was honored by a link in the April '99
On Modeling the Macrocosmic Structure of State Space
I: On temporal and spatial boundaries; radical extremes of gravity, space, and time can be included in any conceptual understanding of all possible states to establish a boundary system and thus a definite model of states infinite between radical extremes.
This modeling of state space is derived from a specific comprehension of order, a model improved over the concepts developed by Boltzmann in his interpretation of entropy. This approach is unique in that it identifies three radical extremes of possibility instead of the previous single extreme of high order, as well as extreme states of contrast adjacent a density gradient, therein accomplishing a definitive model meant to express the macrocosmic structure of all states. The initial addition to aggregate state space is an absolute flat space.
Ludwig Boltzmann  was the first to imagine that it is possible to model the realm of possibilities in the development of what became the second law of thermodynamics. To explain entropy, Boltzmann determined that the disorder of a closed system increases due to a greater measure of possible disordered states compared to ordered states.
Boltzmann envisioned that an axis exists between order and disorder. In one direction along that axis, the number of ordered states decreases toward a state of highest order. In the other direction, the number of disordered states increases indefinitely. If we assume an aggregate perspective of Boltzmann's model, we can generally identify a wedge shaped scale, closing at the end of highest possible order, where we must presume a single extreme state, while in the other direction there is an endless and indefinite expansion of increasingly disordered states, apparently without end.
Once Boltzmann introduced the second law, others assumed this same conceptualization of order, and came to accept this wedge- like model of all possible states as a general description of nature.
The general probability distributions deduced from the wedge model are simple. It is well accepted that the probability of an always greater set of disordered states influences physical events and is the impetus behind increasing entropy and the second law, while many accomplished physicists, such as Stephen Hawking  and Julian Barbour , openly claim this macrocosmic formation to be responsible for the arrow of time.
2. Opposite Extreme States
In the wedge model the direction of increasing order is generally correlated with increasing density, and although the nature of an absolute extreme high order state is not widely agreed upon, without departing from Boltzmann's wedge model, I will here recognize an infinitely hot and dense condition as the extreme or most ordered state, beyond which no other possibilities exist.
The first proposed addition to a macrocosmic formation of state space (MSS) requires very little orientation. The extreme opposite of a condition of infinite density is simply a condition of absolute zero density. Zero density would require a zero energy level, a zero mass, and zero curvature. Now departing from Boltzmann's wedge I will recognize this absolute zero state as an absolute flat space (AFS) and integrate it into the order-disorder scale, as the most extreme state of increased entropy. The initial proposal then is that a single state of AFS exists beyond the bulk of disordered states and can be understood as a boundary limit in aggregate state space.
The initial hurdle is an almost instinctual rejection to the notion of an empty space, which perhaps Einstein instilled in the academic community. However, the effort here is to consider radical possibilities and consider how they might influence space-time. What is considered a possible state in this case can not be evaluated in reference to what is thought to be possible of conditions of space-time, future or past.
Simultaneously, I don't wish to propose an AFS as an abstract concept but rather as a genuine physical possibility. Cosmologists are presently grappling with evidence for accelerating cosmological expansion, and I would argue, we collectively have yet to consider adequately its consequence. What kind of future universe will accelerating expansion produce? A real possibility exists that an ever increasing expansion rate could result in every point in space expanding away from every other point in space, therein stretching the mass and energy density of space to absolute zero.
The reader can be assured in that the AFS state being proposed is not synonymous with the pre-scientific notion of an empty space in which objects can exist or travel. AFS requires that no observable physical objects or energies exist definitively in its dimensionality.
Noting that the universe is continuously expanding toward absolute zero, and may even be accelerating toward a condition of AFS, I propose that AFS be recognized and integrated into the scale of order-disorder, certainly not as a vacuum state located in our past of increasing order, but rather AFS belongs as a singular extreme condition beyond the bulk of all disordered states, an extreme which like the singularity of the big bang is also a boundary limit, beyond which no other possibilities exist. For this reason I will occasionally refer to the dense singularity of the big bang as the alpha state and to AFS as the omega state.
This integration of flat space into the set of all possible states (SOAPS) first produces a definitive gradient of all possible states, thus eliminating the disturbing idea of an indefinite extension of disordered states. Second it exposes clearly a boundary condition along the order-disorder axis in the opposite direction of the alpha state. The set of all possible states is then infinite yet bounded. Thirdly, and most importantly, it requires that the quantity of disordered states decrease as the order-disorder axis approaches the single state of AFS, just as the quantity of ordered states decreases along the axis approaching the alpha state. We can thus recognize a wedge shape at either end of the space of all possibilities.
