The Dynamic Structure of Space:

Relating the Relational Matrix Model to Space-Time and Physical Reality

"I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept of "empty space'' loses its meaning. "

--Albert Einstein, June 9, 1952

Note to the 15th edition of Relativity

Einstein's efforts to uncover a unified field theory were rooted in his belief that the structure of space-time is the key to understanding the characteristics of the electromagnetic and gravitational forces.

The World of Physics, vol. III p. 120

Introduction

Almost 100 years ago, Albert Einstein, in his special and general relativity theories, developed mathematical formulas which told us that matter and energy are equivalent, that space and time are inseparable, that no physical object can travel faster than the speed of light, and that the rate of passage of time for a body in motion is relative to that body's rate of travel through space. In this way, Einstein was able to mathematically demonstrate that these apparently separate aspects of physical reality were all connected.

Einstein understood that all physical phenomena are connected through the spatial structure, existing as extensions of that structure. However, because he was unable to develop a visual model of that structure, he was never able to demonstrate how all these things are connected through that structure.

In this chapter, we will demonstrate that space-time functions as a dynamic relational structure. The relational-matrix model, as a visualizable representation of the structure of space, will be used to explain, among other things, why the physical relationships that Einstein mathematically described exist. Using the relational-matrix model to explain the behavior of physical reality, we will establish a conceptual basis for understanding how physical reality extends from the structure of space. By the end of this chapter, we will also have established a conceptual basis for understanding why nothing can truly be separated from anything else -- i.e., why nothing can be said to exist independent of all other things.

Section 1 The "Big Bang" and the Relational Matrix

The universe is expanding. This observation, based on astronomical measurements, has led to the theory that the universe began in an outward explosion from some point. In general, the idea of this initial explosion and subsequent expansion of the universe is called the "Big Bang" Theory.

The relational-matrix model, as a visualizable representation of space-time, is consistent with the view of an expanding universe that began as a point. We have described the relational-matrix model as the dynamic structure that results when existence repetitively and progressively exists in relation to itself. Yet there's another relationship within existence implied by the existence of the relational matrix that we haven't yet discussed. That implied relationship is between existence that's existing in relation to itself to form a relational matrix, and existence that isn't forming a relational matrix. That is, the relational matrix, as an aspect of existence, must itself exist in relation to another aspect of existence that's not a relational matrix. Putting it still another way, the relational aspect of existence must exist in relation to a complementary nonrelational aspect of existence.

The relational matrix, as a structure, represents a constraint, a limitation, that existence has imposed upon itself, upon limitless borderless nonrelative existence. Infinite borderless nonrelative existence can be imagined as a ubiquitous no-thing, as a nonstructure, like a blank sheet of paper extending forever in all directions. The relational matrix, as a structural imposition upon this structural nothingness, can be imagined as a dot (or point) placed somewhere upon that blank sheet of paper. This dot is relative existence as structure existing in relation to nonrelative existence that has no structure. This dot is the relational aspect of existence existing in relation to the nonrelational aspect of existence. In other words, the first relationship that existence forms with itself must be between finite and infinite existence, between relative and nonrelative existence, between existence as relational structure and existence as nonrelational nonstructure, between the finite point and the infinite nonpoint.

Existence exists whether or not the dot is there. However, the dot can't exist except within the context of existence that's not a dot -- i.e., the dot can't exist other than as finite bordered relative existence in relation to infinite borderless nonrelative existence. The dot is existence existing in relation to itself. The dot is relative existence, existence that is what it is by virtue of its relationship to a complementary aspect of existence. This is why the dot successively dualizes into a relational matrix, because what the dot is is the relational aspect of existence; what the dot is is existence forming a relationship with itself. Therefore, the dot undergoing a process of successive dualization, of repetitive and progressive self-relation, is nothing else than relative existence continuing to be what it is -- i.e., existence that has formed a relationship with itself. For this reason, existential self-relation, once it has happened, becomes an ongoing process.

However, as a relative reality, the dot (i.e., the relational matrix) must do more than internally dualize. As a relative reality, the dot must also penetrate or expand into the nonrelative existence that it exists in relation to. That is, just as the reality cells of the relational matrix maintain their relative existences through the dynamic of continuous interpenetration and interexpansion, the relational matrix as a whole must itself also maintain its relative existence by continuously penetrating and expanding into whatever it is that it exists in relation to, which in this case is infinite borderless nonrelative existence.

The universe conceived as expanding from a point of origin owing to a "big bang" represents our view of the dynamic that must be occurring in order for existence to sustain the relationship it has formed with itself. What we observe as the expansion of the universe isn't other than the ongoing penetration of one aspect of existence into its complementary aspect of existence. What we observe as the expansion of the universe isn't other than the ongoing penetration and expansion of the relational matrix, as relative existence, into existence that's nonrelative. In other words, what we observe as the expansion of the universe is one half of the dynamic involved in maintaining the state of relative existence that is the universe.

