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A Scientist's Notebook
by Gregory Benford

Living In An Eleven-Dimensional World

We have always thought of black holes as distant, shadowy phenomena, bizarrely crunching space-time around themselves. They trap huge masses, as great as those of stars, letting not even light escape their grasp.

Maybe not. To the surprise of many, we may quite soon find tiny black holes, crashing into our upper atmosphere. And this way of possibly making microscopic black holes comes not from astronomy, but from an idea long the favorite of mathematicians---extra dimensions, beyond our humdrum three.

We begin with a simple picture: Smack particles together at high energies and see if a new kind of "particle" emerges. This is how high energy physics has proceeded for a century. Only this time the "particles" may be infinitesimal black holes that last only an instant, allowing us a look at such exotic beasts---before they evaporate in a spray of energetic radiation.

This is the "Hawking radiation," a jet of everything from light to nuclear matter---all coming from a point exactly like a very hot object, the dying black hole itself. This fountain of stuff is an effect Stephen Hawking first predicted in the early 1970s. He was thinking of large, star-sized black holes, but the effect can occur on any scale.

Black holes can have any size, so long as they have the appropriate enormous mass density. Alas, the great bulk of black hole theory has not been verified by experiment---yet. But now it appears that we might be able to conduct experiments without venturing far into the vacuum of space.

Recently particle physicists studying very high energy cosmic rays (including Jonathan Feng, a colleague in the physics department here at UC-Irvine) have noticed that upcoming detectors could detect micro-black holes, and in so doing test the old question of how many dimensions our universe has.

Obviously, extra dimensions cannot be large enough for us to readily see. So we must think small.

In physics, tiny lengths demand going to very high energies. To test the existence of minute extra dimensions requires particles stupendously more energetic than anything we can make in the lab. So we can resort to the vast energies available from cosmic rays, which were made in equally impressive events: supernovas, or the new "hypernovas" which may occur when stars collide, sending neutron stars plunging down the gullets of black holes. (Never underestimate the appetite of astrophysicists for ever-monstrous ideas.)

Whatever the origin of the most energetic cosmic rays, they might give us enough energy to study the whole issue of extra dimensions. Streaming into our atmosphere, cosmic ray protons have huge energies---as much as a thrown baseball, all packed into a single tiny particle. If they collide with the protons in, say, the water of our upper atmosphere, they could spit out mini-holes that then expire in a twinkling.

It turns out that very energetic neutrinos, those "little neutral particles" that come from nuclear processes, seem to be the most effective in making tiny black holes as they lace through our atmosphere. They would send quick, horizontal jets across the sky. These would be made up of the stuff of nuclei themselves---quarks and gluons.

Particle detectors on the ground below might be able to see such singular flares. Searches for them will begin within a few years, when enough detectors are in place.

They would finally, if indirectly, confirm that black holes exist. We would find that showers of holes had been bursting over our heads all the time, unknown. Plus, we would have evidence of extra dimensions beyond our ordinary senses.

What are these dimensions and why should they be there?

*     *     *

First, they must be very small. In ordinary life, by waving your hand you're sweeping through the tiny dimensions without noticing them. Extra dimensions far smaller than an atomic nucleus could have escaped the notice of even recent, high energy experiments.

The basic three dimensions we know: height, width, and depth. Edwin Abbott first expressed the idea of four dimensions (4D) in his founding 1884 novel Flatland. He built it upon ideas already present in mathematics, which treats the number of dimensions as arbitrary. Abbott framed a satirical novel in 2D to give perspective on social problems. Many others took up the idea, ascribing religious heft to 4D. It was where spiritual entities hung out and thus explained ghosts. As well, 4D gave God a way to see everything in our 3D universe at once---omniscience.

Since that era, this curious notion has drifted at the edge of scientific thinking--that our three-dimensional world might be embedded in a larger, spatially four-dimensional universe we cannot readily detect. We would be like an insect crawling over the surface of a basketball, eyes unable to see its true situation. Now many more dimensions have become the hottest idea in theoretical physics, with huge implications.

Physicists began envisioning higher dimensions because they got from the effort a simpler dynamic picture. Mathematically, some of the basic equations describing our world look more elegant in higher dimensions. Principally, Einstein's general relativity theory acquires a graceful symmetry in 4D. But this comes at the price of apparent complication, too.

Why? More dimensions to deal with certainly strains the imagination, but can lead to beauties that theorists love, abstruse elegances. Einstein, in his 1916 mathematical theory of general relativity, invoked the simplicity that objects move in "geodesics"---undisturbed paths, the equivalent of a straight line in Euclidean, rectangular 3D geometry, or a great circle on a sphere---in a four-dimensional space-time. He gained clarity of concept in return for the complication of a higher dimension.

Matter curved his 4D spacetime, an effect we know as gravity. A geodesic near a planet, then, is an orbit---an ellipse, not a straight line. Even though an object moving along this path that looks curved to us seems to be accelerated, it feels no acceleration—zero-g.

This way of thinking replaced a classical idea, force, with a modern geometrical view, curvature of a 4D world.