3. The recognition of a primary attractor and its macrocosmic implications
It is widely held that a larger body of disordered possibilities acts as an attractor to any dynamic system. This is considered to be the actual reason why order decreases and entropy increases in nature. However, disorder increases only if the system originates in an initial condition of high order. In consideration of the boundary system proposed, the question now arises as to whether a system that originates in the most extreme condition of low order will evolve toward greater order.
What I mean this question to highlight, is that in recognizing two boundary states, there would logically exist a balance where a set of states of higher order is equal to a set of states of lesser order. It follows that the quantity of disordered states is not necessarily always greater and also that the influence of that body decreases as a system approaches the balance or a basin of attraction in aggregate state space. We can therefore recognize a center position within the order-disorder axis which logically should act as a universal basin of attraction for all dynamic systems. The principle that a system will evolve toward whatever balance exists between all possible states will be referred to here as the first law of probability evolution.
Yet as we consider the entire evolution of space-time, in contrast to the measure of order that exists in nature, the universe has cooled from an extreme temperature at, or near, infinite on the Kelvin scale, to a temperature only 2.7 degrees above absolute zero. Likewise, the average density is so near the critical density which would carry the momentum of expansion almost precisely to zero, either into a never ending ascent toward zero, or an ascent so near zero until gravity is able to produce a rebounding collapse, that we must be highly curious about the dominating influence of AFS in the SOAPS.
It is my conclusion that there is no evidence to suggest the general direction of time is being directed toward any basin of attraction balanced between the alpha and the omega states, and there is instead evidence to suggest the arrow of time is directed toward AFS. Before I explain my solution to why the arrow of time would naturally follow such a course, it will be benefit my argument to first expose that there also exists extremes of possibility adjacent to any point along the axis between the alpha state and the omega state.
4. Adjacent Extremes
At this point, in my second modification to MSS, it is necessary to temporarily replace the image of an order-disorder axis and instead utilize an average density gradient (ADG) of all possible states, so that we can consider states that exist along, or adjacent to this more fundamental and imaginable axis.
At any point along the ADG excepting the alpha state and AFS there exists a quantity of states greater than one and necessarily infinite. However, this quantity is also bounded by extremes related to the alpha and omega states. What I mean here is that there are extreme possibilities of perfectly smooth versus what I can only refer to as radical lumpiness. These extremes relate to the ordinary concept of contrast, where color tones are either blended into a single averaged color (low contrast) or the color tones of the image blend into two opposing shades of light and dark (high contrast). We can therefore identify a single extreme of smoothness and at least for now hypothesis a single extreme of lumpiness even if such a state is yet difficult to envision. Of course no possibilities adjacent to the ADG beyond these boundaries are describable by physics or even imaginable.
We now direct our attention to the lumpiness of the early universe where it is easiest to apply this gradient of low to high contrast to the question of why the early universe did not remain smooth. In the same light as Boltzmann's original postulate of the influence of more disordered states, at each point along the ADG there exist extremes of smoothness and lumpiness or a contrast gradient (CG) and the probability law requires that the path of a dynamic system will move toward and so follow the basin of attraction balance between the two polar extremes. In recognition of the CG adjacent to any point along the ADG we can conclude that the maintenance of a smooth universe during expansion is statistically near impossibility. The universe remaining perfectly smooth is one possibility among many other possible states where space does not remain smooth. I further submit that the measure of density variation detected since the big bang and the present even distribution of galactic lumpiness is congruent with the basin of attraction in the CG.
It should be noticed at this stage that implementing the CG has revealed that boundary states do exist in all directions of MSS, making the SOAPS definitive as opposed to indefinite, as the diagram below represents.
5. The primary attractor of a macrocosmic symmetry
In consideration of the present temperature and measure of spatial flatness observed in the universe's topology, and considering the general momentum of time which appears to be aligned directly in an ascent, or may now be accelerating toward AFS, it is proposed here that there is sufficient reason to suspect that AFS is the primary attractor in the SOAPS. I wish to note here that the measure of order that exists in nature suggests other variables exist, so that we may return to this issue later in the following section.
The next modification to the macrocosmic formation of state space involves expanding the set of all possible states to include both positive and negative extremes. We are led to expand the model if we reasonably consider the descending momentum of time from the alpha state toward zero.
