis.torsion.

Chapter: Moving Mirrors.

So far, no mechanism has been suggested for the wave transformations we've been exploring. Here, we'll take this mechanism to be reflection. In deriving the Lorentz transform above, two basic assumptions were made. The first was that our waves are tilted by some means which leaves the length of a hyperplane wavefront section unchanged. The second was that, somehow, pro-particles effectively measure time by the phases of their associated waves. Below, we'll see that these assumptions can be superseded by a single, more definitive one: that all our waves have been reflected at some point. To obtain our wave transformation, our basic approach will be to ask what would happen to these waves if the "mirrors" from which they reflected had had different velocities.

Wave transformation mechanism is reflection? Two assumptions: Our waves are tilted by some means which leaves the length of a hyperplane wavefront section unchanged. And..... somehow, pro-particles effectively measure time by the phases of their associated waves. Third assumption superseding: These assumptions can be superseded by a single, more definitive one: That all our waves have been reflected at some point.....all this business about mirrors is about intrinsic internal phase and its outer partner, angular momentum phase.

We'll see that, when the mirror velocity is changed, the reflected waves are transformed such that, within another relativistic frame, they have exactly the same configurations and states of motion that they otherwise would have had. In other words, the effect of this "moving mirror transform" is a complete Lorentz transformation.

Even when mirror velocity accelerates, the reflected waves in another frame is exactly the same configurations and states of motion.

What sort of "mirror" are we talking about? In keeping with the rest of this theory, the mirrors we will be considering here are themselves wave-based phenomena. While the physical reflection mechanism won't be addressed until a later chapter, the point here is this: Unlike "solid" objects, these wave-based mirrors can pass through the wave medium without having to push it out of the way. For example, suppose you had a sound-reflecting concrete wall moving through air; the induced airflow around the wall would influence the propagation of reflecting sound waves. Here, we won't be concerned with such an effect.

What is the mirror? It seems to be other wavefronts generated by the precessing Anu. And the Anu can transmit through the wave medium of space without pushing it out of the way, because they don't move through the medium. In the beginning, there was zero, and one zero: then the one divided to become two contrary Anu, precessing and producing wavefronts which created other vortexes of Anu space.

Since our wave system is redundant along, any wave-based mirror surface that may arise must have an overall orientation parallel to this axis. (That is, on a scale larger than the wave structure's period, s.) We'll also add the working assumption that our mirror surfaces are locally straight and continuous along. (This will be justified later, when the physical reflection mechanism is discussed.)

To begin, we need a reflection law for our moving mirrors. For a stationary mirror, there is the familiar law of reflection: the angle of reflection equals that of incidence, with angles measured with respect to a surface normal. This no longer holds when the mirror moves. Here we'll use Huygens' principle to find a more general law, while making some qualitative observations.

With common stationary mirroring the incoming angle of incidence always equals the outgoing angle of reflection.

Chapter: Moving Mirrors in 4-D.

Given that the mirror is a hyperplane, we can immediately address one of our earlier assumptions: that our waves are tilted by some means which leaves the length of a hyperplane wavefront section unchanged. When the moving mirror and wavefronts are both hyperplanes, the mirror/wavefront contact surface is a hyperplane also. In this case, the effective mirror is flat, of course, and reflection by a flat mirror doesn't change the length of a wavefront section.

*If both sides of this equation are divided by c, it also describes the relativistic reflection of light from a mirror moving in x. When this is done, v /c and v /c are the direction cosines x xr for incident and reflected light rays in, for example, the x-y plane. This equation is given in Einstein's 1905 "On the Electrodynamics of Moving Bodies". However, unlike Einstein, who derived it from a "principle" of relativity, here we've done so from a physical system, without assuming this principle.

Chapter: Relativistic Velocity Transformation.

From our pro-particle reflection equations, now we can derive those for the relativistic transformation of velocity. These are:

Omitted Formulae

where u is a velocity observed in some chosen "rest" frame, and u' is the corresponding velocity measured within a "moving" reference frame, with a relative velocity, v, in the x dimension. (While the previously derived Lorentz equations transform coordinates from a "rest" frame to a frame in relative motion, these equations go the opposite way. This form was chosen here because Eq. (3-57) is the familiar "addition of velocities" equation.)

Our approach will be to compare the final velocities of the same incident pro-particle after reflection by a fixed mirror and by a moving one. We'll see that the effect of mirror motion is to transform the reflected velocity according to Eqs. (3-57)-(3-59) above. The (invariant) velocity, u', will correspond to a fixed mirror, while the transformed velocity, u, will result from a moving one. Also, we'll see that the reference frame velocity, v, is a function of the mirror velocity, w.

To describe the reflection of a pro-particle by a fixed mirror, we can put a zero value for the mirror velocity, w, in Eqs. (3-54)-(3-56). In this case, of course the incident and reflected velocities are equal, except that the x component is reversed. So, calling this reflected velocity u', we can write...

Omitted Formulae

To describe the same incident pro-particle, reflected by a moving mirror, we can substitute these expressions into Eqs. (3-54)-(3-56). Calling the reflected velocity in this case u, we have...

Omitted Formulae

where u' is the (invariant) velocity of a pro-particle reflected by a fixed mirror, and u is that of the same incident pro-particle reflected by a mirror with velocity, w. If we put a zero value for u' in Eqs. (3-63)-(3-65), the resulting velocity, u, has no y or z components and is given entirely by Eq. (3-63). This reduces to...

Omitted Formulae

For a pro-particle which is stationary after "reflection" from a fixed mirror, this gives the velocity of the same incident pro-particle after reflection from a moving one. If the effect of mirror motion is a relativistic transformation of velocity, then this pro-particle should be stationary once again in some new relativistic frame. In other words, its velocity would correspond to that of this new frame. This gives...

Omitted Formulae

where v is the reference frame velocity corresponding to a given mirror velocity, w. (Notice the similarity to Eq. (3-57).) In the case of a pro-particle with an arbitrary value of u', the transformed velocity, u, should have a proper relativistic value in the reference frame specified by the last equation. If we can demonstrate this, it would establish that our moving mirror transform is relativistic for reflected pro-particles in general.

Here we've seen that, using Eq. (3-67) as the velocity of our moving reference frame, all of the relativistic velocity transform equations are obtained. Again, this shows that the 3-D velocity of any reflected pro-particle (not just an initially motionless one) is transformed to its proper value for this moving frame.

As noted previously, reflection from a moving hyperplane mirror tilts wavefronts without changing the 4-D wavefront length between pro-particles. Earlier, we found that, given this condition, we could derive the first three Lorentz equations for the transformation of space. From those equations, plus these just obtained for velocity, the last Lorentz transform equation, for time, can be derived. (This is just a reversal of the usual derivation of the velocity transform from that for space and time.) So, this "moving mirror" transform is a complete one.

Also, in our initial derivation of the Lorentz transform, we only considered pairs of pro-particles, with identical velocities, associated with the same hyperplane waves. As derived here, the transform applies to any ensemble of reflected pro-particles, having any combination of velocities. Thus, if everything were somehow made of such pro-particles, we'd have a relativistic system. Later, when we arrive at more realistic particles, we'll find that, since they exist within the same wave system, they inherit the basic relativistic behavior of these reflected pro-particles.

Section: 4. Flows and the Scalar Potential p42 Contents

So far, we've been treating the waves in this system as though they might be linear ones. However, as mentioned earlier, this theory is based on flow waves, and these are inherently nonlinear.

And so is space...nonlinear.

As a first step toward exploring their nonlinear interactions, here we'll look at interactions of steady flows and waves. In particular, we'll be examining flows directed along the dimension, and their effects on the motion of pro-particles. We'll see that these effects are identical to those of stationary scalar electric potentials on charged particles.

*Just as sound is reflected and refracted by a stream of moving air, so too are the waves in this system, when they encounter flows. In analyzing these effects, we'll use the approach taken for reflection by a moving mirror: First we'll use Huygens' principle to derive a law -- of refraction here -- then we'll apply it to the behavior of pro-particles. We'll be working in just two dimensions again, for simplicity, instead of the full 4-dimensional space.

Yet, reality is 4 dimensions.

Although our refraction equations are accurate, I'd like to mention that the physical picture on which they are based is somewhat oversimplified. Ribner has pointed out that a straight interface between two sharply divided flows is necessarily distorted by the pressures of impinging acoustic waves. Ribner treats the distorted interface as a "wavy wall. The ripples in the wall interact with the flows moving past it on either side and generate additional wave components. (In the context of our wave system, these ripples would have a period corresponding to the structure interval, s.) Of course the phase velocity of the ripples is the same as that of the incident waves which cause them. The result is that the additional components created have the same angles as the basic refracted and reflected waves described above.

I don't know what Ben means by "phase velocity" but elsewhere it means a superluminal velocity.

*Although the wave angles are no different with this effect, the predicted amplitudes change significantly. What's involved is the transfer of energy between the flows and waves. Thus the waves are nonlinear.

We've seen now that pro-particles can precisely model various features of particles having a single rest mass, m. Of course, in nature, not all particles have the same mass. Another apparent shortcoming of this particle model is that, as ray analogues, pro-particles can be partially refracted and reflected. Of course, when real particles, such as electrons, meet sharp changes in the scalar potential, they are either "refracted" or reflected; the whole particle goes one way or the other. Pro-particles are just a construct (wave markers) that we've used to describe some fundamental characteristics of the waves in this system. In a subsequent section, more complex wave-based entities will be introduced, which resemble real particles much more closely. However, because they exist within the same relativistic wave system, they may inherit much of the behavior of our provisional particles -- including their velocity behavior in (phi, phase symbol) flows. The realistic particle model assumes that flows are, in fact, the physical basis of the scalar electric potential.

If the flow of space is what is meant, then yes, space is the basis of scalar electric potential. Space is an electric plasma.

Section: 5. Flow Waves and the Vector Potential p49 Contents

In the last section, we found a correspondence between the behavior of pro-particles in stationary (phi, phase symbol) flows, and that of real charged particles in scalar potentials. Taking a similar approach, here we'll describe pro-particles entering moving (phi, phase symbol) flows. This will be compared to real particles entering moving scalar/vector potentials. In so doing, we'll introduce the vector potential, while further defining the nature of the scalar potential in this theory.