Now our hottest grand Theory Of Everything replaces Einstein's picture of point particles moving in a geometric world with vibrating strings. They are like closed rubber bands of space-time, and are the basic objects that we see as particles. (Brian Greene's bestselling The Elegant Universe is a good introduction to this bewildering view of our universe.)

Such tiny objects have tension and so can hum with characteristic tones like piano strings. These timbres correspond to matter waves, giving the masses of elementary particles. Change the string tension and you get a different particle mass, in the universe as we perceive it. Presto, string theory yields every particle we know, plus gravity (communicated by a particle called the "graviton") and even more. So this is a fresh underlying picture: a variety of tiny strings, each type strumming to a different celestial harmony---the music of masses.

And the payoff of extra dimensions? Just maybe, an explanation of literally Everything.

*     *     *

The trick is that these strings are incredibly tiny and live in an eleven-dimensional space---the four we are now used to, including time, plus seven more. Think of our 4D space-time as a sphere that is actually the boundary of a 5D "bubble." The remaining five or six dimensions (there is some controversy about how many there might be) are curled up.

How come we don't see these tiny add-ons? Because they rolled up into infinitesimal size at the very birth of the Big Bang, so we haven't noticed them.

In Flatland Abbott made his 2D flatlanders "real" by adding a tiny height to them, so they do exist in our 3D world---though they don't know it. This was strikingly prescient. String theories use an analogy with a garden hose. From far away the hose looks like a 1D object, a looped string. But up close, we see that it has another dimension, perpendicular to the long direction. This direction is one of the extra dimensions, unobservably small---perhaps a billion billion billion times more tiny than an atom.

Perhaps we are living in a universe only apparently spatially three-dimensional. Infinitesimal but real dimensions lurk all about us. What's more, those dimensions are curled, so they never "unroll" to be visible to us.

What an odd picture---that you constantly move through the six invisible dimensions, wrapping around them many times, like an insect circling that garden hose. You take no notice.

Why are the extra dimensions tiny? So far, this occurs by what some dismiss as "wantum mechanics"---we want it, so it must happen. Current theories have hand-waving explanations that roll up dimensions by tying them like a roll of dollar bills, with special strings like rubber bands.

Those strings are (we think) the same kind whose strumming vibrations set the masses and charges of particles. Here they have to play a further role, though, having tension that keeps those unsightly dimensions from unrolling and expanding our universe unimaginably. It is almost as if Creation began with the elegant form of eleven dimensions, which mathematicians love, and then had to seal off most of them. Exactly why, we don't know---just one of the arbitrary points of the theory. Indeed, until recently theorists thought that string theory dictated ten dimensions. They then found that mathematically, they could unify the subject better if there were eleven. The jury is still out on the exact number, though the majority favors eleven right now.

All this furious dimensional rolling up and organizing had to happen sometime in the very early universe, too. Otherwise the universe would have dissipated the Big Bang into all the extra dimensions, exhausting the primordial energies that made our universe the size it is today. If the extra dimensions had been free to grow, the universe would have been over, energies spent, before our whole show got started.

Some such curling up must have happened. Without it we would have ended up with unworkable, chilly universes that could not support life.

For example, consider the field theories that tell us what particles can be in our universe. If they had more than three persisting (not rolled up) spatial dimensions, a simple calculation shows that there could be no stable atoms--and thus, no matter more complex than single particles.

Gravity itself gets unruly with more than 3 large spatial dimensions to operate in. Orbits of planets are unstable for 4D and higher---so there will be no solar systems, or even galaxies.

There are many reasons why substantial higher dimensions make trouble. Only in odd-numbered dimensions can waves propagate sharply, without weird reverberations. Maybe that effect alone prevented the other dimensions from unrolling?

Again, the abstruse reaches of mathematical string theory provide no answer. Also, those weird waves could make life impossible by confusing the physical world. Then even simple biological processes could not proceed. Planetary orbits would be unstable if the extra dimensions were large. Perhaps the basic forces would be altered as well, making chemistry very difficult.

Why did Creation stop at only big 3 spatial dimensions, then? We don't know, Maybe an "anthropic" argument is the closest we will ever get to an explanation. This view holds that many kinds of universes could be created, but the one we live in had very special properties---because otherwise, we wouldn't exist to ask such questions.

*     *     *

Perhaps 3D is optimum. For smart life like us, 3D is favored over 2D because there are so few connections and geometric tricks available in 2D. Try to imagine living in Flatland. Seen from our 3D world, the 2D beings must still have basic body functions. Eating means taking something from outside and processing it inside. But to have an alimentary canal means dividing in two!---the paired sides of a 2D animal.

Higher dimensions than ours might provide even more physiological tricks. Maybe other higher dimensional universes exist, beyond our seeing---but they could be boring, because it would be hard to arrange biological processes with so many degrees of freedom. Life there may be no better than 6D slime molds.

Not all the items theorists exclude from the Menu of Universes are dull. You might innocently ask why the extra dimensions must be spatial at all. Why not an extra time dimension?

