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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. 

Devin Harris
February 5, 2001


Abstract

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.

1. Introduction

Ludwig Boltzmann [1] 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 [1] and Julian Barbour [2], 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 this large diagram or 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
 
 
 

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Copyright © 2001 by Devin Harris