The Triunity Report

Mathematical Breakthroughs Establish God's Extra-Dimensional Might

By Hugh Ross

One year ago, while much of the world was preparing to celebrate Christmas, physicists Ed Witten and Nathan Seiberg gave their own special gift to the world. They reduced an entire field of mathematics down to a single short paper. For decades mathematicians had been stymied in their attempts to describe physics phenomena that require four-dimensional space. Their equations seemed impossible to solve, even with the aid of super computers. But a pair of super brains did it. Witten and Seiberg transformed these extremely complex equations into simple ones, almost as simple as the ordinary calculus equations undergraduates work on in their classes.¹

What especially thrilled me about this mathematical discovery was its potential for increasing our understanding of string theory and fundamental particles. I anticipated that breakthroughs in these two areas would further strengthen the case for creation. My guess was that such work would take at least a few years. I've often been teased for making optimistic estimates, but in this case I wasn't optimistic enough. The breakthroughs came in just a few months. In fact, these breakthroughs led to a rare and spectacular occurrence in the world of science--literally thousands of theories suddenly narrowed to just one--and I'm eager to share the story with you.

black holes and strings

First, Witten and Seiberg themselves eliminated an annoying physical absurdity in physicists' theory explaining the unification of the strong and weak nuclear forces. They introduced a hypothetical particle that can become massless, and poof! the absurdity disappeared.² At about the same time physicist Andrew Strominger discovered that a certain type of black hole, what he calls a "charged extremal black hole," could solve a similar problem encountered in string theory. That's the theory physicists use to explain how all four forces of physics (the strong and weak nuclear forces, the electromagnetic force, and gravity) could have started out as one unified force.² Later, Strominger teamed up with physicist Brian Greene and mathematician David Morrison to demonstrate that charged extremal black holes can transform into fundamental particles and vice versa in a manner similar to ice turning into liquid water and liquid water into ice.^{2, 3} Eureka! Strominger, Greene, and Morrison had just shown how several thousand different string theories operating in four, five, six, and even ten spatial dimensions could all be united with perfect consistency into just one theory, the ten-dimensional one. To put it another way, theories invoking "magnetic monopoles," "ordinary strings." "five-branes," "solitons," "type II strings," and "heterotic strings," formerly thought to be competing descriptions of reality, can all be integrated in a single overarching theory.

historical background

Wait! Before you decide this is far too complicated and skip to the next article, let me provide some historical background, define some terms, and promise you that the reward for wading through all this mind-boggling physics and math is a remarkable, faith-building conclusion about God.

You may already know that Albert Einstein spent the last twenty-five years of his life in a fruitless effort to develop theory showing how the forces of physics, relativity, and quantum mechanics could have started as one force (a unified field theory). Some of his peers saw the search as a waste of time. But sixteen years after Einstein's death, particle accelerator experiments proved that at high enough temperatures, the electromagnetic force and the weak nuclear force could have been united as a single force, which they dubbed the electroweak force. Today, particle accelerators ten times more powerful exist. These have led to the discovery of all six of the quarks (subatomic particles) which theoreticians said must exist if the strong nuclear force had ever been united with the electroweak force.⁴ However, direct proof of the unification of these forces would require a particle accelerator forty trillion miles long (not likely to be funded as long as deficit reduction remains a national priority).

Traditionally, fundamental particles had been viewed as point entities of no size, or virtually no size. But in their advancing theoretical work they discovered that if these particles are indeed points, no unification of the forces is possible. It's time to quit--or is it? What if fundamental particles are just points but rather lines or loops of energy, what physicists call strings? Actually, these so-called strings more closely resemble vibrating, rotating elastic bands. They are highly stretched at extremely high temperatures (such as the temperature that existed in the first split second of the universe's existence), but at the lower temperatures in evidence ever since that moment, they are contracted to such a degree that they behave like points.

