
macrocosmicsymmetry.com
Modeling the
Macrocosmic Structure of the Universe
epapers
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 polar extremes.
II:
Defining the Two Opposing Types of Order
III:
On the problem of timelessness, four dimensional space, convergence toward
absolute flat space, positive and negative volume, and the unified state.
Gevin
Giorbran
Related
Work:
Symmetry Mathematics
The
Positive and Negative Volume of Multispatiality
One aim
of this work is to promote the ever deepening knowledge in science, astrophysics,
and philosophy, revealing that the greater universe is infinite. It is
my hope to advance such beliefs through education and awareness, with the
continuing goal of contributing to modern science and cosmology. 

This work
was honored by a link in the April '99
online
issue of Scientific American
after
an article entitled, Is Space finite?
Copyright © 19962001
by Gevin Giorbran
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.
Gevin Giorbran
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 orderdisorder 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 spacetime. 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 spacetime, 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 prescientific 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 orderdisorder, 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 orderdisorder 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 orderdisorder 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 orderdisorder 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 spacetime,
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 orderdisorder 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 antimatter.
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
spacetime 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 spacetime? 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
Gevin Giorbran
February 5, 2001
Abstract
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 orderdisorder axis with a groupingsymmetry 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 spacetime 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.
3. Synopsis
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.
Gevin Giorbran
February 5, 2001
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
stringlike 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 macroscale 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 microscale 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 blocklike 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.
3. The direction of 4D
space or time
The 4D directions of space are unique from 3D directions in that the
construction of the temporal volume (spacetime) 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 microstate and macrostate 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 equipotentially 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 spacetime 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 spacetime moves into a second phase.
As a spacetime 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
manyworlds 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 outer horizon of accelerating expansion is now contracting inward
toward our own galaxy. The boundary at which distant galaxies exceed the
speed of light will shrink until even local galaxies accelerate outward
beyond the horizon. Eventually in a universe cooling ever nearer to
absolute zero the horizon will approach each particle pair. And finally
the universe expands to the extreme of flatness, the point at which
positive and negative volumes collide and collapse, even as the actual
extension of space becomes infinite. 

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 antitime.
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
or:
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
nonspace or a nonexistence to separate a form of existence from another form
of existence. Nonspace 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.
The model above integrates
grouping order and symmetry order into MSS. 
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.
References
[1] 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.
[2] Hawking S. W. A Brief History of Time
[3] Barbour J. The End of Time
Related
essays:
Symmetry
Mathematics
http://macrocosmicsymmetry.com/st_math.htm
The
Positive and Negative Volume of Multispatiality
http://macrocosmicsymmetry.com/st_volume.html
Website:
macrocosmicsymmetry.com
Copyright
© 2001 by Gevin Giorbran 
