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The Omega Zero of Accelerating Expansion

Part Two:  Introducing Two Opposing Types of Order


Gevin Giorbran
January 24, 2004

II. Grouping Order and Symmetry Order

Much in the same way our very existence seems an impossibility, as if instead there should be nothing at all, so also are we perplexed at the order that is such an elementary part of the universe in which we live. There should instead be disarray, it seems much more logical, for we naturally consider the infinity of chaotic universes that could exist in place of the one ordered and systematic universe that is present. Yet perhaps our universe is not unordinary or an exception to what should be, but rather we have made a fundamental mistake in how we conceptualize order.

At present order has a complex yet singular meaning. Order is most commonly defined as a grouping of separate elements or a regular arrangement of objects, colors, or events in time. Although the following is a more accurate and fully developed comprehension of order, what follows is by no means complex or difficult to imagine. There are two principle classifications of order in nature, not merely a single order opposing disorder [9][10][11]. Two orders blend to produce all the diverse shapes and patterns that are observed in nature. Each has its own distinct direction of increasing order and an individual increase in either type produces opposite results.

The more commonly recognized type will be specified as Grouping Order which can be understood as any class, or similar kind of thing grouped together, and thus located in a specific area, or separate place apart from another group. The second type of order is identified as Symmetry Order, which if we simplify its definition to extreme, is an even and regular pattern or arrangement in which all different types of things are combined and distributed uniformly throughout a frame of reference. In extreme this type of order produces a perfectly smooth and uniform pattern. The most relevant clarification to be made is the opposition of these two types. Only as the two orders combine, and cancel the extremity of each, can they produce all the diverse shapes and patterns that we observe in nature. In fact it can be shown that each type of order is disorder to the other, which therein forces a redefinition of the very meaning of order and disorder.

Grouping in reference to similarities is the most commonly recognized order. The prototype example is a grocery store exquisitely divided into multiple sections where each type of product is then also attractively grouped. In nature, the sun and planets together form a group, a solar system. Stars are grouped into galaxies, while galaxies group into clusters and superclusters. Grouped elements create gases, metals, fluids. Elements produce molecules, and grouped molecules produce compounds. The Earth is a collected mass of groups and sub-groups of materials as are all the planets, as is the sun. All such order and structure exists in stark contrast to another universe we might imagine void of grouping, a cosmic soup of all particles blended uniformly so that there are no stars or planets, or further still, the absence of particle form and instead only a smooth matter plasma spread evenly across the entire landscape.

Yet just as groups of elements and solar masses give the universe its definition and bring about order as we know it, grouping is not the only way in which the universe is organized. The universe also utilizes mixing to produce different degrees of uniformity, balance and the formlessness[27]. Elements mix to form molecules. The oceans, the soil, and atmosphere are each compounds of many unique materials. Rock, glass, wood, soil, plastics, and metals such as bronze and steel are all various mixtures of atomic materials. And on the largest scale there is an isotropic distribution of galaxies and dark matter. Yet it is recognized that after such discussion the exact character of mixing and uniformity remains vague.

Piet Hut has said "the paradox of limits lies in the fact that limits combine two opposite functions: setting apart and joining[28]." Likewise, opposite directions of transformation are not uncommon. Particles can only attract or repel, space can only expand or contract, and material form can only create pronounced groups (lumpy) or blend homogenously (smooth). To explain this more clearly, the most lucid analogy I have found that establishes one order apart from the other is the simple method in which a chess or checker game is set up. In preparing the game, black and white game pieces are separated and grouped together. Each color is grouped and set in a location at opposite positions upon a board.

Yet now we change our focus to consider the checkerboard on which the game is played out. Serving as a moderately neutral background, the admixture of colored squares spaced evenly in alternating rows is certainly also a distinct expression of order. The most evident property of this archetypal checkerboard pattern is its overall uniformity and balance produced by the symmetrical placement of squares. This balanced order exists in stark contrast to the set pattern of game pieces which are not integrated but divided purely into two separate groups.

The distinction between these patterns is ever more evident as we consider extremes. If instead the individual squares of the checkerboard gravitate together by color then they would unify on each side of the board forming two solid colors, now grouped rather than mixed evenly. How might we continue to increase the grouping order produced in this way? To push this pattern further would require that we deflate the frame of reference and so increase the density of the particles of each side. As the volume of the reference frame collapses the separated groups move toward an extreme of becoming two points, the extreme of grouping order.

What then is the reverse process? Rather than unify the two colors into separate pure groups, the opposite process of creating symmetry order is to divide and blend the colors evenly, creating the checkerboard pattern. Of course each square represents a measure of grouping the two colors. So to push this pattern toward its own extreme we subdivide each square and evenly distribute the finer pieces. Done repeatedly this moves the pattern toward becoming increasingly variegated and smooth. Eventually the separate colors merge and transform into one color, like mixing two colors of paint. In this direction of order, as many individual parts are either dissipated, stretched, or merged, into a singularity, all grouping order is sacrificed. In extreme this frame of reference expands to engulf all possible space. The final product of symmetry order is a uniformity neutralized of difference and form, yet still the uniformity is the sum of its parts. The chemist Dr. Shu-Kun Lin has exposed similar issues in regards to how we conceptualize order and symmetry[26].