Now, moving flows...

A basis for moving (phi, phase symbol) flows is provided by another feature of our wave system: its flows are not steady ones, but are due to acoustic flow waves. (So, while flows influence the propagation of waves, these also consist of waves themselves.) We'll see that the lateral movement of (phi, phase symbol) flows is made possible by this underlying wave nature. To introduce acoustic flow waves, we'll begin by looking at the familiar example of sound waves in air.

We know that, despite the chaotic motion of air particles at the molecular level, at larger scales, sound wave behavior is given by the average motions of air particles. From this, we can infer that, if the scale of our flow waves is relatively minuscule, the refraction and reflection of larger-scale waves should be determined by only the average flow, U'. (Also, with very short-wavelength flow waves, we can neglect diffraction at the boundary.) So the figure just depicts the usual refracted and reflected of wavefronts resulting from such a flow. This illustrates a nonlinear wave effect which is independent of the wave medium. Instead, it depends entirely on a property of the waves themselves: their associated flow.

Notice that the downward flow, U', in Fig. 5-1 could be realized by either positive density waves (solid lines) traveling downward or waves of negative relative density (broken lines) traveling upward. To meet our assumption that the fluid medium has the same average density inside the flow wave region as outside, these must be a balanced combination of both types. (For example, if we had positive waves only, the net density in the flow wave region would be greater.) As with "ordinary" acoustic waves, here we have equal positive and negative density components. But in this case, they are moving oppositely.

Moving oppositely is a characteristic of certain ambidextrous musical scales. ⁸

Here we return to the present theory, and the mechanism for the movement of localized (phi, phase symbol) flows. These move laterally in the x, y and z dimensions, without a corresponding migration of the surrounding fluid, stuff. For steady flows, this would seem impossible. However, as suggested in Fig. 5-2, such traveling flows can be realized on the basis of flow waves.

Steady, localized phi flows, laterally, in the x,y,z dimensions, without a corresponding migration in the surrounding fluid (Aether) would seem impossible for this theory but not for the Anu Theory. Precessing, spinning vortexes of space is the working mechanism.

Fig. 5-2(a) shows a localized set of positive density flow waves, whose left edge is moving in the positive x direction. Again, in this simplified example, we'll assume their wavelength is arbitrarily short, so diffraction can be neglected. The edge's motion n in the reference space corresponds to that of a pro-particle associated with the waves, represented by vector v in the vector triangle at the right. The vector U ', shown underneath, represents the average flow associated with the waves. Here this has the same direction as the wave motion, with components in the negative and positive x directions.

Here, we begin to experience the dilemmas of plotting spheric flows of 3D spheres upon a 2D plot, with an added twist of applying this to a 4D toroidal Anu. It just doesn't seem to make sense until the edges are folded over to its opposites to be made a sphere.

Another set of flow waves, with the same x velocity, v, appears in Fig. 5-2(b). These are moving to the right, like the last set, but also upward, in the opposite (phi, phase symbol) direction. As indicated by broken lines, these are waves of negative relative density. Here the associated flow, U ', is opposite the wave motion. The (phi, phase symbol) component of this flow is negative, as in (a), while the x flow component is opposite.

Even if this Figure is difficult to interpret, as is, it still indicates correct flows upon a spherical surface. Opposite flows are a characteristic and also the polarities. This 3D spherical arrangement applies to a 4D toroidal Anu, ambidextrous music scale and other unique systems such as the I-Ching, Mayan Tzolkin, the ellipse and binary yin/yang systems such as the electron cooper pairs or photon pairs.

Fig. 5-2(c) shows a combination of two such wave sets. This represents balanced waves of positive and negative density, where again the average fluid density inside the wave region equals that outside it. Because they have the same velocity, v, in the reference space, the two wave sets travel together. The average net flow, U3 , is given by the vector sum of U 1' and U2'. The x components of the latter are exactly opposite, since these are the products of v and the average wave amplitudes. So, these cancel and U ' parallels the (phi, phase symbol) axis.

Balanced wave sets traveling together and oppositely, are a characteristic of ambidextrous music sets. ⁸

(Note that, while the wavefronts in Fig. 5-2(c) are depicted as straight, this may only be correct for small amplitudes. At larger amplitudes, these waves may distort one another, giving "wavy" fronts. Also, at large amplitudes, the 4-D component wave velocities may differ from c. Nevertheless, with appropriate tilts of the component waves, these should still move together in the reference space.)

The wave velocity should be lower than c, however the phase wave velocity ⁹ is claimed to be greater than c, or, the phase wave travels backward or opposite the wave velocity to give the impression that its faster than c.

This introduces another general quality of the wave system in this theory: its flow waves are balanced, such that net flows only occur in the (phi, phase symbol) dimension. (If not, it would follow that light or actual particles could be observed moving faster than c.) Below, we'll see that scalar/vector potentials correspond exactly to localized (phi, phase symbol) flows, moving in x, y and z, without net movements of the fluid itself in these dimensions.

Bens wave system flows are balanced and net flows only occur in the phi dimension. If it didn't, he says it would follow that light could be observed moving faster than c. I'll add that it is very possible to either have an uncollapsed phase wave travel faster than c or it also could be traveling backwards, revealing its "effect" information before its "cause" information. Cause then effect is impossible outside this backward phenomena. However, the Mayan Tzolkin, the I-Ching, DNA strands, ambidextrous music systems and several other binary systems have shown this same forward/backward, cause/effect/cause characteristic.

While we've been primarily concerned with the refractive effects of (phi, phase symbol) flows, they also reflect (phi, phase symbol) waves, as illustrated in Fig. 5-1 for a stationary flow wave region. Earlier, in deriving the Lorentz transform, we assumed a reflection mechanism aligned with the (phi, phase symbol) axis. This was assumed to move through the wave medium without inducing a flow around the mirror. Notice that, in these moving, wave-based (phi, phase symbol) flows, we have such a mechanism.

Quote: "Notice that, in these moving, wave-based (phi, phase symbol) flows, we have such a mechanism." Where is it?

How would the balanced waves of moving (phi, phase symbol) flow regions transform if they themselves were reflected by moving mirrors? For small amplitude waves, our previous "moving mirror" transform applies directly. Transforming a stationary flow wave region, such as that depicted in Fig. 5-1, gives a moving region like that shown in Fig. 5-2(c). As before, the 4-D length of hyperplane wavefront sections is unchanged, while the width of a moving wave region is contracted relativistically by the usual factor. Since they have opposite velocities, the positive and negative density component waves tilt oppositely with respect to the reference space.

Perhaps I'm missing something but I don't see a mechanism in the paragraph, above.

It's assumed that, in combination, the flow waves of this system transform relativistically at larger amplitudes also. (Because they are incomplete, the simplified waves of Figs. 5-1 and 5-2 probably would not behave properly at large amplitudes.) Another important assumption is that each complementary pair of wavefronts crossing the reference space carries an invariant (phi, phase symbol) displacement of the wave medium. (As described later, it should be possible to check these assumptions by computer simulation.) The average (phi, phase symbol) flow is then proportional to the flow wave frequency seen in the reference space.

I see two assumptions in the paragraph, above.

Given this, what is the transformed (phi, phase symbol) flow for a moving wave region?...In this respect, our wave-based flows behave the same as ordinary ones, and our assumption that the associated (phi, phase symbol) flow is proportional to the flow wave frequency seems justified.

I see a premise being formed based upon two assumptions, in the paragraphs, above.

Premise: "the associated (phi, phase symbol) flow is proportional to the flow wave frequency"

We've seen that it's possible, in principle, to have wave-based, localized (phi, phase symbol) flows which move in x, y and z, without the displacement of the surrounding fluid in these dimensions....For a qualitative introduction to the vector potential, we'll assume for the moment that our refracting (phi, phase symbol) flows are effectively steady. To visualize such flows, you could imagine that the responsible waves are of a much smaller scale than the waves being refracted, like the example of Fig. 5-1.

Vectors in assumed steady, refracting, phi flows are controlled by waves that are of a much smaller scale than the waves being refracted. This also points to the Anu toroidal vortexes of space at 10^28 or smaller as the controlling mechanism of these larger waves. The question could be asked again: If the mechanism is not Anu space, what could it possibly be? I cannot imagine space acting in any other way, at this level.

Chapter: Wave Frequencies.

Now, moving systems again...

Here we'll be looking at the effects of moving (phi, phase symbol) flows on the frequency of refracted waves in our system. They will be compared to the effects of moving scalar/vector potentials on de Broglie waves. Later, we'll use these wave frequencies to compare the velocity behaviors of pro-particles and actual charged particles.

Get ready for x, y and z dimensions...

Unlike our previous work with stationary (phi, phase symbol) flows, where we only treated the x dimension of the reference space, here we'll describe all three of its dimensions. What we're after is a general equation for the wave frequency, seen at an arbitrary moving point in the reference space. We'll call the 3 -D velocity vector for this point u. Also, the waves of interest will be characterized by the 3-D velocity, v, of an associated pro-particle.

Chapter: Pro-particle and Particle Velocities.

Earlier, we described the velocity of a charged particle entering a stationary scalar potential region. To solve for the velocity, we used the conservation of energy for a "free" particle. However, the energy of a relativistic particle entering a moving potential region is no longer conserved.

*Instead, here we'll use a conserved de Broglie wave frequency. For a potential interface in motion, at its moving position, the wave frequencies on both sides must match. Then we'll compare the velocity equations obtained to those for to pro-particles entering moving (phi, phase symbol) flows...

As described in Feynman, Leighton and Sands, electric and magnetic fields don't account for quantum mechanical phenomena, such as the Aharanov-Bohm effect. At the quantum level, electromagnetic effects are seen instead in terms of the influence of scalar and vector potentials on the phases of de Broglie waves.

More about mutual flow wave interactions...