If we focus on the supposition that AFS is the primary aggregate attractor we are led to speculate that the density gradient so far discussed is merely half of the SOAPS, and hence we consider how the ADG might be expanded so that the momentum of time toward AFS, as well as decreasing order and increasing entropy, can still be understood to be attributed to state space. Although the ADG spans from zero to infinite density, and thus seems to represent all possibilities, the most simple solution would be the addition of a negative set of states. The greater set of states would thus include an inverse set of patterns, similar to the mathematical plane of numbers, which are identical yet opposite.
This solution should feel intuitively satisfying since it illuminates the previous asymmetric version of aggregate state space. It also carries with it many implications so it should easily be evidenced or disproved. An introduction to negative density also demands a great deal of rethinking.
In physics there has not been reason to designate density as a value that is positive, however, the reason for this would be that a negative mass does not exist in nature. As we continue I will explain that volume is both positive and negative in nature, in respect to two unique directions of time, one which begins from a positive alpha state, the other a negative alpha state. Therefore a negative density can only exist spatially extended in a negative volume, and is only observable in a positive volume as a point particle which mysteriously maintains a finite mass, such as the electron.
The advent of two directions of time and volume toward the same primary attractor, AFS, will eventually squarely resolve the issue as to why our direction of time is preferential to matter over anti-matter. However, it is not the scope of this initial paper to attempt to treat this subject justly. It is more critical that we begin to study the basic probabilities inherent within the proposed model and consider how both the external and internal architecture of this now expanded MSS would influence space-time using the same rational as it has been held that a greater number of disordered states influences a system. Again however, before I continue it will benefit my argument to explain the final modification to MSS.
Given that aggregate state space genuinely explains why an ordered system becomes disordered, why then do ordered systems emerge and why are they maintained? The second law is only one feature of an evolving universe. It seems quite clear that the forces of nature shape the universe to create order within a present trend toward disorder. Do the forces of nature work against the probabilities of state space, or is all physics accountable to state space. Is it possible that an accurate MSS could model the SOAPS enough to explain why there are laws and forces that control the physics of space-time? Is the possible realm fully responsible for order and systemization?
I will now radically improve upon how we understand order and disorder in nature. The method that we presently use to conceptualize order is faulty. Misunderstanding order is the very reason science is yet unable to understand why the universe is ordered and systematic. Note that what follows stands alone as an individual theory and that this precise way of understanding order is without question the most relevant material of this paper.
II: Defining the Two Opposing Types of Order
This specific comprehension of order identifies two opposing directions of increasing order, leading to the recognition that the order in one direction is simultaneously a disorder of the opposing type. In study of this phenomenon it can be realized that it is inaccurate to consider any pattern as exhibiting a general disorder, but rather 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. Note that this comprehension of order is both congruent and evidentiary of the proposed
three radical extremes of possibility previously identified, and also the proposed contrast gradient existent adjacent an average density gradient representation of all possible states.
1. Redefining 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, 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 envision.
There are two principle classifications of order in nature, not merely a single order opposing disorder. Two orders blend to produce all the diverse shapes and patterns that are observed. Each has its own distinct direction of increasing order and an individual increase in either type produces opposite results. The first type to be identified will be referred to 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 together and distributed uniformly throughout a frame of reference. In extreme this type of order produces a perfectly smooth and uniform pattern. The perhaps unexpected element involved is the opposition of these two types. I shall show that each deserves to be classified as a unique type of order and even that each type is disorder to the other.
By far the most lucid exposure of this contrast between orders is seen in the way in which a chess or checker game is set up. Even if the example initially feels mundane, let me reinforce the fact that this example in its simplicity reveals the distinctiveness of each type of order, and illustrates the opposition well enough to act as a lasting template to identify the separate orders in nature.
To prepare for a game of checkers, 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. In fact we commonly divide apart and group a number of objects by classification into a set, ordinary examples being: smaller parts grouped apart from large parts, round objects apart from square objects, or things of a positive nature apart from things of a negative nature. This order requires only that one group be established in dense form apart from another class, or the group is merely distinct apart from a neutral background.
However, if we change our focus and consider the checkerboard, which is in this case serves as a moderately neutral background, we observe a uniquely ordered pattern, unique in that its arrangement is an admixture of colored squares, spaced evenly in alternating rows. The most evident property of this archetypal pattern is its overall conformity and balance represented by the symmetrical placement of squares. Note that this conformity and balance is in stark contrast to the set pattern of game pieces which are divided purely into two separate groups.
Using these two patterns it will be possible now to reveal two opposite directions of increasing order, at first focusing directly on the checkerboard pattern. Since we will transform the checkered pattern it helps to assume a flexible or liquid quality to the shapes.
