What Are Space and Time, Really, and Can We Do without Them?
THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
```(annotated and with added bold highlights by Epsilon=One)
Chapter 15 - Prospects
What Are Space and Time, Really, and Can We Do without Them?
or In many of the preceding chapters, we have freely made use of the concepts of space and of spacetime. In Chapter 2 we described Einstein's realization that space and time are inextricably interwoven by the unexpected fact that an object's motion through space has an influence on its passage through time. In Chapter 3, we deepened our understanding of spacetime's role in the unfolding of the cosmos through general relativity, which shows that the detailed shape of the spacetime fabric communicates the force of gravity from one place to another. The violent quantum undulations in the microscopic structure of the fabric, as discussed in Chapter 4 and Chapter 5, established the need for a new theory, leading us to string theory. And finally, in a number of the chapters that followed, we have seen that string theory proclaims that the universe has many more dimensions than we are aware of, some of which are curled up into tiny but complicated shapes that can undergo wondrous transformations in which their fabric punctures, tears, and then repairs itself.
Through graphic representations such as Figures 3.4, 3.6, and 8.10, we have tried to illustrate these ideas by envisioning the fabric of space and spacetime as if it were somewhat like a piece of material out of which the universe is tailored. These images have considerable explanatory power; they are used regularly by physicists as a visual guide in their own technical work. Although staring at figures such as the ones just mentioned gives a gradual impression of meaning, one can still be left asking, What do we really mean by the fabric of the universe?
This is a profound question that has, in one form or another, been the subject of debate for hundreds of years. Newton declared space and time to be eternal and immutable ingredients in the makeup of the cosmos, pristine structures lying beyond the bounds of question and explanation. As he wrote in the Principia, "Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external." 3 Gottfried Leibniz and others vociferously disagreed, claiming that space and time are merely bookkeeping devices for conveniently summarizing relationships between objects and events within the universe. The location of an object in space and in time has meaning only in comparison with another. Space and time are the vocabulary of these relations, but nothing more. Although Newton's view, supported by his experimentally successful three laws of motion, held sway for more than two hundred years, Leibniz's conception, further developed by the Austrian physicist Ernst Mach, is much closer to our current picture. As we have seen, Einstein's special and general theories of relativity firmly did away with the concept of an absolute and universal notion of space and time. But we can still ask whether the geometrical model of spacetime that plays such a pivotal role in general relativity and in string theory is solely a convenient shorthand for the spatial and temporal relations between various locations, or whether we should view ourselves as truly being embedded in something when we refer to our immersion within the spacetime fabric.
Although we are heading into speculative territory, string theory does suggest an answer to this question. The graviton, the smallest bundle of gravitational force, is one particular pattern of string vibration. And just as an electromagnetic field such as visible light is composed of an enormous number of photons, a gravitational field is composed of an enormous number of gravitons—that is, an enormous number of strings executing the graviton vibrational pattern. Gravitational fields, in turn, are encoded in the warping of the spacetime fabric, and hence we are led to identify the fabric of spacetime itself with a colossal number of strings all undergoing the same, orderly, graviton pattern of vibration. In the language of the field, such an enormous, organized array of similarly vibrating strings is known as a coherent state of strings. It's a rather poetic image—the strings of string theory as the threads of the spacetime fabric—but we should note that its rigorous meaning has yet to be worked out completely.
Nevertheless, describing the spacetime fabric in this string-stitched form does lead us to contemplate the following question. An ordinary piece of fabric is the end product of someone having carefully woven together individual threads, the raw material of common textiles. Similarly, we can ask ourselves whether there is a raw precursor to the fabric of spacetime—a configuration of the strings of the cosmic fabric in which they have not yet coalesced into the organized form that we recognize as spacetime. Notice that it is somewhat inaccurate to picture this state as a jumbled mass of individual vibrating strings that have yet to stitch themselves together into an ordered whole because, in our usual way of thinking, this presupposes a notion of both space and time—the space in which a string vibrates and the progression of time that allows us to follow its changes in shape from one moment to the next. But in the raw state, before the strings that make up the cosmic fabric engage in the orderly, coherent vibrational dance we are discussing, there is no realization of space or time. Even our language is too coarse to handle these ideas, for, in fact, there is even no notion of before. In a sense, it's as if individual strings are "shards" of space and time, and only when they appropriately undergo sympathetic vibrations do the conventional notions of space and time emerge.
Imagining such a structureless, primal state of existence, one in which there is no notion of space or time as we know it, pushes most people's powers of comprehension to their limit (it certainly pushes mine). (Epsilon=One: It's time that physicists and mathematicians understood the pluperfect chaos of Infinity, which is beyond the infinitesimal and the infinite. Such understanding is the crux of Philogic, a discipline that overarches and unites the disciplines of Science, Theology, and Philosophy (STP). Philogic is based upon the Elliptical Constant's (EC) disproof of Gödel's Incompleteness Theorems (GIT).) Like the Stephen Wright one-liner about the photographer who is obsessed with getting a close-up shot of the horizon, we run up against a clash of paradigms when we try to envision a universe that is, but that somehow does not invoke the concepts of space or time. Nevertheless, it is likely that we will need to come to terms with such ideas and understand their implementation before we can fully assess string theory. (Epsilon=One: YES!!! You are correct. And, "to fully assess string theory" requires a discipline of logic—Philogic—that is beyond the quantitative. The referred to "space" and the more complex "time" require the serendipitous uniting of dimensionless motion—Seminal Motion (SM)—beyond the locus of the Universe/Reality, which motion manifests as the symbolic Emergent Ellipsoid (EEd)—the Pulsoid/"dark" matter—such phenomenon is, basically, the First Postulate of Reality (FPR).
