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On Modeling the Macrocosmic Structure of State Space

III: Four Dimensional Space

Devin Harris
July 14, 2003

The last chance to discover a finite Universe vanished with the return of data from the Boomerang and Maxima telescopes, and the Wilkinson microwave anisotropy probe further verified the geometry of deep space is flat, indicating profoundly (with a forgivable suspension of relativity) that if we could observe galaxies at a common age they would extend infinitely in all directions without end. We no longer need question whether the universe is infinite or not. Only now we have arrived at a question that seems less scientific or at least far more difficult to answer. How infinite is the Universe? Is existence bounded in any way? Evidence for an infinity of galaxies or space-time bubbles was not entirely unexpected, but what of all conceivable universes and beyond, most completely unlike our own? Are there any identifiable boundaries to the knowable universe?

The case for a mode of timelessness in which all things exist is no less compelling than the case for a many worlds universe, and I propose that the existence of all possible states may be the extent to which existence is infinite, serving as a foundation and limiting temporality to space-time as we know it. It is well known that Einstein's later conclusions were that all of space-time forms a unified four dimensional existence. In the book Relativity Einstein wrote, "Since there exist in this four dimensional structure no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence." A more heartfelt testimony of his conviction 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." Richard Feynman came to define time as a direction in space, and Stephen Hawking has become increasingly adamant in expressing that time is self contained and has no boundary.

The foundational matrix of a four dimensional existence doesn't evolve and is even unable to change, it simply is. In this modality, there is no distinction between the words existence and time. We can refer to this as timelessness or as a primary reference of time which has no beginning, middle or end. I sometimes define this time as one enormous moment. Feynman coined the term imaginary time. The philosopher Huw Price refers to the perspective as the view from nowhen. Yet clearly, in a view of space-time from there, it is not easy to reconcile how we so convincingly experience the a moment of now and perceive change, be it illusion or not.

It is self evident that our regular reference to time includes two distinct components, physical existence and change. Any physical system must primarily exist, and so the component of change in ordinary time could conceivably be a secondary component. The time embedded in a four dimensional existence has two components also. One component is a linear string-like path extended across the permanent landscape. The path of a dynamic system, like a story 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 the multiplicity of words and pages, or moments, into linear form, that being at least our temporal experience. I shall refer to this as the linear component or as linear time.

Simultaneously, the time of change requires a transition through unique states or patterns. There must exist differences from point A to B necessarily lateral to the linear evolution of time. Each state must possess a distinct identity apart from others along the linear path. Without an independent identity there could not be the temporal experience of a singular present so there would not be for us the illusion that existence evolves, as is commonly assumed. We can make reference to the necessary transition from state to state as the lateral component of time. Like the four dimensional existence itself, each quiescent state is without beginning or end, and is thus unable to contribute any measurable time duration. I shall refer to this as the lateral component or as lateral time.

The problem of the block universe view or 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. Any fused series of spaces form a whole space and thus would seem to forfeit the original separateness. If we then maintain each state as an individually distinct dimension, like a series of photographs, there is no indication of why we experience continuity and order between each moment of time.

The problem of trying to reconcile the two components and the problem of trying to reconcile our experience of 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 linear and continuous paths, 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.

My suggestion here is that 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 block universe from another? The question is then not unlike other spatial issues regarding the relationship between two locations in space or different references of time for say distant galaxies near the outer horizon of expansion in comparison to local galaxies or our own milky way. Note that there has never been an intuitive rejection to the integration of two dimensional slices of space into a three dimensional continuum, and likewise there is no reason to expect that three dimensional blocks would not link naturally to form a four dimensional spatial continuum.

The last conclusion then from inducting absolute zero into the SOAPS, primarily based on the new construct of symmetry order, is that in addition to all the ordinary expected directions embedded within and constructing the continuity of any three dimensional block of space, there also exists directions in space which travel across or through the existing multiplicity of all possible states. This interconnects select configurations of three dimensional block universes and forms a fourth dimension of space which we refer to as time or space-time. These directions in space are no less natural and inevitable than those which build a three dimensional continuity, except for the critical feature that each single direction of four dimensional space probabilistically constructs the lateral component of its surrounding conditions relative to itself. In essence, each linear direction in four dimensional space constitutes a unique space-time bubble, and since each observer invariably surrounds a linear direction, the lateral component is composed relative to each observer.

The resulting four dimensional volume is structured systematically in reference to the macrocosmic structure of state space and that volume is unique from any contributing three dimensional volume. Each linear path, rather than traveling freely instead encounters the inherent probabilities that exist within state space relative to its present state. Applying the model of state space proposed, each linear path inevitably begins confined by grouping order in a state denotable as positive or negative, and in escaping is probabilistically directed toward becoming neutral. The overall cosmology of this model predicts there are two arrows of time, one producing a positive volume of space containing matter and the other producing a negative volume containing a stable anti-matter.