In this section, we've carefully avoided the issue of mutual flow wave interactions. Here we've only looked at the behavior of small-amplitude waves, in (phi, phase symbol) flows driven by relatively short-wavelength flow waves. In this artificial case, there is no reciprocal effect of the former waves on the latter. (This is basically the same assumption made in the study of electromagnetism, when test charges are taken to have no effect on surrounding fields.) Still, the flow waves in this system do interact mutually. In this case, feedback arises. For example, wave set A refracts and reflects set B, which, by altering B's effect on A, the n changes A -- and so forth. While such effects can be modeled by computer simulation, they are difficult to treat analytically in more than one dimension. Typically, feedback in nonlinear wave systems leads to pattern formation. While the waves, in this system remain repetitive in the (phi, phase symbol) dimension, the nonlinear nature of flow waves, should lead to additional patterns within the overall structure. Such self-organizing patterns are taken as the basis for the realistic particle model introduced in the next section.

Time for realistic models...

Section: 6. Wavicles p65 Contents

Let's define the "wavicle" again : "...since they also behave as waves, elementary particles could just as well be referred to as "wavicle", Richard Feynman. Ben calls wavicles "these hyperconical flow wave patterns, which form the basis for charged particles".

Just as this theory involves a nonstandard interpretation of relativity, an alternate interpretation of quantum mechanics is also involved. As we'll see below, in the context of this wave system, this permits a new, realistic model of elementary particles.

In the usual textbook interpretation, de Broglie waves are taken to be linear waves of pure probability, whose squared moduli determine the likelihood of finding particles in particular states. These nonphysical waves propagate through increasing volumes of space (at speeds greater than light) until instantaneously "reduced" by a measurement. In the times between measurements, particles are taken not to exist in any definite state.

In the paragraph, above, we see the source of "velocities greater than the velocity of light", are called de Broglie "linear waves of pure probability, whose squared moduli determine the likelihood of finding particles in particular states."

However, as discussed by Bell, what constitutes a "measurement" has never been clearly defined. Despite its widespread acceptance and its usefulness as a calculational tool, the standard interpretation of quantum mechanics brings severe conceptual difficulties. This has also been pointed out by de Broglie, Schrödinger , Einstein , and Dirac -- each an architect of the existing quantum theory.

Science has come to find out that even an observation of an experiment constitutes a "measurement" of the wave and causes the wave to collapse into probability.

A second, distinctly different interpretation of quantum mechanics exists, which is equally consistent with experiment. (At least in the nonrelativistic case.) This is the "hidden" variables theory of de Broglie, Bohm, and Vigier. Here, de Broglie waves are taken to be real, nonlinear ones, and particles have definite states in the times between measurements.

Two pararaphs ago, de Broglie waves were defined as "linear". Above, we see it defined as "nonlinear'.

* In such a theory, Heisenberg uncertainty derives from inherent limitations in the measurement process. The present theory can be considered a relativistic extension of this one.

Until Bohm's paper of 1952, it was generally held that a self-consistent hidden variables theory was impossible. A frequently cited proof to this effect had been published by von Neumann in 1932. (Although a serious flaw in von Neumann's proof was pointed out by Grete Hermann in 1935, her finding went largely unnoticed at the time.) Bohm refuted this idea by actually constructing a self-consistent theory of this type. As Bell put it later, "in 1952, I saw the impossible done".

Bell's Theorem was developed in response to Bohm's work, to define the requirements for a valid hidden variables theory. It indicates that, in any self-consistent theory of quantum mechanics, there are necessarily non-local effects, as there are in Bohm's. While Bell was a proponent of hidden variables, their required non-local character has been taken by some as evidence against their existence. However, it will be shown that similar non-local phenomena can be found in ordinary macroscopic systems. So, while the present theory will be seen to involve particle-like entities, existing more-or-less continuously in definite states, this is not in conflict with the usual laws of quantum mechanics.

As mentioned, here elementary particles and their fields are based on self-organizing wave patterns. What types of patterns might be expected to form within this repetitive, nonlinear system? In the absence of computer simulation, we'll take as a guide the behavior of nonlinear, three-dimensional acoustic waves in ultrasonic wave tanks.

What types of patterns might be expected to form within this repetitive, nonlinear system?

Here's a clue, again: ..."a cloud of dust being affected by a repeated non-linear force will separate into rings with orbital periods which match the harmonics of the forcing period." R.Tomes ⁷

A characteristic effect arising in ultrasonic tanks is acoustic cavitation. This involves the formation of microscopic bubbles, which expand and collapse with impinging waves.* While bubbles are easily formed when the liquid contains dissolved gasses, these also arise in purified, degassed liquids. Here they consist of a vapor or other form of the primary liquid. In clouds of such bubbles, individual ones can exhibit surprising persistence. A variety of theories have been proposed to explain this, many involving assumed impurities in the liquid.

Above, we see nonlinear forces creating rings in clouds of dust and cavitation sphere-bubbles in water.

Usually ignored in such theories is the self-organizational capacity of strongly nonlinear wave systems. While waves determine where the bubbles are**, the latter also influence the propagation of waves (directly by reflection and also indirectly through the nonlinear interaction of reflected and other waves). So it may be that these pulsating bubbles are sustained by feedback, where waves are directed toward the bubble sites. We'll assume that this is so. (This would also help explain the large wave amplifications observed.) Bubbles then occupy the centers of more-or-less spherical standing wave patterns, with amplitudes varying as the reciprocal square of the distance to the bubble center.

Could similar patterns arise in our 4-D wave system? The simplest 4-D analogy would involve hyperspherical waves. However, in this repetitive system (4D wave system), isolated hyperspherical patterns can't exist. Instead, there would necessarily be an overlapping series of these, repeating in the (phi, phase symbol) dimension with the structure interval, s. At some distance from the x, y, z center, the fronts of the combined waves would approximate hypercylinders, aligned with the axis. Like 3-D spherical ones, the average amplitudes for such waves would vary as 1/r , where the radius, r, parallels the reference space. (For isolated hyperspherical waves, 2 it would be 1/r .)

Above, Ben realizes isolated hyperspherical patterns cant exist. He then makes the necessary logical step by mentioning, "there would necessarily be an overlapping series of these, repeating in the (phi, phase symbol) dimension with the structure interval, s." Hence, the Anu tori are also slightly overlapping spirals of space that should exist in the phi dimension.

Notice that, while we are constrained to repeating waveforms, our four-dimensional system still has another degree of freedom not found in a three-dimensional one. Besides hypercylindrical patterns, hyperconical ones of various shapes are also permitted. (The former are a special case of these.) Fig. 6-1 depicts sections of several hyperconical fronts (resembling nested paper cups), with respect to (phi, phase symbol), plus an arbitrary two of the three reference space dimensions. These are arrayed along a common axis paralleling the (phi, phase symbol) dimension, and again repeat with interval s.

*A remarkable aspect is the extreme concentration of wave energy occurring during bubble collapse. In water, this can cause a bluish or violet light emission called sonoluminescence. Energy gains of over 10 have been reported. The energies attained are so great that, for 12 bubbles containing a deuterium/tritium mixture, measurable thermonuclear fusion may be possible.

Above, "A remarkable aspect is the extreme concentration of wave energy occurring during bubble collapse. In water, this can cause a bluish or violet light emission called sonoluminescence. Energy gains of over 10 have been reported." This is COP of 10-12, meaning Co-efficiency of Performance, interpreted as 10 x Unity, meaning it puts out 10 watts with 1 watt input.

**This is demonstrated clearly in single-bubble sonoluminescence experiments, where the bubble's position is governed by focused waves, overriding its gravitational tendency to rise.

Hyperconical wavefront sections, depicted in terms of ????, plus an arbitrary two of the three reference space dimensions. These represent a wave array which extends indefinitely in all directions, repeating in with the usual structure interval, s.

Fig. 6-3. These wavefronts characterize four wave arrays comprising a single "wavicle". As indicated by solid lines, (a) and (b) represent incident and reflected waves of positive density. In (c) and (d), broken lines signify corresponding waves of negative relative density, moving oppositely with respect to A 1/r (phi, phase symbol) flow is associated with the waves.

Within a central "core" region, where the amplitudes are great, we'll consider these hyperconical waves to be nonlinear. Consequently, they are reflected and/or transmitted through this region with phase shifts. For simplicity, here we'll take it that the reflection is total and abrupt, as shown in Fig. 6-2. As indicated by arrows, the cone in (a) represents an incident wavefront, while the thin cylinder at the center indicates the nonlinear core. The front's pro -progressive reflection is depicted in (a)-(d), such that in (d) the wavefront is entirely reflected.

Above, the quote: "Within a central "core" region, where the amplitudes are great, we'll consider these hyperconical waves to be nonlinear." These are the de Broglie waves. Also within each Anu tori vortex of space there is a central passage or hole where waves spiral through to the other side of the Anu tori. The waves can attain light velocity in the spiraling center of each Anu. Any matter waves that spiral into these centers becomes light. This Anu hyperconical core is also nonlinear.

Assuming that the waves in these patterns are flow waves, then, from the last section, for every wave of positive relative density we can also expect a balancing negative one. Combined in the same pattern, this would give four wave sets all together, as illustrated in Fig. 6-3. While (a) represents an incident wave of positive density, (b) represents a corresponding wave of like density after reflection. Both move positively with respect to (phi, phase symbol). As indicated by broken lines, (c) and (d) are the corresponding incident and reflected waves of negative density, moving negatively in the (phi, phase symbol) dimension. Of course each of these represents an array of hyperconical waves, with these crisscrossing wave sets sharing the same core region.

Above, a quote: "Combined in the same pattern, this would give four wave sets all together." Evidently, after checking elsewhere in this pdf document, I found that Fig. 6-3 represents a "wavicle" or "particle". This Figure includes the necessary incident wave (a) of positive density and reflected negative (b) densities, moving positively with respect to the phi dimension, these both having their corresponding negative density waves (c and d), moving negatively in the phi dimension. This 2 pair arrangements can also be found in the Trinary Relativity Theory ¹⁷, the Mayan Tzolkin, the I-Ching, pairs of Cooper pair electrons, ellipse geometry, egg geometry and ambidextrous music scales, among other systems.