If we first imagine the direction toward grouping order, we imagine the individual squares of the same color gravitate together. Enclosed within the square frame of reference, this motion simultaneously forces the opposite color to group as well. The extreme result is two uniquely colored rectangles at opposite ends of the board. The black color is now fully separate from the white color. The only way to push this pattern further in the direction of increased grouping order would be to increase the density of the individual points of color which would deflate the frame of reference, and the red and white squares would shrink toward becoming the extreme of two infinitely small points.
Now if we reverse this same process, starting from these two points, we inflate the frame of reference, and begin to mix the two colors, although not evenly. We maintain a measure of grouping order dividing the red and black areas into squares which are then mixed to recreate the original checkered pattern. Now the pattern is transforming in the direction of increasing symmetry order.
To continue in this direction toward the extreme of symmetry order we further subdivide the checkered pattern, and then evenly distribute the more miniature squares, which causes the pattern to become increasingly variegated. Continuing to subdivide, the checkered pattern can become ever more finer in its distribution until we are unable to detect the fine squares and visually only observe the smooth result of this perfectly symmetrical spacing. Our observations reflect how the pattern is transforming ever nearer to an extreme where two distinct colors are blended into one single color, this being the ultimate extreme in this direction of increasing symmetry order.
Like two liquids blended together, this direction of increase produces an order of a nature precisely opposite to grouping. Rather than two pure and separated groups, this fully opposite direction of order produces a singular result, a uniformity, neutralized of difference and form, yet not truly absent of form. The contrast of black and white becomes the balance of gray. Shapes and form become formless and neutral. Balance, uniformity, neutrality, combination, in extreme becomes formless, yet ordered, and thus not dissimilar to absolute flat space (AFS).
The gradient increasing from a checkered pattern to the extreme of a uniform pattern exposes the relationship between evenly distributed patterns (EDP) such as the original checkerboard and an absolute uniform pattern which will here be recognized as an extreme form of order of a symmetrical nature, identified here as symmetry order. I shall consider AFS as the physical reification of symmetry order.
The same gradient increasing along the axis in the opposite direction exemplifies the more common type of order of grouping where parts or classes are densified and consequently increasingly pronounced or definitive. It is this type or order that is ordinarily recognized as general order while the direction toward symmetry order is associated with high entropy and even disorder. Where AFS relates to symmetry order, an infinitely dense and hot singularity relates to grouping order. In fact I shall argue that the big bang singularity is the reification of extreme grouping order, an inseparable positive and negative duality, which on a macrocosmic scale, verifiably results in two directions of time, not simply the one containing matter which we observe.
Note that the directions we have just encountered do also establish more clearly the contrast gradient previously explained in the first essay, but much more significantly they demonstrate the major proposition of this paper, the replacement of the order-disorder axis with a grouping-symmetry order axis.
2. From an ordered to an ordered state
The second law of thermodynamics describes the mixing of materials and the increasing entropy of a system as an increase in disorder. That an evolution is taking place of increasing entropy is not in doubt, however, we must recognize in principle that the material within an area of any pattern can only either separate or integrate, and its topology can only expand or contract. I submit that what we perceive at present to be a trend toward disorder is instead an evolution that begins from grouping order and ends at symmetry order.
As the most simple example, gases that dissipate from a condensed grouping, and spread evenly throughout a room, or any frame of reference in which it escapes from confinement, until it reaches a state of equilibrium, is not a general increase in disorder but rather an increase in the balanced distribution of a gas throughout its reference frame and therefore constitutes an increase in symmetry order. The immediate or short term settlement into an equilibrium state can be associated with the basin of attraction within the contrast gradient (CG), as determined by the system's position along the average density gradient (ADG). On a much greater time scale the system is moving toward a radical equilibrium, toward perfect symmetry order or AFS, due to spatial expansion toward flatness and cooling toward absolute zero. While the contrast gradient recognizably influences the system toward an equilibrium state along the density gradient, the total evolution of any system is relative to macrocosmic state space (MSS) and thus we recognize the general direction of time toward the balance and formlessness of AFS.
Increasing symmetry order has been mistaken for disorder because the observable history of space-time most evidently records the divergent evolution from the most extreme state of grouping order to an intermediary transitional phase (ITP) between both orders. The ITP in any transition from grouping to symmetry order can be viewed 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 choose one game piece for each move, at any point in time along this procedure until it is completed there exists what we normally consider to be a general measure of disorder. In actually each area of the board can be seen to be retarded toward grouping order or advanced toward symmetry order. Note that in the middle of this process the transition appears to have no objective. As a whole the pattern appears to be moving toward disorder when in fact we are observing a transformation from one type of order to another.
