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The choice of shape depends entirely on the type of force involved: When the forces of surface-tension are involved then the cell tries to minimize the surface area. When the force involved is that of "negative pressure" then the tendency is to maximize the surface area. The truncated octahedron has a surface-to-volume ratio of 5.315; the rhombic dodecahedron has a surface-to-volume ratio of 5.345 (both expressed in terms of the geometrical invariant: ratio = S/V2/3). The difference is subtle —so small that it only appears in the 3rd significant digit. Nevertheless, this difference means that for equal volumes the truncated octahedron has less surface area than does the rhombic dodecahedron. Thus, surface tension cells, striving to minimize their surface area, take the shape of truncated octahedra. While negative pressure cells, striving to maximize their surface area, take the shape of rhombic dodecahedra. Soap bubbles are considered surface tension cells; thus they tend to be shaped as truncated octahedra when packed together. The cosmic cells of the DSSU are negative pressure cells. The negative pressure is the manifestation of the process of space expansion (according to Postulate #1 of DSSU theory). Space expansion is the primary-process of the universe. Thus the cosmic cells of the DSSU tend to be shaped as rhombic dodecahedra (and not as truncated octahedra).[5] A word about soap bubbles. It should be pointed out that soap bubbles are not regular in shape even when experiments strive for constant volume. They tend to be highly irregular tetrakaidecahedra.[6] The reason is that gravity induces film thickness distortion. However, it is predicted that under weightless conditions soap bubbles will be shaped as truncated octahedra (if equal volume bubbles are produced). The truncated octahedron is, of course, a tetrakaidecahedron.
Back to the cosmic structural cells. Space expansion sustains a central void region. Why this process is equated with negative pressure is not easy to explain. It certainly seems counterintuitive but such is the nature of dynamic space. It may be of help to think of the region as being under tension (space is being ‘pulled’ apart, as it were). There is a tension across the cell (along any diameter). In a moment we will see what is aiding this ‘pulled’ action. Each cell, with its void, interfaces with twelve others as each cell tries to maximize its volume and surface area. The result is a twelve-faced structure —the rhombic dodecahedron. The result is a cosmic cell with fourteen nodes. Each node of this cell is a center of gravity —the center of gravity of a galaxy cluster. The fourteen galaxy clusters are linked by 24 filamentous arms. These arms are simply the extensions of the various galaxy clusters. The entire network surrounds the central cosmic void. (See Fig. 2.)
Now mentally draw lines through the structural cell and join opposite centers of gravity; the tension mentioned earlier should immediately become self evident. The tension is always present since the nodal galaxy clusters never come together. Always keep in mind that the overall cell-size has a certain degree of stability. And speaking of cell size: Although the cells are discussed in rather casual terms, one should not lose sight of the enormity of the scale involved. All cosmic cells have dimensions in the range of 300 million lightyears.
The cell nodes are logically the centers of
gravitational cosmic cells. 3 The Cosmic Gravitational CellsA striking feature of the structural cell is that there are two distinctive types of nodes —distinguished by the number of arms. There are major nodes and minor nodes; six of one and eight of the other. Now here is the amazing part: when one relates the nodes to respective galaxy structures then one finds a FOUR-branch galaxy cluster at minor nodes and an EIGHT-branch galaxy cluster at major nodes! We have here the underlying reason for variation in size and density of galaxy clusters. (The Platonic dodecahedron, of course, has all its nodes identical; and for other reasons will not work for modeling the universe.) Real cosmic cells are never isolated; nodes are always shared. And geometry requires that these shared nodes must have either four branches or eight branches as shown in Fig. 3.
Obviously, there must be two types of gravitational cells. The geometry demands there be a distinct shape for each of the two types of nodes. The four-armed node requires a tetrahedron. The eight-armed node calls for an octahedron. These two shapes, when combined, will totally fill 3-dimensional space (as they must). But unlike the cosmic structural cells, the gravitation cells have no visible boundaries! The tetrahedral gravitational cell. The center of gravity of a minor-node galaxy cluster coincides with the geometric center of the tetrahedral cell. The four arms of the cluster pierce the four sides of the tetrahedron (the arms are more or less perpendicular to the tetrahedral faces). The vertices of the tetrahedron extend deep into the four surrounding voids. Fig. 4 attempts to show this arrangement; the fourth void (and fourth vertex) is hidden from view.
The next figure (Fig. 5) provides representations (in perspective) of the tetrahedral gravity cell; its three images focus on the cell’s geometry, the cell’s gravitation flow lines, and the cell as an isolated gravitational field. The flow lines represent the streaming of aether-space; they also represent the trajectories of comoving matter. The flow lines clearly reveal the cell’s four internal lobes. The four lobes act to funnel the space-and-matter flow towards the regional center of gravity.