Associated with such flow wave patterns are net (phi, phase symbol) flows, corresponding to the (phi, phase symbol) components of the wave vectors. (There is no net flow with respect to the reference space.) These flows are proportional to the wave amplitudes, which, again, vary as 1/r. So a wavicle contains a stream, whose flow increases towards the core. Inverted patterns, with opposite (phi, phase symbol) flows (charges), are also permitted.

Above, we can conclude that for every visible pattern of flow there is always a hidden corresponding, complimentary flow associated with the visible pattern. However, from music study, we have concluded that the complimentary flow is like the Major relationship is to its minor. The compliment is not a mirror image but has an oscillation limit that compliments in limits of the number 9. For example, if one side is 5, the other side is 4. These sets will always total 9: 1/8, 2/7, 3/6, 4/5, 5/4, 6/3, 7/2 and 8/1 again which has its roots in the before mentioned enneagram. ⁴

A key assumption in this theory is that, while the system is driven to form such patterns, the (phi, phase symbol) flow attainable at the cores has a sharp limit. This limiting velocity is regarded as a general characteristic of the wave system, like the characteristic wave velocity, c. With positive feedback acting to increase the core flow, this limit then becomes the defining nonlinear element of these patterns, setting the flow wave amplitudes.

Attributing electromagnetic potentials to flows, as described earlier, we then have particle-like entities with quantized charge, energy (mass), and proper Coulomb fields. Also, particle "spin" can be attributed to an extra degree of freedom of these 4-D these standing wave patterns. In an introduction to quantum electrodynamics, Richard Feynman remarked that, since they also behave as waves, elementary particles could just as well be referred to as "wavicle".

Here we'll adopt Feynman's term as the name for these hyperconical flow wave patterns, which form the basis for charged particles in this theory.

(The axially symmetric configuration of Figs. 6-1 to 6-3 only characterizes a stationary wavicle. As described below, at relativistic speeds, the hyperconical fronts are tipped with respect to the core, and open out. Also, in an actual wavicle, the wavefronts would be somewhat irregular, unlike the perfectly symmetrical hypercones depicted.)

Of course wavicles depend on incoming waves, originating in remote parts of the system, for their continued existence. Thus, unlike the usual conception of a particle, they can't be considered to exist independently of their surrounding environment. The source of a wavicle's incoming waves is taken to be others in the system. Likewise, its outgoing waves are also incoming ones for those. (Like the reflecting waves in a large cloud of cavitation bubbles.) Consequently, the waves comprising a wavicle are not exclusively its own. (This is manifested in the inseparability of particles and observing apparatus in quantum-mechanical experiments.)

For a conventional charged particle to have finite size, additional "Poincaré stresses" must be introduced to hold it together against the effects of its own field. (Finite size avoids the serious problem of an infinite field at the particle's location.) One immediate advantage of wavicles is that no Poincaré stresses are called for, since these are contained naturally by the inward momentum of their incoming waves. (The wavicle model also seems to answer the long-standing problem of the basis of radiative reaction in charged particles. This calls for "half-advanced" and "half-retarded" waves, where the former anticipate the future particle position.)

Chapter: Moiré Wavefronts.

Another premise of this theory is that certain wavicle patterns are more stable than others. These have characteristic wave angles and frequencies, in the stationary case, and correspond to different elementary particles or sub-particles. As proposed by de Broglie, we'll take the frequency and mass to be proportional, via the Planck and Einstein relations

Above, the premise that certain wavicles are more stable than others is also reflected in the musical mapping of wave lengths and wave numbers. Some musical interval are known to be very stable...the octave, the 5th and 3rd.

Given a stationary wavicle, a moving one is obtained by applying our usual relativistic transformation, shown to hold for this system. (The defining conditions for a wavicle are taken to transform along with its waves.) While the component waves have a single frequency in the rest case, this is no longer true when a wavicle moves. However, in combination, they comprise "Moiré wavefronts", which still have a single frequency. Here we'll find that such wavefronts correspond, in more than one way, to the de Broglie waves of particles with various rest masses.

Fig. 6-4 illustrates a cross-section of a stationary wavicle in two dimensions, showing only positive density waves. The two crisscrossing sets, marked by thin lines, are the same waves, before and after reflection from the core. (The core is shown as the vertical gap at the center.) In this cross-section, these waves have just two orientations, with incident and reflected waves on opposite sides of the core sharing the same angle. As denoted by vectors with magnitude c, the waves of both orientations are moving positively with respect to (phi, phase symbol) . Together, they form an unchanging pattern, moving parallel to the (phi, phase symbol) axis. The motion of the pattern's nodes is indicated on the right by the vector, N.

A striking feature of any standing wave pattern is that, regardless of its size, all regions undergo synchronized behavior. As seen in the reference space, the extended wave field of a stationary wavicle undulates or pulsates in unison, at a specific frequency. This corresponds to the (phi, phase symbol) movements of the component wave patterns through the reference space. It's these pattern movements that we'll be describing in terms of Moiré wavefronts.

Quote: "the extended wave field of a stationary wavicle undulates or pulsates in unison, at a specific frequency." B.Fuller speaks of this same pulsation. The Anu Theory also assumes that each toroidal Anu pulsates or breathes in and out, creating spherical waves.

If the positive component waves of Fig. 6-4 were drawn with thick lines, from the Moiré effect, you might see alternating light and dark bands, running horizontally across the nodes. Moiré wavefronts, depicted here by gray bars, have the same orientation; hence the term. Representing phases of the overall wave pattern, Moiré wavefronts are defined as having the same (phi, phase symbol) period, s. (This omits half the lines which would be perceived visually with a Moiré pattern.) Thus, in the reference space, their frequency represents that of a wavicle's pulsations.

For a stationary wavicle, the component wave and Moiré frequencies are all identical. As before, we'll characterize the component waves in terms of associated pro-particle velocities. (Knowing the relativistic transformation equations for pro-particles, we can then use these to describe the transformation of wavicles.) Working in just the x and dimensions of Fig. 6-4, with representative positive density waves of just two orientations, we'll call the characteristic pro-particle velocities u ' and u'. So we have...

Omitted Formulae

Fig 6-5 depicts the same wavicle, moving at a relativistic speed, v. In addition to the core, the pattern nodes must also have this x velocity. (Since the component wavefronts are parallel within each set and meet at nodes at the core surface.) Again, the component waves have just two orientations, with incident and reflected waves on opposite sides of the core matching in angle. As shown, the Moiré wavefronts are tilted in this case.

For a moving wavicle, at a position traveling with it, we know the frequencies of both component wave sets are decreased by simple relativistic time dilation. (This can also be shown formally from the transformation equations.) At such a position (the core, for example)

Next, in terms of its node spacing, we'll describe the contraction of a moving wavicle, having velocity v in the x dimension. We'll call the x distance between successive nodes on the same Moiré wavefront d. Referring to Fig. 6-5(b) again, from the node where wavefronts a and b cross, to the segment, s, (of this (phi, phase symbol) length) the distance is d/2. From the figure, this distance, the slopes of a and b, and s are related by...

Omitted Formulae

(Here I'd like to mention another difference between the transformations of component waves and Moiré wavefronts. Recall that, as the former are tilted in four dimensions, the spacing between associated pro-particles is invariant. However, because comparable Moiré fronts undergo greater tilts, the 4-D spacing of the associated nodes increases with tilt. In terms of the reference space, though, the node spacings undergo the same relativistic contraction as pro-particles.)

Formulae Omitted

In his original thesis, de Broglie hypothesized that particles have some "periodic inner process" corresponding to their masses, with which waves are associated. Here we find an appropriate process, in the inherent pulsations of wavicles. We also have a physical basis for the relativistic rest energy of elementary particles, and the equivalence of mass and energy.

(Here we've seen that Moiré wavefronts inherit the basic relativistic behavior of their (phi, phase symbol) component waves. However, in four-dimensional terms, there are significant differences. One obvious difference is (phi, phase symbol) velocity. This is greater for a Moiré front, and contributes to a 4-D velocity greater than c. Comparing the transformed wavefronts of stationary pro-particles and wavicles, the latter's Moiré fronts have a greater slope. Thus, as a function of distance in the reference space, these manifest larger (phi, phase symbol) offsets. Nevertheless, from its greater (phi, phase symbol) velocity, a Moiré front still arrives at the reference space at the proper relativistic time.)

So we again have Lorentz/Fitzgerald contraction. Since the wavicle core is defined by nodes, this is also contracted, in addition to the overall wave pattern. (Here I'd like to mention another difference between the transformations of component waves and Moiré wavefronts. Recall that, as the former are tilted in four dimensions, the spacing between associated pro-particles is invariant. However, because comparable Moiré fronts undergo greater tilts, the 4-D spacing of the associated nodes increases with tilt. In terms of the reference space, though, the node spacings undergo the same relativistic contraction as pro-particles.)

Chapter: 4-D Wavefront Transformations.

Fig. 6-6 shows how individual hyperconical wavefronts transform for a wavicle with velocity v in the +x direction. Part (a) illustrates the configuration in (phi, phase symbol) and x, plus one of the remaining dimensions. As shown, the hyperconical axes remain parallel to the node velocity vector, N, which is tipped here with respect to the core and (phi, phase symbol) axis. Part (b) depicts the relationship between, v, and vector V, which is the (phi, phase symbol) phase velocity of a Moiré wavefront at an x position moving with velocity v. (For example, consider the (phi, phase symbol) motion of a node at the moving core surface.) From v and V , we can find N...

Omitted Formulae

(In analyzing this system, a possible source of confusion is the fact that the 4-D Moiré wavefront velocity is somewhat less than N. This results from the fact that, in a moving wavicle, N and the Moiré wavefronts are not exactly perpendicular.) From the figure, the angle (beta), between and the (phi, phase symbol) axis is given by...

Omitted Formulae

From Eq. (6-23), notice that as the wavicle velocity, v, approaches c, N also approaches c, as a lower limit. Thus for values of v close to c, the ratio on the right in the last equation approaches 1, (beta) approaches 90, and vector N approaches the x axis.

Although the component waves are still hyperconical, their shape also changes with wavicle velocity. In Fig. 6-6(c) the line segment F represents a section of a component wavefront, while (alpha) is its angle with respect to the hypercone axis and vector N. While N represents the motion of a node associated with F, the perpendicular vector, c, indicates the movement of this component wavefront section. As shown, (alpha) is given by...