A key to understanding and appreciating the subdued nature of symmetry order is in recognizing that that extremes of balance, uniformity, and neutrality, are produced from the union of groups or particles into the reference frame, rather than a destruction, cancellation, or absence that leaves the reference frame empty. Order is plainly evident in any chequered pattern, and our failure in the past has been in not relating that order directly to the less apparent order of uniformity, the order David Bohm identified as Implicate Order[27], which has just been shown to be the extreme or intensified case of visible measures of symmetry order.

The very nature, the tendency of extreme symmetry order is toward formlessness which is starkly overshadowed by the pronounced nature of grouping order, this being why it is not yet fully recognized. In extreme, the patterns of symmetry order unify with the Implicate Order identified by David Bohm. The patterns of symmetry order are by nature indicative of an underlying order, in Bohm�s words, �a total order is contained in some implicit sense, in each region of space and time.� Examples of extreme yet visible or detectable symmetry order include Einstein-Bose Condensate, the particle-less form of an isotropic dark matter, the expansion and flattening of the universe, the even distribution of galaxies, and finally ordinary space, which not only utilizes balance to maintain a formless uniformity against a consortium of virtual particles, but notably also maintains uniformity against the infinity of potential universes.

III. From Grouping Order to Symmetry Order

The observable history of our universe most evidently records the divergent evolution from an extreme state of grouping order to an intermediary transitional phase between both orders. This phase in any transposition from grouping to symmetry order can be considered rather plainly if we imagine setting up a checkerboard game and move the game pieces out of their initial grouping order positions toward a pattern which identically matches the symmetry order of the board of squares. As we randomly select game pieces to move toward our symmetrically ordered objective, at any point in time along this procedure until it is completed there exists irregularities within both orders or what we would normally consider to be a measure of randomness or disorder. In fact no general disorder exists, since the condition of any such microstate can only be retarded or advanced in either type of order. Interchanged adjacent squares in a chequered pattern inevitably produces an isolated increase in grouping, in which case the symmetry order of the pattern is lessened. Likewise, the decay of grouping inevitably integrates opposing groups and balances the reference frame toward uniformity. Surprisingly, yet quite congruent with a mysteriously ordered universe, is the fact that a concept of general disorder has no application to nature.

There is no such thing as general disorder, only irregularity. It is inaccurate to consider any pattern as exhibiting a general disorder. Any definition whatsoever is a form of grouping order. Any lack of form is a product of symmetry order. And in this construct of two orders, the order of one type is the disorder of the other type. It follows that all patterns are produced from a combination or synthesis of two separate types of order, the only exception being the two extremes or highest order of each type.

IV. Integrating Two Orders into State Space

The second law presently describes the dissipation of materials as an increase in disorder. That an evolution is taking place, that entropy is increasing, or that equilibriums exist, is not herein doubt, however, a gas that dissipates from a condensed grouping, spreading evenly throughout a room or any frame of reference in which the gas escapes from confinement, until reaching an equilibrium, is not at any point a case of increasing disorder but rather an increase in the balanced distribution of the particles throughout its reference frame, and therefore constitutes an increase in symmetry order. Any short-term settlement of a system into an equilibrium state can be associated with the local basin of attraction within the contrast gradient. While on a much greater time scale under a much more gradual evolution we recognize that all systems in a process of integration are converging together toward the same macrocosmic equilibrium.

Once these concepts are accepted and applied, the complex struggle between two orders, and the multi-faceted transition from grouping to symmetry is visible in everything from red hot flowing materials that solidify into rock or steel, to droplets of water which crystallize into a snowflake. At ultra cold temperatures, order is less complex than a snowflake and consequently expresses the simplicity of the archetypal checkerboard pattern. At temperatures near absolute zero, materials such as cesium gas particles even organize into orderly columns and rows. Less than a millionth degree away from zero the definition of the particle itself is lost as atoms blend into a unified Einstein-Bose condensate[29], perhaps the most evident expression of symmetry order. Even hidden within the symmetry of a seemingly empty space, virtual particles leap out and back, when for an instant grouping order emerges spontaneously from formlessness until the balance of symmetry order returns.

To integrate two types of order into the SOAPS model requires only that we associate the extreme of grouping order (the example of checkers divided by color into two pure groups) with the positive alpha and the negative alpha states, and we associate the extreme of symmetry order with absolute zero and the omega state.

Figure 9: Integrating Two Orders

What I would like to do now to further reinforce the unifying nature of symmetry order is introduce an initially surprising switch in mathematical values. Ordinarily we see the world from a perspective derivative of the definition of grouping order. Much if not all of modern physics is based upon the axioms of grouping order. We gauge the universe according to grouping order and see the world from its definition oriented perspective. Grouping order is literally the order of finite objects or thingness and dictates how we presently acknowledge physical form. We recognize only dualistic forms as thingness. The absence of definition and multiplicity is to us zero things and we judge that zero, the uniformity of symmetry order, to be a nothing, even though in lesser measure we easily denote the chequered pattern, Einstein Bose Condensate, or the even distribution of galaxies, as order.

Generally we see the physical world as more than nothing. The universe and the integrity of form is defined differently from this perspective of symmetry order. Rather than viewing the substantive world as being more than nothing, symmetry order reveals a perspective where matter is less than a uniform, seemingly empty, space. In this new perspective, what we ordinarily define as empty transforms to become a composite of all finite possibilities. In extreme, perfect symmetry order is the ultimate singularity; a nothing that is everything, a oneness of all times, all thought, all things, located not in our cosmological past but in our future.


Part Three: Symmetry Mathematics



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