The intermediate patterns seem disordered yet each is simply part of the vast majority of possibilities produced by uneven mixtures of grouping and symmetry order, patterns which must be utilized in the transition. In respect to this new model of order it becomes necessary to abandon the general meaning of disorder since no area of a pattern is without order of either type, and since the order of one type is necessarily the disorder of the other.
While the future convergence from ITP states to the single extreme state of perfect symmetry is not observable at this point in history there is a great deal of evidence to support the transformations and changes suggested and later predicted by this model. The 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 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 condensate. And finally, hidden in the symmetry of space, virtual particles leap out and back, for an instant form emerges spontaneously from formlessness until the balance of symmetry order returns.
This notion of the one order being the disorder of the other is more acceptable when considering an AFS as the most disordered state of the more commonly recognized grouping order, and less acceptable when considering an increasingly dense state as the disorder of symmetry order. However, the central issue is in differentiating between the two unique directions of order, as well as observance that either direction involves the necessary increase of order for one type, to decrease the order of the other.
It can be recognized that the breakdown of each type of order is required, in any transition toward the other. We recognize the breaking of either order without difficulty, if we imagine a misprinted checkerboard where two red squares were accidentally placed together. If the placement of squares is uneven in the slightest measure, the order of the pattern is lessened. The balanced symmetry of the board would be visibly decreased yet the grouping of red squares is increased in that displaced area. Likewise, if we consider we mistakenly displace one red checker with one black checker in setting up the board, a mistake in sorting, has made the two separated groups less pure and less ordered yet this has also initiated the necessary mixing of any transition toward symmetry. Again I will mention and so reinforce the principle that the material within a space can only either separate or integrate, and its overall topology can only expand or contract. It is in recognizing the extremes of separation and integration, or expansion and contraction, that we discover the inevitable transition between extremes.
There is in our thinking minds an expectation about the universe, and then there is the natural world, or our experience of the real world. Much in the same way our very existence seems like a miracle to us, as if 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 chaos, it seems much more evident to us, for we naturally consider the infinity of less consistent universes that could exist in place of the one ordered and systematic universe that is present. Yet suppose here for a moment that our universe is not unordinary or an exception to the absolute chaos possibility, but rather we make a mistake in how we model order. I hope the reader can sense here that when we fully understood order we find that there is nothing extraordinary about an ordered universe even in comparison to the whole of possibilities. In fact it is our notion of disorder that is an anomaly and unreal.
Before ending this article we should consider how commonly and automatically we group things. In a well organized home, books are placed on a shelf, dishes in the cupboard, canned food in its own location. The vegetables and the fruits are kept in separate groups. The bedroom has a separate drawer for shirts, pants, and underwear. At the store there is a meat section, a bread section, a dairy section. An at the library books are organized alphabetically or by subject. If instead all that is mentioned here were all mixed together the result would be a world in disarray, something we might expect after an earthquake.
In this same way we can also consider the basic elements of the material world and fortunately the universe isn't just a cosmic soup of particles randomly in motion. Grouping of elementary particles produces pure chemical elements, gases, metals. Our planet is a grouped mass of materials, as is each stellar body, while the sun and planets form a group. There are cluster and supercluster groups of galaxies. Amassed groups of elementary particles represent the most basic expression of grouping order as opposed to an easily imaginable admixture of all subatomic particles.
Yet as groups of elements and solar masses give the universe its definition and bring about order as we know it, this grouping type of order is not alone in creating the universe that we observe. The universe also requires uniformity and balance. The moderate combination of elements creates for us our oceans, the soil, and the air that we breath. The materials most common to us are medleys, such as composites of rock, glass, wood, soil, plastics, metals such as bronze or steel, or gases such as petroleum and propane.
At the macrocosmic scale, the even distribution of galaxies reflects the even distribution of lumpiness in the early universe and the initial smoothness of inflation and expansion. At the microcosmic scale any closed system settles into an equilibrium state. And finally, perhaps the most important expression of symmetry order is the measured neutrality and formlessness of outer space.
There is a stark and dramatic difference between the nature of these two orders, an opposition that is responsible for all the complexity and the beauty of ordered patterns in nature. One nature involves division, separation, distinction, individuality, density, pronouncedness, opposition, and conflict, while the other expresses combination, uniformity, homogeneity, singularity, formlessness, balance, symmetry, and unity. The contrast and struggle between two orders is why existence itself is comprehensible, and why spacetime is complex in its systemization and orderliness.