Omitted Formulae

At large wavicle velocities, where N diminishes toward c, the quantity on the right again goes to 1, and (alpha) to 90. Consequently, the hypercones open out, and approach hyperplanes in the limit. So, at velocities very close to the speed of light, the component fronts approximate hyperplane waves, traveling in the x direction, with velocity c. (Further, the incident and reflected portions of a single wavefront no longer have the same axis, although both axes parallel N. Projecting both hypercones inside the core, the vertex of each is at the core center. However the two vertices are offset in the (phi, phase symbol) dimension, so the two axes are displaced from each other, as shown in Fig. 6-6(a). Speaking in terms of the three dimensions of the figure, the core node where the two [hyper]cones join is an ellipse. This shape also characterizes the nodes in general.)

Above, we have a strange light velocity displacement where a single center point axes becomes offset to create two center axes, commonly associated with an ellipse. We have studied ellipses ¹² and egg shapes ¹³ before and found that they are perfect shapes for both generating and maintaining vortical flows.

In contrast to the component waves, which remain hyperconical, Moiré wavefronts are essentially hyperplanar. As shown in two dimensions in Fig. 6-4, in a stationary wavicle, these are perpendicular to the (phi, phase symbol) axis. For a wavicle moving steadily in the x reference space dimension, the hyperplanes are tilted in x and, as illustrated in Fig. 6-5. Also, from our relativistic transform, there is no tilting with respect to y or z, so the resulting hyperplanes remain perpendicular to the x, (phi, phase symbol) plane.

The basic shape difference between component and Moiré wavefronts is a crucial one. Since the Moiré fronts of a uniformly moving wavicle are hyperplanar, these appear as infinite plane waves in the reference space, exactly like the de Broglie waves of a uniformly moving particle. It follows that, knowing only the spatial arrangement of its Moiré wavefronts, one can infer the momentum of such a wavicle, but not its position.

Chapter: Flow Wave Effects and the Wavicle Core.

As described, a stationary wavicle has a flow wave pattern with an amplitude and average (phi, phase symbol) flow varying as 1/r . Since the wave pattern of a moving wavicle contracts relativistically, its flow pattern must do this also. In addition, its average (fixed-position) flow wave frequency increases relativistically. Given that a wavicle's flow is proportional to both wave amplitude and frequency, total (phi, phase symbol) flow is then conserved. This matches the conservation of charge in an actual particle, where contracted (ellipsoidal) equi-potential surfaces enclose increased potentials. For a wavicle in an external (phi, phase symbol) flow (corresponding to a charged particle in a potential), its wave pattern can be expected to move with the effective flow, as described previously for pro-particles. As depicted in Fig. 6-3, we have component waves of both relative densities, moving in oppositely with respect to (phi, phase symbol). Consequently, half are augmented in frequency, while the other half are decreased by an equal amount. This gives an average frequency and associated flow which are unchanged. I.e., net (phi, phase symbol) flow is still conserved, just as charge is for an actual particle in an external potential. Thus we have a complete model of a relativistic, quantized charge.

Again, for a given wavicle pattern having a specific rest frequency, an inverted pattern with an opposite (phi, phase symbol) flow is also possible. As you might expect, the two cases are taken to represent corresponding particles and antiparticles. Of course wavicles with positive (phi, phase symbol) flows are the ones we'll choose to equate with positively charged particles. In the simplified wavefront diagrams above, we've assumed that a wavicle's component's move at a constant velocity, c, and thus can retain a hyperconical shape. Clearly this is reasonable at large distances from the core, where the amplitudes and nonlinear effects are vanishing. What happens in the region close to the core (this may be relatively small), where the flow wave amplitudes are great? Here the picture is less clear.

Above, Ben's logic and calculations begin to interpret opposite flows as corresponding particles and antiparticles. Also, we now arrive at the question of what happens inside the core.

For individual component waves taken in isolation, it may be that their speed would vary with amplitude. (Like familiar shock waves, the waves with greater density might move faster.) Taken together, we also expect a wavicle's components to simultaneously reflect, refract, and displace one another. In a balanced system, where the overall density remains constant, some of these nonlinear effects may tend to cancel. So it's conceivable that the effective component wave velocities might remain approximately c near the core. (This would imply that the flow wave interactions within wavicles differ from those between wavicles. Similar behavior is observed in solitons, ¹¹ where the component wave interactions differ from those of whole solitons.)

Whatever transpires near the wavicle center, it's required that, after leaving this region, the various outgoing component waves should be the reflected equivalent of those incoming. (This is necessary to conserve (phi, phase symbol) flow, density, and energy together.) Since wavicles are taken to be self-organizing, there should also be feedback in the core region, actively adjusting the waves to fit this pattern. It's hoped that such behavior can be verified by modeling wavicle's numerically. And the core? The example of acoustic cavitation suggests the possibility of a distinct surface, representing a sharp discontinuity in the properties of the wave medium outside and inside the core. (To simulate such a wavicle numerically, it would be necessary to model a separate set of conditions existing inside the core.) With an overall alignment paralleling the (phi, phase symbol) axis, the surface conceivably might be a tubular one, rippled by impinging waves. Or, it could consist of separate bubbles, in a periodic string with the same orientation.

Above, Ben asks, "What his happening inside the core?" I believe the core look like protons in the larger atoms, kept in place by the Any spiral of space. only the so called protons are now cavitation bubbles. The core is tubular because the core of the Anu tori is tubular. The single center of the tube is now a relativistically torsioned, two center ellipse or egg, where all matter is born in pairs, from light, which is spiraling in the center of the tori tube. Ben's premise that, "the various outgoing component waves should be the reflected equivalent of those incoming", isn't necessarily so. As it is in the Toroidal Universe, when the tail end of the cycle of all of universes matter, spirals into the toroidal core and is ripped apart into light, by being spun through the toroidal core at light velocity, so it is in the Anu toroidal core. Here in the core, lower velocity is spun up to high energy light. However with atoms, as atoms aggregate from the centers of each Anu, I previously surmised that gravity-space is the incoming information into the atom centers while light and EM force are the reflected outgoing information, for light only manifests when it is involved with atoms and so it is also with electric and magnetic forces.

To describe the possible interactions of wavicles, we can begin by considering the responses of individual wavicles to external (phi, phase symbol) flows. Along the lines of our earlier work with pro-particles, we can approach this from the standpoint of an individual wavicle encountering a "sharp" change in (phi, phase symbol) flow (electrical potential). However, here all external flows are to be attributed to other wavicles. So in this case, the external flow wave pattern is necessarily complex, with the actual (phi, phase symbol) flow at a given instant depending on the positions, phases, etc. of the various other wavicles.

Above, Ben begins by postulating a wavicle/particle that encounters a sharp change in electrical potential. This assumes that the core of atoms has EM forces present by some undefined mechanism, already.

Earlier, we saw that the component waves in this system are simultaneously reflected and transmitted at a sharp (phi, phase symbol) flow interface.

However, for a wavicle to persist, the overall system must "decide" whether the whole entity is to be transmitted or reflected. The system's behavior must be such that, after the wavicle's motion changes, waves originating from prior times continue to arrive at its future core position. To conserve the total momentum of the system, other wavicles necessarily undergo opposing changes of motion. And these also must continue to receive incoming waves.

*To this end, a very similar model of electrons and muons was proposed by Dirac in 1962. In it, the electron is viewed as "a bubble in the electromagnetic field", of finite size. The muon is then taken to be an excited state of the electron, involving radial pulsations of the bubble and a spherically symmetrical wave field. Given that our system behaves this way, we have entities which both generate and respond to potentials as actual particles do. And, based on different characteristic wave angles, particles of different masses can be modeled. Tentatively, we'll take individual wavicles to represent the charged leptons: the electron, muon, tauon and their antiparticles. Since there is no evidence of internal structure in these, single wavicles with small cores may be an accurate representation. Again, this avoids the problem of infinite fields encountered in standard field theory,* where these particles are treated as point charges.

Above, Ben mentions particles and antiparticles again which is the correct answer. Yes, it is the frequencies of this side called the wavicles....plus the hidden frequencies of the other side...the antiparticle side, that furnishes us with the needed phase wave that already knows what our so called point particles are going to do and conserve. These expanded points of the other side, are our Anu tori.

Ben now realizes the system must conserve its momentum so that the system must also have the forwarned ability to, not only "decide" if it wants to conserve the whole entity to be transmitted and reflected, but, the system must also have the ability to decide this in the time it takes before the whole system transmits....this is the impossible "effect before cause" situation.....except that there are real, phase waves that already exist in the phase-space and have already decided what to do. These phase waves are either faster than light velocity or they are traveling backwards with "future to past" information. This logarithmic phase-space should exist in the core at 10^28 wavelength or less, as Anu tori, where the smaller the entity is, the more energy it has. The Anu also has a form of unconscious intelligence, called "intellect", that can take energy and make decisions about how to use it for better organization and more complicated forms in its future. Intellect is not our common daily intelligence. Intellect is raw Life Force and has more in common with the psychic, than with outer, human intelligence. The Life Force seems alive but it is not quite what we call "Life", yet. Life belongs to conscious organ.isms that have organs and have high organ.ization.

Section: 7. Future Additions Contents

Chapter: Quantum Mechanics.

One added section will address quantum mechanics, with particular attention to the Einstein-Podolsky-Rosen, or EPR, effect. The starting point is the observation that, for a wavicle to persist, even its simplest behaviors require the coordinated action of the overall wave system. Thus a wavicle's actions are necessarily determined by non-local factors. Such non-locality is also characteristic of the EPR effect. It's sometimes said that each part of a nonlinear wave system "knows" what the other parts are doing. The quasicrystalline wave structures mentioned in Section 1 are a clear example. (As Penrose points out, the formation of a quasicrystalline patterns requires knowledge of remote parts of a system.) Connected, non-local wave phenomena of this sort can be seen as the result of nonlinear coupling. (Like that of nonlinearly coupled pendulums or oscillators.) Such coupling is expected with the pulsations of wavicles, and is taken as the basis for quantized de Broglie wavelengths, such as those of electrons in atoms. Again, the present work is related to Bohm's "hidden variables" theory, where particles exist continuously in definite states and follow definite trajectories. In it, de Broglie waves and particles are influenced by an additional "quantum-mechanical" potential or "quantum potential, which has a non-local aspect. Bohm's theory is based on the non-relativistic Schrödinger wave equation...