Some readers may be wondering, Why doesn’t the cell (or gravity field) collapse over time? The short answer is that the voids keep on expanding. That is, the voids are forever supplying newly expanded aether-space to feed the flow. Furthermore, matter itself is continually precipitating from, and within, aether-space; further feeding the flow. An idealized dynamic image of an isolated tetrahedral gravity cell is shown below.
The following drawing (Fig. 7) shows the shape, the lobes, and the trajectories of the octahedral gravitational cell.
4 How the Gravity Cells Fit TogetherFor a two-dimensional representation of how gravity cells fit together we could use the trefoil of Fig. 4 and tile a sample region. The hexagon is readily revealed as shown in Fig. 8 below. The hexagon, of course, is the two-dimensional representation of the rhombic dodecahedral structural cell.
Now what about the tetrahedral and octahedral volumes? Even though these volumes consist of the three types of dynamic space —expanding, flat, and contracting— standard theories alone fail utterly. The General Theory of Relativity struggles with the basic interaction and configuration of the very same expanding-, flat-, and contracting space. Meanwhile, Standard Cosmology is busy hypothesizing and adjusting a growing number of parameters of its single-cell universe. Multicellularity has not yet been recognized! General relativity measures the geometry or curvature of each volume of space —whether that volume is expanding, flat, or contracting. But ...
You read that correctly. For the determination of the shape and topology of our Universe some physical understanding beyond standard cosmology, beyond relativity, is required! To say that relativity (a powerful mathematical theory) requires a physical something is a remarkable admission. Maybe what is required is that physical something missing from Einstein’s relativity theory; that essence substance often discussed on the Cellular Universe Website. Yes, understanding is within grasp. But what a long detour it has been ... If only Einstein, those many many years ago, had not discarded the physical aether; discrediting it as a superfluous relic of a pre-relativistic age. And this is why we turn to DSSU theory. It provides the vital pieces of the puzzle for just such a physical understanding. It tells us precisely how the three types of space “volumes fit together” to form the characteristic pattern of each type of gravity cell. And further, DSSU theory then tells us how those gravity cells “fit together to give the universe its overall shape —its topology.”
Here is a guide on how the tetrahedral and octahedral volumes fit together. Think of the center of a void as a reference point. A void, because of the geometry of the structural cell, is surrounded by 8 minor nodes and 6 major nodes. This, in turn, means that a void is surrounded by 8 tetrahedral and 6 octahedral cells. In fact a total of 14 gravity cells meet at the reference point at the center of a void. And the tetrahedral and octahedral cells do fit together. The tetrahedron and octahedron comprise what is called a dual space filling system.[8] In assembling the gravity cells it helps to realize, firstly, that they all have faces consisting of identical equilateral triangles; secondly, that octahedra meet octahedra edge-to-edge; thirdly, that octahedra meet tetrahedra face-to-face, and finally, that tetrahedra meet tetrahedra edge-to-edge. These rules, along with a bit of cerebral effort, permit one to visualize an assembly of all 14 fields. Use Figure 9 as a guide.
We normally think of the dodecahedral cell as being surrounded by twelve others. The reason is that we associate each of the twelve faces of one cell interfacing a corresponding number of neighbors. Actually our structural unit is linked to a total of eighteen others. The gravity cells do the linking; they provide the dynamic bonding.
We have established that there are 14 gravity cells associated with a structural cell. Let us sum the vertices of all 14 cells. Each minor unified field (tetrahedron) has 4 vertices that extend into 4 different void centers. Each major unified field (octahedron) has 6 vertices that extend into 6 voids. Total vertices is (8x4) + (6x6) or 68. Each of these vertices, of course, must terminate at a void center. We know that 14 of these vertices meet at the center of the dodecahedron leaving the remaining 54 vertices free to extend into the 12 surrounding units (the 12 units with which interfaces are shared). Each of these 12 dodecahedra receives 4 of the field vertices. This should be self evident purely from the fact that 4 nodal structures (of a rhombic face of a dodecahedron) are shared between adjacent dodecahedra. But this allocation can account for only 48 of the 54 external field vertices! Six of the field vertices projecting from the subject unit-universe still need to be allocated. It is not at all obvious; it happens that there are 6 additional unit-universes with which no interface surface is shared but with which one nodal structure is shared, respectively. And so, the 14 fields of a sub-universe join to a total of 18 surrounding sub-universes. Thus, the gravity cells of a sub-universe extend into the obvious 12 surrounding units and also into 6 other units —one at each of the 6 major nodal clusters.