III: On the problem of timelessness, four dimensional space, convergence toward absolute flat space, positive and negative volume, and the unified state.
1. Introduction to timelessness
Albert Einstein's later conclusions included that all of spacetime forms a unified existence. His most heartfelt testimony of this was a letter to the family of his lifelong friend Michele Besso, who died shortly before his own death. Einstein wrote that although Besso had proceeded him in death it was of no consequence, "for us physicists believe the separation between past, present, and future is only an illusion, although a convincing one."
If we imagine an endless moment where past and future are intertwined, mated into a single enormous moment of now, it is not then easy to reconcile how we so convincingly experience time and perceive change. A four dimensional existence (FDE) is static and unable to change. Duration of time into past or future has no meaning. It simply is.
It is self evident that the time utilized by physics has at least two elementary components, physical existence and change. Of course a system which is dynamic must primarily exist, however, an existence certainly does not require change. We are led to ask then if the dynamic time we perceive can be real, and not an illusion, if Einstein was correct about a FDE, and thus change is a secondary component of static universe.
The time of a FDE has at least two components also. One is a linear string-like path extended across the permanent landscape. The path of a dynamic system, like a story of a birth and death in a book, could conceivably be solidly imprinted into a static existence. Although like any story in a book, there must be a sort of binding which fuses at least our temporal experience. I shall refer to this as the linear component or as linear time. We might envision linear time much like we envision a single direction passing through an ordinary Euclidean space from point A to B. Simultaneously, the time of a FDE requires a transition through unique patterns or conditions. There must exist differences from point A to B necessarily lateral to the linear evolution of time.
We should expect that the lateral patterns necessarily must be distinct. Each must possess a separate identity or dimensional form apart from other conditions along the linear time path which somehow links the series of instances. Those differences between each individual state may be immeasurable, infinitesimally small, yet without difference there could not be temporal experience of a singular present or individual state and also there could not be for us the lesser illusion that change is primary in nature, as is commonly assumed.
We can make reference to the necessary transition from state to state as the lateral component of time, and imagine each static state to be like a solid block of space. Each state is synonymous with a single possibility. Like the FDE itself, each space has no measurable time duration. I shall refer to this as the lateral component or as lateral time.
And so now we confront the usual dilemma. A fused series of spaces form a whole space and thus would seem to forfeit the original separateness. Yet if we maintain each as an individually distinct dimension, it seems that time as we experience it cannot exist, which does not merely suggest time is an illusion. The discontinuity of three dimensional definitive states existing solidly in stasis conflicts altogether with the necessary union of a continuum.
This problem in trying to reconcile the two components, and the problem of trying to reconcile our experience of a transitional time with a timeless existence is the same paradox faced in resolving the distinction between quantum theory and the general theory of relativity. At the macro-scale we observe objects to move along a linear and continuous path, and in knowing the position and momentum can predict the future or past. At the micro-scale it is not possible to decipher both position and momentum, and we conclude that particles travel as a wave from one position to the next without having a definite position between points A and B.
2. Four dimensional space
The problems of multispatiality have been concerned with how it is possible that many individual blocks of space which are necessarily distinct dimensions can simultaneously be spatially linked to form a fourth dimension of space which we refer to as time. It may be that the simplest solution is the only possible solution.
Arguably the focus should not be upon how such spaces are linked, but instead how such spaces are maintained in nature as individually separate. What separates one static spatial dimension from another? The question suddenly is not unlike other spatial issues regarding the relationship between separate positions in space and different references of time for say distant galaxies near the outer horizon of expansion in comparison to local galaxies or our own milky way. The answers are decreed in relativity theory in general. Even more plainly, there has never been an intuitive rejection to the integration of three dimensions into a collective space. The first three dimensions feel inevitable of any physical existence. Why would we expect 3D block-like spaces would not form a spatial continuum as we expect of the first three dimensions?
I suggest that in addition to all the ordinary expected directions embedded within and constructing the continuity of a three dimensional block of space, there also exists directions in space which travel across or through a multiplicity of 3D spaces. These directions in space are no less natural and inevitable than those which build a three dimensional continuity, except that each direction independently constructs the lateral component of its surrounding conditions. And thus each linear direction in 4D space forges a unique path through the realm of multispatiality.
We can now consider the basic probabilities inherent within the proposed state space model.
The 4D directions of space are unique from 3D directions in that the construction of the temporal volume (space-time) results as a product of the the macrocosmic structure of state space (MSS). Each 4D spatial direction does not travel in a free fashion through the patterns of state space. Instead a direction through multispatiality encounters the inherent probabilities that exist within MSS relative to the lateral component or present state of a system. Note that this conclusion is the same as the idea that a greater number of disordered states is thought to influence time.