Above, Ben brings up the problem of non-locality by stating, "Again, the present work is related to Bohm's "hidden variables" theory, where particles exist continuously in definite states and follow definite trajectories. In it, de Broglie waves and particles are influenced by an additional "quantum-mechanical" potential or "quantum potential, which has a non-local aspect."

Now we wont find the answer to non-locality in the classical level of atoms. If we look deep into the hidden variables, the Anu tori can precess and spin at almost infinite velocity. During this cycle it may have the ability to produce a musical A note, trillions of times a second. All other Anu in the vicinity and the universe are also producing this same musical A note. All A notes can be considered as the same A note, no matter its locality or non-locality. These hidden variable A notes exist in definite states and definite trajectories...that state is the A note and the trajectory is a circular precession of each Anu tori. Within the whole system of uncountable Anu, additional potential are interacting, non-locally. The whole system is already wholly synchronized and can communicate nearly instantly.

Omitted Formulae

He then showed that, if the quantum potential were to fluctuate randomly, such particles would behave exactly in accordance with the usual statistical laws of quantum mechanics -- despite following well-defined trajectories. (Striking computer-modeled trajectories of particles in quantum potentials can be found in Philippidis et al. or Vigier et al. ) Bohm and Vigier subsequently proposed random fluctuations in a fluid wave medium as a physical basis for the quantum potential. Toward a relativistic theory, Vigier has since proposed a "sub-quantum Dirac ether" as the fluid medium. Unlike real fluids, the elements of a Dirac ether have no specific states. (Dirac describes it as analogous to the concept of particle clouds, where particles lack definite states.) "Manifest" relativistic covariance then is permitted by the fact that there is no overall state of motion. However, this is inconsistent with the basic de Broglie/Bohm theory, where particles have definite states and the wave medium is taken to be physically real. On the other hand, the present theory offers an appropriate medium which is both relativistic and realistic. At this point, we'll introduce another feature of wavicles. In the previous section, their wavefronts were illustrated as perfectly symmetrical hypercones, for simplicity. However, in a realistic case, where the source of a wavicle's incident waves is others, the patterns are necessarily irregular to some degree. (There is no way to generate perfectly symmetrical hyperconical wavefronts from sources at discrete, scattered sites.) While feedback maintains a wavicle's average flow, such asymmetries would result in intermittent fluctuations in the (phi, phase symbol) flow seen at the core, and changes in its motion. Chaotic flow fluctuations of this nature are taken to correspond to Bohm's quantum potential.

Above, Ben says that a wavicle/particle's incident wave patterns are asymmetrically irregular and can be called Bohm's "quantum potential".

Chapter: Gravitation and Cosmology.

In Einstein's version of general relativity, gravitation is based on a varying non-Euclidean space-time, and an absolute speed of light. In this theory, gravity is associated with local variations in the speed of light, while space and time (in a preferred frame) are absolutes. For very strong gravitational fields, or large astronomical distances, the two theories make very different, testable predictions.

Above, Ben associates gravity with light and he considers space and time as absolute. As I believe that gravity is space vortexing and that light does not show up in deep space but only near matter, then we can expect that any of Bens gravity or light formula to reflect these premises. I also believe that time is gravity which Ben therefore considers time as absolute but this also implies that gravity is absolute since I expect gravity to be what space does and time doesn't exist. Since Ben does not recognize that gravity is 4D-0D absolute, as I do, his calculations should show these omissions.

Like the electromagnetic forces, the source of gravitation here lies in the wave fields of wavicles. In concentrations of matter containing oppositely charged wavicles, the average (phi, phase symbol) flows tend to cancel at large distances, like the electric fields of conventional particles. However, the underlying wave fields do not cancel. The cumulative waves fluctuate more-or-less randomly, with an rms amplitude varying approximately as 1/r from the center of 2 mass, like the wave fields of individual wavicles. The resulting irregular fluctuations of the wave medium are taken to represent gravitational potentials. (Thus these and the quantum potential are related.)

Above, Ben makes ol' Al's mistake, along with all other relativists when he says, "Like the electromagnetic forces, the source of gravitation here lies in the wave fields of wavicles."

A wavicle/particle and its field is considered as mass and this mass is considered as source rather than space being the source of gravitation, therefore all subsequent calculations should not reflect reality. The same advice applies to Gravity Probe B. ¹⁸ The experiment assumes the very same premise that mass is somehow dragging and twisting space. That is precisely backwards.

The key to gravitation in this system is the dependence of the rate of physical processes on the 4-D wave speed, c. Our wave-based gravitational potentials act by reducing this general velocity. (This may be attributable to disruption of rectilinear wave propagation by the medium's fluctuations. For example, a ray traveling from point a to point b experiences small-scale excursions which increase the total path length, effectively decreasing the wave velocity.) As c is reduced, everything is slowed proportionately -- the movements of wavicles, the propagation of electromagnetic waves, etc.

Above, as Ben goes on, the gravity statements become rather bazaar. Let's see how it develops. This above paragraph doesn't make sense to me.

Clocks in gravitational potentials are perceived by outside observers to be slowed, as usual. Light is also bent in a gravitational field. In this case, though, the effect corresponds to ordinary refraction. (Of course refractive index goes as the inverse of wave speed.) As a result, the local behavior of physical systems in gravitational fields matches that in accelerating frames -- i.e., Einstein's principle of equivalence is met.

Above, the quote, "Light is also bent in a gravitational field. In this case, though, the effect corresponds to ordinary refraction.".....this is exactly the conclusion I came to also.....It is the optical medium, space, that distorts (bends) the optical phenomena, light.

For comparing Einstein's account of gravity with this one, the concept of optical path length is useful. Often used in evaluating optical systems, this is computed by multiplying the lengths of light rays in optical elements by the refractive indices there. While treated as distances, these products are actually a measure of the time required for a wavefront to transit an element. (In an ideal imaging system, the summed optical path lengths between corresponding object and image points are the same for all rays. This says that all parts of a wavefront arrive at an image point simultaneously -- in phase.) Still, in terms of light wavelengths, a material with an index above one behaves as though additional space is compressed inside it.

Above, to clarify space as an optical medium and what it is capable of, here is a quote, "It is as if empty space behaves like a vast piece of superconducting metal", Scientific American Magazine, January, 2002, Mathematics and Universe, pg. 21. The redeemable point of this quote shows that space is the superconducting, optical medium that can bend what science calls "light within it". As noted before, there is no light in deep space, so the superconducting, optical medium called space is bending some other property of itself, rather than the phenomena called light. Gravity is space spiraling around mass. Gravity affects mass, not the other way around. The least number of close packed Anu that defines a "gravity unit", is the 13 sphere, Vector Equilibrium of B. Fuller. These 12 tori manifest gravity in the center 13th tori. The 13th tori is empty and doesn't exist. The gravity unit is a centerless, massless center. So much for earth gravity, pulling.

*Large ocean waves are now thought to grow from smaller ones overtaken. Einstein assumes that optical path lengths in gravitational potentials are the same as spatial distance. Here, as in ordinary optical systems, they aren't. As a result, different arrangements of things in space are predicted. For weak gravitational fields and modest astronomical distances, like those within the solar system, the differences are minute. At cosmological scales, however, these should be apparent.

Above, this paragraph seems also slightly incoherent and unable to build on his previous premise.....

Because c isn't sacrosanct in this theory, an alternate basis for the Hubble redshift is also permitted. Here, c is taken to be gradually increasing. Since this corresponds to the rate of all processes (at the macroscopic level), at the time of emission, the spectra of remote galaxies would have been lower in frequency than present ones. So we're again invoking a varying wave speed, instead of a varying space-time.

Above, Ben changes the constant of light velocity.

To provide for a changing c, we'll take the wave medium, stuff, to resemble a real gas, with particle-like constituents. The characteristic acoustic wave velocity then depends on the effective temperature and density. We can also suppose that the constituents of stuff are also wave-based entities (like tiny wavicles), associated with some finer coherent structure. If energy is gradually transferred between wave structures at different scales, we then have a mechanism for changes in these qualities of stuff at the macroscopic level.

Ben's quote: "To provide for a changing c, we'll take the wave medium, stuff, to resemble a real gas, with particle-like constituents."

Anu tori are the perfect particle-like constituent, however each one exists at one point but it is a spiraling bundle of waves, as Ben says, "wave-based entities (like tiny wavicles), associated with some finer coherent structure".

(Stuff is assumed to have a fractal-like nature, with wave structures arising and subsiding at widely differing scales. In this respect there's a resemblance to "inflationary" cosmological models.)

Above, Ben recognizes that the Atheric "stuff" must have a fractal-like nature and the Anu tori have a fractal-like nature.

Such energy transfers occur naturally in nonlinear wave systems. Not only from large waves to small, but also in the opposite direction.* An important example was discovered in computer-modeled waves by Fermi, Pasta and Ulam in the 1950's. Prior to their work, it 10 was widely believed that nonlinearity in waves inevitably leads to thermodynamic behavior, where orderly large-scale waves degenerate into random small-scale ones. The system studied was one-dimensional, with a discrete length. Initially, a large sinusoidal wave was seen to transform into various configurations of smaller ones. However, the process eventually reversed, with the small waves coalescing back into the starting waveform. (The effect is now called FPU recurrence. Fermi, Pasta, and Ulam also inspired the computer experiments of Zabusky and Kruskal, discussed earlier.)

Above, Ben surveys "energy transfer"...noting correctly that the transfer was not only the downgraded entropy that we all are led to believe is a one way heat-death for universe, but that this entropy has a valid counterpart called negentropy where energy eventually reverses and upgrades itself. ¹⁰ ¹⁴

It seems clear that general qualities of the universe do undergo long-term changes. In the course of stellar evolution, a substantial fraction of the collective mass in stars is being converted to neutrinos. However, the bulk of these are undetected and unaccounted for. It's conceivable that much of the lost energy is transferred to a smaller-scale wave structure, helping raise the effective "temperature" of stuff at that level, and the value of c.