String theories cannot work in just the three spatial dimensions (length, width, and height) familiar to us. They need more room to operate. However, they need that room--some extra spatial dimensions--only for one moment, just a split second after the initial creative burst. After that moment, they are no longer necessary to the universe's development.

dimensional split

At the very heart of string theory is the proposal that the universe experienced a dimensional split just 10^-43 seconds (a ten millionth of a trillionth of a trillionth of a trillionth of a second) after the creation event. At that instant, the ten-dimensional expanding universe split into two: a six-dimensional piece that permanently ceased expanding and never produced any matter, and a four-dimensional piece that became our observable dimensions of length, width, height, and time, continuing to expand and eventually producing matter, galaxies, and stars.

Another way of picturing this dimensional split of the cosmos is to see all the spatial dimensions of the universe originally curled up in a very tiny "superball." In the beginning, these spatial dimensions began to uncurl. At 10-43 seconds after the creation event, six of these dimensions stopped uncurling and the rest (our observable dimensions of space and time). To this day, the six uncurled dimensions remain curled up in a "ball" no bigger than 10^-35 meters in diameter. Exactly where, we do not know, for we humans are confined in our measuring capacities to just the four dimensions of length, width, height, and time.

Given ten dimensions of space, scientists can show how quantum mechanics once integrated with general relativity and how all four forces of physics were once unified. The theory involves "heterotic strings." These are closed loops vibrating in two directions. The clockwise vibration operates in ten dimensions of space, the counterclockwise in twenty-six dimensions. Don't panic. Sixteen of these 26 compactify, leaving us with just ten, in effect. String phenomena are manifested in all ten dimensions, but the strings operate in several different possible contexts within the ten--one dimension, four dimensions, five dimensions, etc. When researchers encounter strings within these different contexts they may give the strings different names and describe their different characteristics and operations, but they are really just exploring different slices of the ten-dimensional pie.

massless black holes?

As most students of science and viewers of Star Trek realize, a black hole is an object so massive that its gravity sucks in anything--even light--that gets close enough. But, for Strominger's black holes to fit neatly into string theory, black holes must become massless at critical moments. This necessity raises an obvious question: How can a black hole be massless without violating the definition of a black hole or, more difficult yet, without violating the principles of gravity? Simply put, how can there be gravity without mass?

The answer lies in the spatial configuration of a black hole in extra dimensions of space. Strominger discovered that in six spatial dimensions, the mass of an "extremal" black hole (one with a mass and charge so tiny as to be comparable to one of the fundamental particles) is proportional to its surface area. By making this area smaller and smaller, eventually the mass becomes zero. To answer the question another way, Einstein's theory of special relativity (E = mc²) tells us that under certain circumstances, mass and energy are interchangeable. His theory of general relativity extends this principle to space and time. In other words, if the lines of space are curled up tightly enough, mass and space are interchangeable. For the tiny black holes Strominger is describing, the space curvature is easily tight enough to do the job. As if this finding weren't exciting enough, Strominger found that his extremal black holes become massless in precisely those circumstances--and only those circumstances--necessary to eliminate the remaining physical absurdities of string theory. The whole community of string theorists is dancing over this breakthrough. Black holes of all types now fit neatly into string theory. We are not forced, as before, to choose one of the five different kinds of strings proposed and reject the other four. Instead of trying to find the one out of thousands of string theory solutions to match to the real universe, we can now focus on refining this one.

experimental evidences for strings

Before embracing the theological implications of this grand new theory, you may want to know whether or not string theorists have any more going for them than just an amazingly elegant set of equations. Is there any hard, experimental evidence to back up their claim that the universe really was created with ten initial dimensions and a unified set of physics forces? Let's look at evidences arising from four different areas of research.