The FPR, after a long process of reduction/simplification—and a final critical proof published by C. A. Bjerknes and reported by Ludwig Prandtl that was quickly provided by Philip Morrison—was where string theory started as the Unified Concept (UC) in 1955.
The limit of reduction meant the UC/FPR must be the simplest of all that exists while also being the most complex because it must consist of every quality that exists—the whole cannot be greater than its parts. A there is nothing that exists without motion, the FPR can be simply stated as: "something" moves. Describing that something at the first instant is the tricky part. Hint: A dimensionless point moves within a dimensionless sphere. This is what required Kip Thorne's verification while he graciously took a few moments in his office before rushing to an author's first introduction of a very popular book he had written.
The UC describes a serendipitous "happening" of infinitely, chaotic, dimensionless motion uniting (somewhat analogous to Feynman's QED diagrams) such that various forms of oscillation "harmonized" and "resonated," which was most important for Reality because the organized SM was no longer chaotic; and, consequently the motion was slower because of the variant oscillations.
The symbolic geometric description of the complex oscillations was confirmed, hastily, by Kip Thorne as most likely ellipsoidal. The symbolic, salient, structural parts (SSP) of the FPR were the "strings" of string theory and described the string theory's basic geometry without being encumbered by the enigmas of the Standard Model.) The reason is that our present formulation of string theory presupposes the existence of space and time within which strings (and the other ingredients found in M-theory) move about and vibrate. This allows us to deduce the physical properties of string theory in a universe with one time dimension, a certain number of extended space dimensions (usually taken to be three), and additional dimensions that are curled up into one of the shapes allowed by the equations of the theory. But this is somewhat like assessing an artist's creative talent by requiring that she work from a paint-by-number kit. She will, undoubtedly, add a personal flair here or there, but by so tightly constraining the format of her work, we are blinding ourselves to all but a slender view of her abilities. Similarly, since the triumph of string theory is its natural incorporation of quantum mechanics and gravity, and since gravity is bound up with the form of space and time, we should not constrain the theory by forcing it to operate within an already existing spacetime framework. Rather, just as we should allow our artist to work from a blank canvas, we should allow string theory to create its own spacetime arena by starting in a spaceless and timeless configuration.
The hope is that from this blank slate starting point—possibly in an era that existed before the big bang or the pre—big bang (if we can use temporal terms, for lack of any other linguistic framework)—the theory will describe a universe that evolves to a form in which a background of coherent string vibrations emerges, yielding the conventional notions of space and time. Such a framework, if realized, would show that space, time, and, by association, dimension are not essential defining elements of the universe. Rather, they are convenient notions that emerge from a more basic, atavistic, and primary state.
Already, cutting-edge research on aspects of M-theory, spearheaded by Stephen Shenker, Edward Witten, Tom Banks, Willy Fischler, Leonard Susskind, and others too numerous to name, has shown that something known as a zero-brane—possibly the most fundamental ingredient in M-theory, an object that behaves somewhat like a point particle at large distances but has drastically different properties at short ones—may give us a glimpse of the spaceless and timeless realm. Their work has revealed that whereas strings show us that conventional notions of space cease to have relevance below the Planck scale, the zero-branes give essentially the same conclusion but also provide a tiny window on the new unconventional framework that takes over. Studies with these zero-branes indicate that ordinary geometry is replaced by something known as noncommutative geometry, an area of mathematics developed in large part by the French mathematician Alain Connes. 4 In this geometrical framework, the conventional notions of space and of distance between points melt away, leaving us in a vastly different conceptual landscape. Nevertheless, as we focus our attention on scales larger than the Planck length, physicists have shown that our conventional notion of space does re-emerge. It is likely that the framework of noncommutative geometry is still some significant steps away from the blank-slate state anticipated above, but it does give us a hint of what the more complete framework for incorporating space and time may involve.
Finding the correct mathematical apparatus for formulating string theory without recourse to a pre-existing notion of space and time is one of the most important issues facing string theorists. An understanding of how space and time emerge would take us a huge step closer to answering the crucial question of which geometrical form actually does emerge.(Epsilon=One: It's the Emergent Ellipsoid that perpetually emerges from the duality of Infinity, which is referred to as a Pulsoid, which is composed of 9 forms of oscillation . . . and the Pulsoid/"dark" matter can be said to oscillate itself through the Universe from the infinitesimal to the infinite, which sets the direction of "time's arrow.")