Chapter: Nuclear Forces and Sub-particles.

This part of the theory is more tentative; at this point it's only qualitative. Presently, nuclear forces are taken to be relatives of the Casimir effect. The latter involves vacuum fluctuations (random electromagnetic waves occurring in "empty" space) which are suppressed in regions between parallel conducting plates. As a result, waves are reflected disproportionately from the outside plate surfaces, creating a small pressure driving the plates together. The force varies as the inverse of the plate spacing, to the fourth power.

Above, Ben, I suppose, is showing us the regular explanation for the Casimir effect. It also can serve to show that "vacuum fluctuation" waves other than Tesla/Bearden longitudinal waves can exist in space, near mass. However, a Casimir experiment on the massive earth proves these waves exist but has it been done in deep space? No. Perhaps a Casimir experiment wont work in deep space.

Due to their finite sizes, similar effects may arise between reflecting wavicle cores. Although these are not flat plates, in close proximity, they would shield one another somewhat from incident component waves. Also, since the component wave amplitudes are extreme near the cores, a large attractive force could arise at short distances. This effect, which depends in part on the wavicle core sizes and the characteristic hyperconical wave angles, is the assumed basis of nuclear forces. (The feedback which sustains the individual wave patterns is also taken to oppose the complete merging of wavicles.)

Above, the shielding effect theory originated with Charles Brush, in 1924.....Shadow Theory ¹⁵ says that there are gravitic forces in direct lines between two separate entities, that do not exist anywhere else around the entity. This once carried some weight with me as these unique and direct line-ups between mass particles, built a pulling gravity field...however, once it is realized that space is vortexing around all of these so called mass particles, we then have the correct mechanism to evaluate, concerning forces between any two, separate entities.

Since multiple nonlinear effects are involved, it appears difficult to test this idea by analytical methods. However, it may be possible to verify it through computer simulation of the wave system. (A possibly related effect is seen in ultrasonic wave tanks, where the cavitating fluid contains particulate impurities. The wave action tends to drive these together, forming aggregates which precipitate out. The process is sometimes used to purify fluids.

Above, Ben's assertion that sound can, indeed, push together mass with incredible force, is true. After all, the so called mass is actually made of the same wavelengths as the sound wavelengths. Moreover, sound could also be involved with atomic gravity or the Casimir effect.

Suspended particles of metal powder can be driven together so forcefully that they partially melt and fuse.

Besides constituting nuclei, bound groupings of wavicles may also be needed to account for the internal structure of hadrons. If so, the binding forces might be similar to those of nuclei. In the prevailing quark model, the constituents of hadrons have fractional charges. On the other hand, in the current version of this theory, uniform (or nearly uniform) elementary charges are called for. A compromise might be to assume that both hadrons and leptons have constituents with charges of � e. A model of this nature has been proposed by Harari, for example.

Above, Ben also has trouble accepting that there exists a fractional charge.

Still, fractional charges have never been observed directly. Also, the prevailing quark model is contradicted by recent measurements of the proton's spin magnetic moment, which give only about one third the predicted value. (The "spin crisis.) Since charge and spin magnetic moment are related, one wonders whether this might indicate that hadrons actually have constituents with integral charges. As described by Nambu and Han, various models based on quark-like sub-particles with integral charges have been suggested in the past.

Chapter: Computer Modeling.

Again, some wave behaviors required by this theory are difficult to verify analytically. (The evolution of nonlinear waves in a gas-like medium can be viewed as an extreme example of the many-body problem -- with each particulate constituent a separate body.) However, it may be possible to do this though computer modeling. (No modeling has been attempted at this point.) Some basic questions to be answered are:

1.) Can a wave system of this kind remain balanced? (Complimentary positive and negative density flow waves, balanced such that net flows only arise in the dimension.)

2.) To arrive at the vector potential, we assumed that the effective flow experienced by pro-particles at their moving positions is proportional to the frequency of flow waves encountered. Does this hold?

3.) Are self-organizing flow wave patterns resembling wavicles observed?

4.) Do these exhibit quantum-mechanical behaviors?

As discussed in Section 1, the computer experiments of Zabusky and Kruskal modeled an infinite one-dimensional system of nonlinear waves. Because these were periodic, it was only necessary to model a single region equal in length to the period. Waves were wrapped around from one edge of the region to the other. With respect to the(phi, phase symbol) dimension, we can do the same for the periodic waves of this system.

Fig. 7-1. 3-D representation of a rectangular hyperbox-shaped region for modeling the evolution of waves in this system. Depicted are (phi, phase symbol), plus two arbitrary reference space dimensions.

While only a single layer of the system needs representation in the (phi, phase symbol) dimension, a relatively broad region needs to be covered in x, y, and z. A simple choice of region to model would be a thin, rectangular hyperbox, illustrated in three dimensions in Fig. 7-1. The box height, s, is the (phi, phase symbol) period of the wave structure.

Waves at the top and bottom of the hyperbox would wrap around. To prevent waves from escaping, the sides could be treated as mirrors. Of course standing waves in a cavity are strongly influenced its shape. (A contained wavicle might be seen to behave like a quantum-mechanical particle in a box.) A hyperbox with an irregular footprint in the reference space might give a better approximation of waves evolving in an infinite space.

Another possible way to maintain the waves would be to also wrap them from side wall to opposite side wall, instead of reflecting them. Further strategies could be used to reduce the regularity of the "cavity. For example, different sections of a given side could be wrapped to sections of various other sides. Instead of wrapping directly across, opposite sides could be wrapped with a twist. Wrapping and reflection could be combined. (Reflection is essentially wrapping a side to itself.) Etc . . .

The medium, stuff, could be represented either as a continuous fluid, or one with discrete, particle-like constituents. For a realistic simulation in four dimensions, the required number of particles or fluid elements is huge -- almost certainly more than 10. (Enough to challenge a massively parallel supercomputer. ) Modeling an analogous three-dimensional system would cut the computational demands greatly.

Something similar to wavicles, with conical rather than hyperconical wavefronts, might arise in 3-D systems. However, if such patterns occur, their associated (phi, phase symbol) flows would vary as 1/r, rather than 1/r, giving them very different dynamical properties. Because wavicles depend for their existence on interactions with others, lacking the same dynamics, their analogues may not form. Even so, basic questions about the behavior of 4-D wave systems should still be answerable from three-dimensional experiments. (For example, questions 1 and 2 above.)

Probably the biggest obstacle to constructing an accurate model is the fact that the specific characteristics of stuff are unknown at this point. Like real fluids, the behavior of stuff may change abruptly at critical points. From the example of ultrasonic cavitation bubbles in pure water, stuff inside a wavicle core may have sharply different properties.* A possible approach to modeling wavicle formation would be to take an arbitrary set of balanced flow waves, and "seed" it with hyperbubbles, aligned with the (phi, phase symbol) axis. (The stuff inside these could be assigned a much higher wave velocity, for example.) Waves might nucleate around these, forming wavicle-type patterns, with hyperbubbles as cores.

Zabusky and Kruskal's modeling of a one-dimensional, repeating wave system was very illuminating. In higher-dimensioned systems like this one, it seems likely that richer forms of self-organization will be found. Whatever the wave behaviors may be, it's certain they'll be interesting.

Section: 8. The Course of Physics p89 Contents

All of modern physics is built on Einstein's interpretation of special relativity. Included is his view that, a priori, systems with preferred frames, like Lorentz's, must be ruled out. (In contrast, Lorentz was willing to concede the possible validity of Einstein's space-time approach.) In the early years, this exclusionary position was criticized by leading theorists. Sommerfeld, for example, called it "unhealthy dogmatism. However, after the apparent confirmation of Einstein's general relativity, his views were adopted by the physics community at large.

The various founders of quantum mechanics unanimously took space-time as its framework. In his stand against the ether, Einstein had argued we should not speak of things that can't be measured. Heisenberg, Bohr, and others extended this philosophy also to quantum mechanics. Their Copenhagen interpretation says that, for the same reason, we shouldn't speak of hidden variables. This viewpoint found its ultimate expression in Bohr's statement that the quantum mechanical microworld "doesn't exist".

As we know, Einstein was dismayed by this, and took a lonely (and courageous) stand in defense of the principle of causality. Eventually, a talk with Einstein turned Bohm against the Copenhagen interpretation, and spurred the development of his hidden variables theory. Bohm's success also inspired de Broglie to resurrect his related "pilot wave" theory. Neither was endorsed by Einstein, however, who saw a conflict between his own conception of relativity, and the non-local effects described by Bohm.

Both de Broglie and Bohm were devout believers in Einstein and Minkowski's space-time. However, Bell has noted that their theory appears to require a preferred frame of reference.

He writes:

I think that conventional formulations of quantum theory, and of quantum field theory in particular, are unprofessionally vague and ambiguous. Professional physicists ought to be able to do better. Bohm has shown us a way. It will be seen that all the essential results of ordinary quantum field theory are recovered. But it will be seen also that the very sharpness of the reformulation brings into focus some awkward questions. The construction of the scheme is not at all unique. And Lorentz invariance plays a strange, perhaps incredible role . . .
...I am unable to prove, or even formulate clearly, the proposition that a sharp formulation of quantum field theory, such as that set out here, must disrespect serious Lorentz invariance. But it seems to me that this is probably so. As with relativity before Einstein, there is then a preferred frame in the formulation of the theory . . . but it is experimentally indistinguishable. It seems an eccentric way to make a world.

Bell further points out the legitimacy of a preferred reference frame in "How to teach special relativity" , where he advocates the approach of Lorentz and Poincaré. In his long search for a unified theory, Einstein followed a belief in the underlying simplicity of physical phenomena. He said "If the answer is simple, God is talking.

He also looked to geometry as the source of this simplicity, believing that natural phenomena should be describable in geometric terms. His early paper, "On the Electrodynamics of Moving Bodies, showed that, in a space-time representation, electric and magnetic fields are exactly the same. Einstein took this unification as proof of space-time, and an essential step toward a unified field theory. Still, space-time geometry has not delivered such a theory. In accordance with Einstein, it is now generally held that proper mathematical descriptions of relativistic systems should be "manifestly covariant.