First (and perhaps weakest) came the findings (described above) made possible by particle accelerators. Since 1971, accelerator experiments have given us ample proof that two of the forces of physics, electromagnetism and the weak nuclear force, are unifiable, and at least partial proof that the strong nuclear force is unifiable with these other two. Though we do not yet have experimental evidence to show that gravity is unifiable with electromagnetism and the weak and strong nuclear forces, the movement of findings lies in the right direction and suggests that we're on the right track. Evidences we still need may be helped along by the gravity wave telescopes recently built by Caltech and MIT. Researchers are hoping these instruments will bring the first-ever detection of gravity waves. Have patience, though. String theory predicts that these new machines will spot gravity waves only if a head-on collision occurs either in our galaxy or one very near between two neutron stars or two massive black holes.

A second set of evidences also has come through particle accelerators. They have enabled us to detect the existence of quarks and leptons, particles predicted by a (four-dimensional) subset of string theory called "supersymmetry." This finding is a good start. But supersymmetry also predicts that for every fundamental particle of matter known as a fermion there must exist a wavelike particle known as a boson that mediates the fundamental forces of physics. In other words, for every existing fermion there must be a matching boson. While particle accelerator experiments have detected fermions and bosons in abundance, none has ever detected a matched fermion-boson pair. At least we know why such a detection hasn't been made. The theory tells us that experiments to date lack the power necessary to find a matched pair. The good news is that the next generation of particle accelerators may have that power, maybe even as soon as the turn of the century.⁵ (Such a detection would have been an easy task for the cancelled superconducting supercollider.)

The third and strongest category of evidence comes via experimental proofs for the theory of relativity. To be viable, string theory must yield the theories of both special and general relativity. If physicists had been able to discover string theory before they knew anything at all about relativity, the theories of special relativity and general relativity would have easily and straightforwardly fallen out of the analysis of strings. Without assuming any of Einstein's equations or principles of relativity, the requirement that strings move self-consistently throughout space-time demands the operation of Einstein's equations and relativity principles. Thus, the experimental proofs that affirm special and general relativity simultaneously serve as evidence for the validity of string theory. Such proof is now quite staggering. As I describe in the second edition of The Creator and the Cosmos, recent measurements on a binary pulsar affirm general relativity to fourteen places of the decimal, that is, to a precision of better than a trillionth of a percent.⁶ And even stronger evidence exists for special relativity. It is affirmed to twenty-one places of the decimal, that is, to a precision of better than a ten millionth of a trillionth of a percent. ⁷ These confirmations make relativity one of the best established principles in all of physics. This, in turn, establishes string theory or at least the many components of string theory that are linked with relativity.

A fourth evidence is the unique role string theory plays in solving major mysteries of physics. All previous quantum field theories ruled out the possibility of gravity, and all gravitational theories were at a loss to explain the properties of fundamental particles and quantum mechanics. If quantum mechanics were true, there should be no gravity. If gravity were true, there should be no quantum mechanics. And yet we possess overwhelming experimental evidence for both gravity and quantum mechanics. String theory is a quantum theory that demands the operation of gravity. It is the only theory that self-consistently explains all the known properties of the known (100+) fundamental particles, all the properties and principles of quantum mechanics, all the properties and principles of both special and general relativity, the operation of all four forces of physics, and all the known details of the creation event.

theological significance

An obvious theological implication from string theory is that the Creator of the cosmos must have the capacity to operate in at least as many dimensions as are needed to explain the existence of the cosmos--plus one. String theory tells us that the universe required ten. Therefore, the Creator possesses the ability to operate in a minimum of eleven (the early cosmos's ten plus one) dimensions.

Why do I say eleven? The space-time theorem of general relativity derived by Stephen Hawking, Roger Penrose, and George Ellis in the late 1960s places the cause of the universe outside its space-time dimensions.^{8, 9} Since cause and effect occurs in some dimension of time or its equivalent, I conclude that the Creator must operate in at least eleven dimensions or their equivalent. (God may possess super dimensions or special spiritual properties that encompass space-time capacities and much more.)

Another theological implication of the space-time theorem of general relativity is that the ten dimensions required by string theory must have a beginning. A beginning means they are all created, which implies that the Creator has the capacity to create space-time dimensions at will. He can bring them into existence any time He wants and, as the book of Revelation suggests, take them out of existence any time He wants.