5 Discussion of Unified GravityGravity alone might be driving everything ... —Nature 2003 July 3 [9]
Why are the cosmic gravitating regions referred to as unified gravity cells? There are several reasons. The fundamental reason is that two kinds of gravity effects are actually being combined. In technical terms the positive energy field of L (the cosmological constant) is combined with the negative energy field of conventional gravity (contractile gravity). When I say “combined” I mean they become separate regions of a single field. The logical reason is that a single definition of gravity serves to describe all regions of the cell. All regions of the cell are accelerating towards a common core —the heart of the gravity cell. The key word is acceleration. In a gravity field there must be acceleration. Aether-space is accelerating along the trajectories (we visualize them as flow lines) and likewise all the comoving matter. Another way of looking at the unifying definition is this way: Imagine placing a test object anywhere in the gravity cell. It will, over the long term, tend towards the nucleus of the cell. Sprinkle lots of test objects all over a vast region and notice the gradual taking-shape of boundaries of relative emptiness. The boundaries of relative emptiness separate the individual cells, as shown in Fig. 8 above. The isolation reason. Except for the exchange and flow of radiation a gravity cell is totally isolated from the rest of the universe. (In DSSU theory gravity is NOT considered to be a form of radiation.) No object, no massive galaxy, no matter how supermassive it may be, has any gravitational influence beyond its home cosmic gravity cell. There is a simple and dramatic way to describe the unifying feature of a gravity cell. A unified gravity cell defines that region of space (a more or less symmetrical region) in which any and all comoving bodies are on a common collision course. (See Fig. 10.) The field lines are the trajectories, the comoving paths —diverging in the Lambda portion of the gravity field and then converging in the contractile portion of the field. The nodal supergalaxy —the focus of the trajectories— is the common collision point. Bodies may temporarily deviate from the purely comoving paths, as in the case of interface interactions and collisions. But ultimately —always keeping in mind the enormous multi-gigayear time scale— the fateful paths resume and the final freefall collisions occur.
Implications There can be no doubt of the profound and far-reaching implications in the discovery that gravity and Lambda (G & L) act in harmony and, through that harmony, help sustain cosmic cell structure. Obviously, the discovery spells disaster for the conventional worldview. The concept of G & L in harmony is the key to a Pandora's Box of devastating consequences for all universe models based on general relativity. The naive notion that our universe can be coded in a pair of equations as if the universe is a single monolithic gravitational field is doomed. The hypersphere of general relativity, used to model the monolithic universe, will return to its obscure role as a mathematical oddity. Gravity fields that extend to infinite, as the old theories claim, are doomed. Doomed by quantized gravity ---gravity quantized into natural gravity cells. With G & L working in harmony to bring about cluster cohesion there is absolutely no need for mysterious dark matter. It means the demise of dark theories. We may finally witness the end of over 30 years of long fruitless searching; the end of speculations masquerading as science. Then there is the implication for the central dogma of 20th century cosmology: The expansion of the universe will seem pointless. If the cosmic cells don’t expand then surely there is no reason for the universe to expand. G & L are in harmony. This is the key. Lambda and gravity in their easily understood manifestations —space expansion and space contraction— are in equilibrium. The treatment of G & L as harmonious effects leads to finite gravity fields. These lead to steady state cell structure which leads to a nonexpanding universe ... which leads us to a further implication. And this one will exact a heavy toll. If, as we have seen, the universe does not expand then neither does it evolve. Of course, processes and systems (and countless subsystems) within the cells are perpetually evolving, but the universe itself is not evolving. The Universe simply is. Theories that say otherwise will, in the light of reality, become untenable and will not survive. The evolving universe is not supported by logic and not supported by observations; it is untenable. But guess what? All Big Bang universe models are scenarios of evolving universes. In fact all expanding universe models are classed as evolving universes. Academic cosmology is a grand collection of theories, hypotheses, and speculations —all based on a common theme. Each member of the collection represents one or another aspect of the evolving-and-expanding universe. The focus is on fine-tuning the abundant parameters of their exploding-and-changing universe. Almost never are the fundamentals questioned. Theories and research papers are endlessly cross-referenced and stand in support of each other and the official theme. What you have then is a vast collection of inbred theories nurtured by Academic Cosmology. A most unnatural situation. No wonder outspoken physicist and cosmologist Sean M. Carroll questions the naturalness of the current Big Bang model[10] and refers to it as the preposterous universe. In fact he sums up his extensive paper[11] with a section heading in boldface lettering: "Conclusions: the preposterous universe". Now the meaning of preposterous is, according to my Webster dictionary, quite clear: "Contrary to nature, reason, or common sense; utterly foolish; absurd." And there you have it, without any personal bias, 20th century cosmology is contrary to nature!
The seeds of the new cosmology have been planted. The revolutionary concept of the intrinsically cellular cosmos is growing. Meanwhile, the breeches in the old cosmology grow ever wider; its claims undefendable; its flaws unrepairable. The overthrow of the “preposterous” expanding universe by the natural cellular cosmos is the 4th revolution of cosmology. * * * *
090818 Copyright © 2009 by Conrad Ranzan E-mail: DSSUresearch@aol.com www.CellularUniverse.org
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