That is, they should make no reference to any sort of preferred frame. However, even in classical mechanics, this leads to difficulties. According to Dirac , we now know that "the Hamiltonian form for the equations of motion is all important.

(His italics.) On this representation of mechanics, Goldstein's graduate text observes:

As with the Lagrangian picture in special relativity, two attitudes can be taken to the Hamiltonian formulation of relativistic mechanics. The first makes no pretense at a covariant description but instead works in some specific Lorentz or inertial frame. Time as measured in the particular Lorentz frame is then not treated on a common basis with other coordinates but serves, as in nonrelativistic mechanics, as a parameter describing the evolution of the system. Nonetheless, if the Lagrangian that leads to the Hamiltonian is itself based on a relativistically invariant physical theory, e.g., Maxwell's equations and the Lorentz force, then the resultant Hamiltonian picture will be relativistically correct. The second approach, of course, attempts a fully covariant description of the Hamiltonian picture, but the difficulties that plagued the corresponding Lagrangian approach are even fiercer here. ...there seems to be a natural route available for constructing a relativistically covariant Hamiltonian. But the route turns out to be mined with booby traps.

Goldstein also shows that the preferred frame method easily gives a concise, non-covariant Hamiltonian (Eq. (5-16) in this paper). Applying Einstein's own dictum about the simple answer, in this case it says that manifest covariance is wrong.

As mentioned earlier, space-time suffers other drawbacks in comparison with the preferred frame approach. One is its inconsistent treatments of linear and rotational motions. Although forbidden for linear motion, a preferred frame defined by "the fixed stars" remains for the rotational case. So, instead of a single reference frame, there are two very different types. Again, an egregious shortcoming is that space-time by itself can't account for the direction of entropy. Since its time dimension must be exchangeable with its spatial ones, time necessarily has a bidirectional character, with no favored direction.* Another parameter, like the unidirectional, independent time of the preferred frame approach, is required. Thus Minkowski space-time avoids neither a preferred spatial frame, nor apparently an independent time -- this despite its added geometric complexity.

In the present theory, Einstein's space-time view is abandoned. However, several of his most basic ideas remain: That the universe is fundamentally simple and describable in terms of a special geometry. His requirement of causality. And the same relativistic principles are followed -- both Poincaré's principle of relativity, and Einstein's principle of equivalence. Some other key ideas of this theory are these:

1.) Contrary to the prevailing view, transverse wave phenomena can arise in continuous fluid media. Where there are nonlinear wave structures, transverse waves of interaction can arise within the waves. Such waves of interaction are taken to represent electromagnetic ones.

2.) The unlimited velocity of matter waves is directly explainable on the basis of a repetitive four-dimensional wave structure. Its geometry is Euclidian, and the waves are redundant in one dimension, (phi, phase symbol). (Consequently, this dimension isn't obvious to observers.) When the wave movement parallels, the apparent 3-D velocity is infinite.

3.) The wave medium is an elastic fluid. Hence its waves are acoustic and have a characteristic 4-D velocity, c, under standard conditions. Moving wave-based reflectors, aligned with the (phi, phase symbol) axis, transform the waves relativistically.

4.) The scalar potential can be exactly accounted for by flows in the (phi, phase symbol) dimension, from their refractive and reflective effects on matter waves.

5.) These flows are driven by flow waves, balanced such that net flows only arise in the (phi, phase symbol) dimension. This preserves the relativistic character of the system, and also accounts for the vector potential.

6.) Like other nonlinear waves, those of this system are self-organizing, forming additional patterns, called "wavicles, within the overall wave structure. These behave as elementary particles. Involved are approximately hyperconical waves, reflected at a central "core" region where the amplitudes are great. (Wavicles are also the above wave-based reflectors.)

*It's sometimes argued that this problem can be resolved by assuming that, when the time dimension of space-time is reversed, entropy is too. The reversed case would be perceived as normal by observers, since their thought processes would run backwards also. However, since space-time is symmetrical, this still provides no basis for the acknowledged difference between the forward and reverse cases.

7.) A wavicle's components are flow waves. The resulting (phi, phase symbol) flow pattern corresponds to the electromagnetic potentials of a charged particle. Noninverted and inverted patterns represent corresponding particles and antiparticles. Quantized charge and energy result from a characteristic limit to the (phi, phase symbol) flow attainable at the core.

It is the whole of space that implodes in the logarithmic phi ratio, however, at the core is the place where phi-space implodes and passes through, or is reflected, as EM waves. In other words, the Anu are now instantly communicating throughout space, in a very specific, logarithmic ratio or relationship.

8.) Wavicles are inherently non-local phenomena, interdependent on other wavicles and their reflected waves for their existence. Their behavior is that of extended objects, of arbitrary extent. Like solitons, wavicles move and interact as wholes.

9.) The synchronous pulsation of a wavicle's standing wave field can be characterized in terms of "Moiré wavefronts, representing surfaces of equal phase. These correspond to de Broglie waves, and define the quantum mechanical behavior of wavicles. Nonlinear coupling of the pulsations, both within and between wavicles, is taken as the underlying mechanism.

10.) In concentrations of matter, the average (phi, phase symbol) flows of oppositely charged wavicles tend to cancel at large distances, like the electric fields of conventional charged particles. The underlying waves do not cancel, however. Consequently, intermittent flows arise, with an rms amplitude varying, like the individual wave fields, as 1/r from the center of mass. These intermittent flows decrease the effective velocity of waves; i.e., the value of c is locally reduced. This slowing is taken as the basis of gravitation. Since the 4-D velocity, c, determines the rate of all physical processes, these are observed to slow also, as in Einstein's general relativity. In this case, the gravitational bending of light corresponds to ordinary refraction.

In statement 10, above, I have to question the assumed basis of gravitation. If it is a correct premise we should see it developed and substantiated, in the future.

11.) The wave medium, stuff, is assumed to have a fractal-like character, with additional wave structures at much larger and smaller scales. As in FPU recurrence, wave energy can be gradually transferred up or down between scales, changing the effective temperature or density of stuff at those levels. Because acoustic wave velocity depends on these parameters, c is also allowed to change over time. (Again, this determines the rate of physical processes at the macroscopic scale.) An increasing c is proposed as the cause of the Hubble redshift seen in light from distant galaxies.

The wave medium, the Anu is fractal.

Until recently, the Hubble redshift has been taken as final proof of Einstein's general relativity. The effect was thought to be readily explained on the basis of a finite, expanding universe, allowed by a curved Minkowski space-time. However, the original Big Bang model is contradicted now by a variety of observations. An example cited previously is the distance to the galaxy M100 measured by the Hubble Space Telescope. Based on the standard Big Bang model, this puts the age of the universe at about 8 billion years. This is under the estimated age of the oldest stars.

Above, the Big Bang also cannot happen in a universe built upon the toroidal Anu as basic building block. Each so called point of space is an Anu toroid. Each toroid spirals space through its center, as light, at light velocity, controlled by its leading phase waves. No bang ever happens at the micro or macro levels. The only things banging through each center is energy and consciousness. This is what is called "The center of universe is everywhere". At this level of raw space, it is unconscious and limited in organ.ization.

It's also difficult to reconcile the Big Bang with the discovery of very-large-scale structures, such as the Great Wall or the Great Attractor. Most importantly, there is the flatness problem. From the observed distribution of galaxies, the large-scale curvature of the universe is relatively small, or nonexistent. Again, according to Linde, the discrepancy between the observed curvature and that predicted by general relativity and the Big Bang is roughly sixty orders of magnitude. Astronomical observation, once taken as confirmation of Einstein's general relativity, now speaks against it.

In contrast, the theory presented here allows a macroscopic universe older than its stars, with mature structures, and predicts an inherently flat geometry. (In addition, it predicts new nonlinear wave effects, which may be verifiable through computer simulation.) There is also the broad unification of physics, in a much simpler paradigm. For the first time, relativity and quantum mechanics are joined. Both the wave and particle aspects of elementary particles find a single, coherent representation. And there appears to be a truly unified physical basis for the known natural forces.

Above, I don't believe I've seen a wave/particle defined by Ben's theory.

Einstein argued that a preferred frame should not be hypothesized if it can't be identified experimentally. However, at least a very special case of linear motion is precisely defined by the cosmic microwave background. This apparently corresponds to the overall system of celestial matter -- the same one Einstein took as the preferred frame for rotation. Since there presumably is some coupling between its different scales, it's no less reasonable to take this as the frame of our wave medium, stuff.

Above, we can ask, "What is the correct reference frame of the Anu, that spiraling bit of space"? There are at least 4, documented, reference systems in universe.

Physics has seen so little fundamental progress, for so long, it's often remarked that "physics is dead". Is it proper, then, to continue taking our most fundamental physical assumptions on faith? Shouldn't we have the courage to explore valid alternatives, such as the relativity of Lorentz and Poincaré, and the quantum mechanics of de Broglie, Bohm and Vigier? To solve a maze, sometimes it's necessary to double back and take a different path.

Why are you still sittin there. Get to work.

REFERENCES:

1. The Spin Wave (GIF)
2. 134 The Anu Building Block
3. A New View of Universe by Ben Kristoffen (PDF)
4. 99.79.1 The Enneagram
  99.79.16 The Enneagram
  99.79.17 The Enneagram
  99.79.18 The Enneagram
  99.79.19 The Enneagram
5. 131 The Toroidal Universe
6. 53 Evolution and Creation
7. Ray Tomes
8. Double Sets of 14 Pairs of Music Scales (GIF)
9. Welcome to Superluminal Phasewave Civilization (PDF)
10. Symmetry and Resonance in Periodic FPU Chains (PDF)
11. Solitons, A Brief History (PDF)
12. 99.58.11 Ellipses
13. 99.72.11 Egg Shapes
14. CreatMomentum by Byers: Energy Upshift via Mixing
15. Gravity Shadowing- Byers
16. John Worrell Keely
17. 136 Trinary Relativity Theory
18. 145 Gravity Probe B

Impossible Correspondence Index