At each position from point A to point B along the linear time direction there exists a distinct lateral space inseparably connected to that point. As for each proceeding space, the micro-state and macro-state conditions of each lateral space leads to a probabilistic decision, one that shapes both the future and the indeterminate past of the linear path's lateral identity. The particular states or patterns that each direction passes through are naturally determined relative to the definition of previous patterns and the construction method can be evidenced as being purely probabilistic with the only other variable being the nature of space.
Each 4D direction inevitably travels through the MSS from an extreme state of density to the extreme of flat space in accordance with and in response to the probabilities of that body. At the alpha state all other states are less positively dense than infinite density as shown below.
All percentage of probability attracts lateral conditions toward the lesser dense states. This gross imbalance causes the direction of time to explode through its state space toward the negative initially without any temporal oscillation (TO). The decrease of positive density is due to an integration of negative density which produces expansion.
Once expansion has occurred there are a great number of conditions or possibilities which are more positively dense than the now slightly evolved present, as shown below. Once the density of the system is decreased the state of 4D space has changed relative to the MSS and temporal oscillations reduce the smoothness of inflation. The set of states of greater positive density than the evolved state of the system, or the Alpha set, increases while larger Omega set set decreases. This creates a probability for time to be reversed which slows expansion equi-potentially and leads to the original fluctuations in a measure relative to the basin of attraction in the contrast gradient.
The alpha and omega sets are in a constant state of flux, evolving as the system evolves. The omega set includes all negatively dense states, half of the polar spectrum, which we can refer to as the Beta set, and also includes all states which are less positively dense than the present state of the system. Consequently the omega set is always of greater measure and it dominates throughout the course of time over the alpha set, until the two opposing sets are equalized.
As the alpha set becomes ever more influential the momentum of time is increasingly more defined into a radial trajectory directly toward AFS, where the probability for time to move backward is equalized with the probability for time to move forward.
As space-time enters its state space it steadily confronts an expanding number of unique possible paths, as shown below. The path through the first quarter of state space is called the Period of Divergence. During divergence the passage toward zero is slowed by the increasing influence of the expanding measure of states, until space-time moves into a second phase. As a space-time system crosses the mid point it enters the period of convergence. The adjacent possible begins to decrease and expansion begins to accelerate as the direction of time is aligned into a radial trajectory toward flat space.
Note that the general probabilities of MSS implicate gravity and expansion as two opposite directions in time. The conclusion here is that although time has a general direction, gravitation and even particle density since the big bang are the product of active time reversal. Time does not have a singular omnipresent or inherent direction. Gravitation is literally time moving backward along the density gradient, and expansion is time moving forward along that gradient. The middle ground, which is also the point of greatest TO, is what we presently describe as the stationary stars and galaxies.
In this work I have been led to the conclusion that our forces of nature are engineered in a way to bring about a specific future. Forces are not arbitrary, just the way nature happens to be, without reason. Instead, spacetime has a destination, and forces guide spacetime along that path toward the specific predestined goal of AFS. All of the possible paths along that that course from the alpha state to the omega state comprise what we would describe as the many-worlds universe first proposed by Hugh Everett III.
With a deeper study of these probabilities and consideration of the radial convergence to AFS it is possible to recognize how all forces fit into the scheme of nature. Cosmological expansion, electromagnetism and the weak force are probabilities for time to move forward, while gravitation and the strong force maintain the universe's position along the density gradient and are consequences of time moving backward, which the mathematics of the model will reveal further. So in the same way that the heavily dense states pull time toward alpha, the more dominant influence of AFS can be understood as the future influencing the present and setting the course of time.
An inevitable future shapes its past. I cannot stress this point enough since it leads to extraordinary insights into the behavior of nature. Note first that the consistency of mass and structure of the proton and electron relates to the archetypal checkerboard pattern in which each square must be identical. Such symmetry is a requirement and it will be the role of electromagnetism to produce a supersymmetry of protons and electrons stationed in orderly rows and columns throughout the final topology of space. Electromagnetism has the potential to spread all particles evenly through out the greater expanses of space in the absence of gravitation. The weak force has the potential to break down all complex atomic material into protons and electrons in the absence the strong force. In the same way that gravitation was no match for inflationary expansion, in the distant near zero future the forces of reversed time will give way to the mechanics of symmetry order.