This formula should be particularly enticing because if we can adequately describe space-time as a fourth dimension of space it would explain why we experience physical reality as we do, not from the anthropic premise, but rather because this particular finely tuned universe is the fourth spatial dimension. If proven it would reasonably eliminate all the many universes with different constants that otherwise might exist, excepting the fifth, sixth, seventh spatial dimensions and so on. Everything would be reducible to space.

Accelerating Expansion

As is presently thought, the source of accelerating expansion is a property of space itself and so not evident in the probabilities of state space. Some acceleration to expansion is built into the process of convergence occurring as the contrast gradient narrows. However, a fully independent acceleration force occurs more dominantly due to the nature of time itself. If it were not the character of the ultimate singularity to be witnessed relative to present cosmological conditions as a hyper expanding space, the momentum toward zero would be maintained nearer to an ever decreasing rate, and highly organized particle annihilations would be necessary to produce the final equilibrium. However, accelerating expansion demonstrates that from our perspective, the state of absolute zero is the product of all possible directions in four dimensional space, as predicted by symmetry order.

Prior to the discovery of accelerating expansion, it was assumed that a state of absolute zero or a perfectly flat space would, if entertained as being physically real, be envisioned simply as a static three dimensional block of empty space in which ordinary properties such as distance have no meaning. As I integrated acceleration into this state space model it gradually became evident that we are simply witnessing the most innate property of a four dimensional existence. As symmetry order indicates, absolute zero is an integration of all four dimensional directions in space, the four dimensional whole, and thus the composite of all possible space-times.

The End of Time

With the direction of time following the basin of attraction within the contrast gradient we can expect a more complex scheme for the end of time than Caldwell's Big Rip scenario. The dominant quantity of isotropic patterns near flat space require a gradual and increasingly uniform descent to zero more reminiscent of the beginning of time than a late-time shredding of whole galaxies. Since 1994 I have explained that as space-time approaches zero, stars and galaxies and all complex atoms will be systematically broken down into a supercooled condensate of protons and electrons stationed in orderly rows and columns.

One of the more interesting spin-offs of this model is how an inevitable future dictates the past, that being our present. If a single state in the future is probabilistically predestined then that state will shape and focus the probability densities of its own past. Absolute zero is the great attractor in aggregate state space that literally sets in motion the ordered and systematic process of time, different from a universe energetically forced outward from a past event. This leads to discovering several causes located in the future. All dominant trends in nature toward integration, balance, equilibrium, uniformity, any dissolving of grouping order, such as occurs from cosmological expansion, electromagnetism and the weak force, are properly causally associated with the future, rather than any event in the past. From the very outset of time, an inevitable future reaches into its past, fine tunes the universe, in order to create itself.

The ease with which the probabilities of this model correlate with each of the forces of nature, indicates that although a general arrow of time is built into the SOAPS, there is no fixed single direction of time. The general probabilities of this model indicate that gravitation is time moving backward and expansion is time moving forward. Gravity can be understood principally as a probability attempting to recreate the density of the past. The group of states which are more dense than the average density of the system produces a general measure of probability which inhibits expansion, while the basin of attraction in the contrast gradient determines a specific measure of lumpiness presently in the form of stars and galaxies. Likewise, cosmological expansion can be understood principally as time moving forward along the density gradient.

In fact it is possible to recognize how future-caused forces are visibly engineered in a way to bring about a gradual breakdown of definition and form in the final transition from grouping to symmetry order. Each force has a specific role in this hidden scheme of nature. The weak force can be seen to have the potential to break down all complex atomic material into protons and electrons with the gradual weakening of the strong force predicted to occur during convergence. This would allow electromagnetism to dominate and spread all proton and electron pairs evenly throughout the greater expanses of space, this occurring as quantum gravitation equalizes with Hubble expansion. The final  role of electromagnetism will be to produce a symmetry of protons and electrons stationed in orderly rows and columns, such as what is witnessed when cooling gases into Einstein-Bose condensate. In the final moments hyper-expansion stretches all remaining matter and energy flat. Space-time collapses even as the actual extension of space becomes radically infinite. In that instant our universe completes its integration with its inseparable parallel partner. The two opposite arrows of time become omni-directional turning into inflation, producing at time's end the ultimate singularity; a oneness of space and time and things, which is simply the native state of the Universe.


[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

The chemist Shu-Kun Lin has initiated issues of concern in regards to how we conceptualize order and symmetry, in part by pointing out that "symmetry is in principle ugly in that it is associated with information loss".

Related essays:   Symmetry Mathematics

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Copyright © July 14, 2003 by Devin Harris