The other half of that dynamic involves the universe as relational matrix, as finite bordered relative existence, being penetrated by whatever it is that it exists in relation to, which, again, in this case is infinite borderless nonrelative existence. That is, as the universe expands into the surrounding nonuniverse, that surrounding nonuniverse must also be expanding into the universe. Putting it another way, as the relational matrix penetrates and expands into existence that is nonrelative, nonrelative existence must also be penetrating and expanding into the relational matrix.

It's these penetrations of the relational matrix by nonrelative existence that create what we have previously defined and described as distortions of the relational matrix. That is, distortions of relational-matrix content originate in areas of the relational matrix that have been penetrated by surrounding existence which isn't the relational matrix. Distortions are patterns of reality-cell content within the relational matrix that differ from the uniform or baseline pattern and are at some level the opposite of the uniform pattern. The positive/negative polarity or complementarity of reality-cell content arises as the uniform relational matrix is penetrated by existence that's not the relational matrix.

As we will explained in upcoming sections, what we perceive as the fundamental forms of electromagnetic and gravitational energy are not other than the propagation of these distortions of reality-cell content through the relational matrix, once they've come into existence, with that propagation being driven by the dynamic intrinsic to the relational structure of space-time. This situation is somewhat analogous to what happens when the uniformly calm surface of a body of water is penetrated by some object, with the surface of the water in that area becoming then uncalm, or distorted, in relation to the uniformly calm pattern, followed by the propagation of that distortion from its point of origin outward as a water wave.

To summarize, what we observe as the expansion of the universe is our perception from within the universe of the process whereby one relative reality or the relational aspect of existence penetrates or expands into its complementary nonrelative reality or the nonrelational aspect of existence. Also, what we experience as propagating distortions -- i.e., what we observe as the electromagnetic and gravitational energy of the universe, as well as their material products -- is the result of the nonrelative nonuniverse having penetrated the relative universe.

Thus, the universe contains infinite form, endless structural variations, because it's part of a process whereby finite structural existence is expanding into infinite nonstructural existence, while infinite nonstructural existence is also expanding into finite structural existence. The seeming infinity of form observed in the universe is the result of an ongoing dynamic between existence as structure and existence as nonstructure. In this way, the interplay or interrelation between structural constraint and unconstrained possibility creates a universe of infinite form and endless structural variation, wherein no snowflake is identical to another snowflake. This is finite structural existence embodied (i.e., taking shape) within, and in relation to, infinite nonstructural existence. Look at a flower, and what you're seeing is the marriage of the infinite to the finite, the marriage of existence to itself, as it exists in relation to itself. Look at anything else, or look into a mirror, and you're observing the same.

Section 2 Space-Time and the Relational Matrix

Einstein's relativity theory demonstrated the inseparability of spatial and temporal existence by revealing that the rate of passage of time which an object is observed to experience varies with object's rate of travel through space. This connection between the passage of time and material velocity established the idea that space and time are the dual aspects of a single underlying reality, which is now referred to as space-time.

The structural and dynamic aspects of the relational-matrix model also have been described as the dual aspects of a single underlying reality. We will show that space and time are inseparably linked because they're the manifestations of the structural and dynamic aspects, respectively, of the dynamic relational structure that underlies our perception of the universe, as depicted in figure 31.

Figure 31 Diagrammatic representation of the dynamic structure we perceive as space-time. "Space" is derived from the static aspect of the spatial structure, wherein areas of existence are defined in relation to each other as reality cells of a certain size or volumetric existence (VE). The "time" aspect is derived from the dynamic aspect of the spatial structure, which involves the continuous exchange of spatial content between reality cells.

In the relational-matrix model, space is the manifestation of the structural aspect of the relational matrix, i.e., the volumetric existence (VE) of the reality cells. A reality cell defines a spatial construct, an area of relational structure within existence. The area so defined exists as spatial content, as an area of space. Space doesn't exist "within" the reality cell; space is the reality cell, and the structure of space is derived from the relationships between reality cells. As we will describe in upcoming sections, there's no empty space for things to be "in"; there's only the dynamic structure of space, which, as existence repetitively and progressively existing in relation to itself, composes the energy, the matter, and then the experience of those things as existing "in" space.

Time, then, is the manifestation of the dynamic aspect of the relational matrix. Essentially, time will be shown to be nothing more than a measure of the cyclic or periodic activity of compound distortion processes or matter. Since time doesn't exist until there exists matter, we can't explain how the dynamic aspect of the relational matrix relates to time until we have first shown how matter arises within the context of the unified model of reality.

To demonstrate that space-time functions as a dynamic structure, and to eventually show how matter arises within the context of that dynamic structure, we will now relate reality-cell distortions and distortion propagation to some fundamental aspects of electromagnetic radiation and gravitation.