4. Accelerating expansion
If it were not the nature of AFS to be witnessed relative to present
cosmological conditions as an absolutely expanded space, the radial trajectory
toward zero as evidenced by expansion would appear to be ever decreasing.
However, since from our perspective, AFS is a state in which every position in
space is expanding away from every other, accelerating expansion is necessary in
order for the topological state of spacetime to become absolutely flat. I
first presented a basic macrocosmic state space model and predicted that the
universe would expand to flatness, in my first book, The Structure of an
Infinite Universe, written in 1994. I believe that prediction has been
scientifically verified in observation of accelerating cosmological expansion
which took place in 1998.
The present theme is that the future reaches into the past to create the checks and balances which create our present measure of orderliness and symmetry. It follows that spacetime is not the result of a fluctuation in a vacuum. Nor is it a causal product of the Big Bang, or a creation from any initial condition. Time has no boundary  and has no need of existential development. The probabilities dictate that any past must originate from the alpha state with no need of a vacuum and any future must conclude as AFS.
5. The density of multispatiality
The proposal of negative density carries with it the necessity of anti-time. For every spatial universe such as our own there is an identical but opposite direction of spacetime, moving toward the same point of equilibrium. The two worlds begin from opposite sides of nature, and each direction produces its own spatial volume which are positive and negative to each other.
As linear time passes through a multiplicity of spaces a volume is created within which we measure all material density to be positive. There is no negative density within our spacetime and there cannot be negative density within a positive volume, since this would necessarily be a negative mass. Mass is always positive or principally neutral, being the fundamental property of definition or grouping order.
So we write:
mass = positive density x positive volume
mass = negative density x negative volume
A negative density cannot exist in our positive volume, because it would then be a negative mass. This does not mean that negative density does not exist. It is actually a very fundamental feature of our own spacetime, it is just not visible in our spatial surroundings. This is the most obvious distortion to our volume produced by 4D space. Negative density exists always beyond a point of zero volume, such as the point of the electron. This is why the electron point particle does not have infinite energy, does have a definite mass value, and does have a negative electromagnetic charge, because it is a negative density existing in a negative volume.
The following philosophical argument shows the consistency of this approach. Mass is related to the density of space while space is fundamental. We of course presently attribute space to mass which is not entirely different than attributing mass to space. It follows from recognizing AFS that space is real and that it is in essence physical existence. There is no such thing as a non-space or a non-existence to separate a form of existence from another form of existence. Non-space cannot be. The extension of flat space is infinite. There is no place where space does not exist. If mass is related to fundamental space then negative mass cannot exist, since it would indicate a negative existence.
6. Unified spatiality
The recognition of symmetry order brings with it the most dramatic modification to axioms possible in physics, which may explain why I have saved it for last.
Much if not all of modern physics is based upon the axioms of grouping order. We gage the universe according to grouping order and see the world from its definition oriented perspective. Everything above the oneness and seeming emptiness of space is thingness. The absence of definition and multiplicity is to us zero things and we judge that zero, the oneness of symmetry order, to be a nothing, even though in lesser form we quickly recognize the patterns of symmetry order, such as the checkerboard, or the even distribution of galaxies.
Since even the smallest individual particle or measure of density represents grouping order, we begin to recognize grouping order is responsible literally for creating finite objects and thingness, finite form as we know it. Elementary speaking, grouping order relates to definition and we should look for it to exist, at very least, as a duality, in a larger frame of reference as the model above shows.
In the case of symmetry order we see in the extreme that all density and all definition is reduced to a uniform zero and yet it would be wrong to say there is no longer a pattern, or that the pattern is no longer substantive or has become nothing. On the contrary, since symmetry order requires a union or combination of parts into a single medium. This leads to an inversion in how we think of substance. Space is not less substantive than mass or density, but rather is more substantive than matter.
Precisely what we are accustomed to thinking of as empty space, is the union of all possible states into a single state. It is only the absence or displacement of a state or a system that allows the opposite form to be definitive. We can see this somewhat as we relate the physical conditions of infinite density to an extended flat space. This means comparing an infinitely small point of space to an infinitely extended space. In absolute extreme, symmetry order is the ultimate singularity; a oneness of space and time and things. In comparison either the positively dense or negatively dense singularity is precisely half of the greater whole which flat space becomes with the conjugation of the opposite densities which we observe to be expansion. In fact the entire evolution of spacetime can be understood as the conjugation of positive and negative density into a neutral whole.
 Boltzmann L. On the relation between the second law of the
mechanical theory of heat and the probability calculus with respect to
theorems of thermal equilibrium.
Positive and Negative Volume of Multispatiality