Many skeptics feel compelled to reject Christianity because of its "impossible" doctrines. They point out, for example, that the Trinity is a mathematical contradiction, and so is the idea that God grants his creatures free choice without comprising His complete sovereignty. However, such biblical teachings are contradictions only if we insist they be resolvable within the four dimensions of space and time we humans experience. In the equivalent of eleven or more space-time dimensions, these doctrines are easily resolved.

The very presence of these paradoxical (as opposed to genuinely contradictory) doctrines in the Bible suggests that the message of the Bible must come from a supernatural source. (Impossible doctrines presented in other "holy books" remain impossible in any number of dimensions.) Since humans' visualizations are limited to the four space-time dimensions in which we experience phenomena, human speculations about God will naturally confine Him to our four-dimensional context. Indeed, the Bible is the only holy book among the religions of the world to reveal God as simultaneously singular and plural (triune). No other book asserts the truth of both free-will and predestination. These unique features indicate that the Bible alone among the world's holy books comes to us from the Being who created our space-time dimensions.

String theory may also help us accept many more of the Bible's claims about God's awesome's powers. Given the extra-dimensional capacities of God established by string theory, it is fairly straightforward, for instance, to demonstrate that God really can pay attention to every action, word, and thought of all six billion human beings alive today and that He has both the power and wisdom to intervene in our lives.

strings: the cutting edge of missions

I can see more implications, and I imagine my readers can see more, also. Perhaps you can see why I view string theory as the cutting edge in Christian apologetics. Two years ago I interviewed one of Caltech's most brilliant graduate students on my television program. I asked him why he, as an evangelical Christian with a strong interest in missions, decided to pursue a career as a string theorist. He replied that after very seriously and prayerfully considering becoming a full-time missionary, he concluded that he could have a much greater impact for the advance of the Gospel by advancing string theory. Two years before completing his Ph.D. and two years before any of these incredible discoveries had been made, Gerald had the foresight to recognize that string theory would yield many significant proofs that will help convince skeptical minds of the truth of Scripture and of Christ's claims. I believe, as he does, that the days ahead will yield many more such proofs.

What if every Bible college and missionary training school in the country incorporated relativity theory and string theory into the curriculum, along with other courses in the sciences? Dream on you might say. Yet, every Bible college and missionary training school with which I 've had contact in the past ten years has been receptive to the idea--once the leaders got a glimpse of what's taking place at the frontiers of science. This dream can come true if we can raise up an army of Geralds and others like him. Please join me in praying that God will bless our efforts (and others') to do just that.

References:

1. K. C. Cole, "Two Physicists Simplify Study of Four-Dimensional Space," Los Angeles Times (November 29, 1994), pp. A1, A29
2. Gary Taubes, "How Black Holes May Get String Theory Out of a Bind," Science, 268 (1995), p. 1699.
3. Taubes, "A Theory of Everything Takes Shape," Science, 269 (1995), p. 1513.
4. Hugh Ross, "Quark Family Now Complete," Facts & Faith, vol. 8, no. 3 (1994), pp. 3-4.
5. Ivars Peterson, "Beyond the Top: Now that Physicists Have Found the Top Quark, What's Next?" Science News, 148 (1995), pp. 10-12.
6. Ross, The Creator and the Cosmos, 2nd ed. (Colorado Springs, CO: NavPress, 1995), pp. 73-75.
7. S. K. Lamoreaux et al., "New Limits on Spatial Anistropy from Optically Pumped 201Hg and 199Hg," Physical Review Letters, 57 (1986), pp. 3125-3128.
8. Stephen W. Hawking, and George F. R. Ellis, "The Cosmic Black-Body Radiation and the Existence of Singularities in our Universe," Astrophysical Journal, 152 (1968), pp. 25-36.
9. Hawking, Stephen and Penrose, Roger, "The Singularities of Gravitational Collapse and Cosmology," Proceedings of the Royal Society of London, Series A, 314 (1970), pp. 529-548.

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