We know the idea of repeating a pattern in space, returning to the same spot. (Most dances are like that---repetitions we enjoy.) The bug walking around the outer rim of a the garden hose can circumnavigate its world and come home again.

But what would moving through an extra dimension in time feel like? The bug would return to a prior moment---time travel.

Again, we would not notice our arm sweeping through tiny slices of past time. But events could cycle in time, changing the way atoms or particles work together. How could this be coherent? The imagination flags.

This weird notion so violates our intuition that few string theorists have taken it up. There seems no fundamental reason why it should be excluded, but it's, well, disturbing. Even theory has its limits---as do theorists.

*     *     *

Can such small dimensions matter? They do lead to beautiful equations, but can the larger picture lead to major changes in the way we think?

Gravity is key. It has always stood apart from the other forces (electrical and nuclear). Compared with them, gravity is very weak It reigns supreme in the cosmos, making galaxies whirl and structure form, only because the other forces have such a short range. Gravity rules over large distances.

In string theory, gravity is similarly isolated. It may be the only force that senses these other dimensions. Current theory supposes this is so. On such small scales gravity lives in many dimensions, and this makes it brutishly strong on tiny scales.

We've never noticed any deviation from the familiar gravitational law in the motions of planets, of course. But on tiny scales the theory is unchecked. It is very difficult to measure the weak gravitational attraction between iron balls at separations smaller than a tenth of a millimeter.

We can think of the extra dimensions as added space to stuff the gravitational force into. Gravity may only seem weak to us 3Ders because we don't know about the extra dimensions. Gravity may be leaking into all those extra tiny dimensions, dissipating its force so that it looks weaker than big, robust electricity.

Picture gravity as spreading over an expanding area, the way light dims far from a street lamp. Get closer and the attractive force rises rapidly. Now add extra dimensions. The closer two small, gravitating masses are, the steeper their gravitational attraction gets, because it has extra room to spread. This means stronger attraction at tiny distances, so that gravity can draw the masses tighter together. Near enough, and gravity wins over any repulsive force (say, if the particles had the same charge).

Presto, the amplified gravity will slam the particles together. At a high enough mass density, you find that ordinary two-particle collisions can form a black hole.

*     *     *

Such practical ideas are fine, and may increase funding---but the wonder of living in a many-dimensioned world is more fun.

Some recent theories believe there may be very large extra dimensions, not rolled up at all. These would be spaces above and beyond our own.

Edwin Abbott taught us to think about a 2D being, suddenly moving through our 3D world. That Flatlander would see only slices of our reality---cross sections of trees and rocks and moving cars. How could it stitch this into a coherent view?

If it did, it could make a 2D symbol or picture and we would understand it as a flat scene. But for the 2D creature what we took as an image would be the whole object, not just a photograph. A photograph to us would be a world to the 2D citizen.

Similarly, we the dimensionally destitute, trapped in our narrow 3D, could not see dimensions above. So big extra dimensions may lie beyond our senses.

To process light we use a basically 2D retina fit at the back of a spherical eyeball. Then we reconstitute in our brains our 3D world picture. We're so good at this stunt, we never think about it.

But consider an analogy. A 4D creature must have a 3D eye, then. A retinal sphere, not a mere plane, could provide the same service, to image the 4D world.

In this way, maybe we can intuit 4D, even if we can't see it. Consider 2D. A Flatlander would see a human finger as a 2D blob that changed size and shape as the finger thrust down through its world, punching through the 2D sheet on which it lived.

How about us, here with our blinkered perspective? If a 4D creature moved through, we would see 3D blobs appearing mysteriously, moving past in confusing ways. We could not comprehend how they fitted together into something that extended away, in an unseen direction.

If the 4Ders spoke, we would hear a strange symphony of booms and clatters and screeches coming from the air all around, and even from inside us. These would be sounds as they are in 4D, where the waves spread out in a different way, in complex packets and eddies.

Some distinctions in 3D-space mean nothing when viewed in 4D. Distinctions we take as basic may evaporate in the larger perspective.

To see why, consider 2D first---say, the sense of left and right. Picture a hand drawn on transparent glass. The 2Der lives on that plane and can't escape it. We can. Viewed from one side of the glass, the hand looks right-handed. Now we flip the glass. From the other side, it looks left-handed.

Handedness is a 2D distinction. Being able to look at a 2D difference fully makes it trivial to the 3D person viewing it.

A 4D entity looking at 3D objects also has a wider understanding. It sees all aspects of our 3D world, simultaneously, with nothing blocked by angle of view. What would that be like?

Consider when we look at a 2D painting. We see everything in it from one viewpoint. Suppose you go to an art exhibit to see a sculpture of a woman. There are ten copies of it, each one rotated a bit, standing against a wall. You stand in one place and can look at the entire woman without moving.

This has been tried. People who see such a sculpture often do not recognize the ten different angles as showing the same object.

Maybe this is something like being a 4D creature, which can then see everything in a 3D scene, without moving the viewpoint.

*     *     *

Perhaps the most intriguing aspect of all these new theoretical models is what they don't explain.

If there are large extra dimensions, why don't we see any signs? Blobs appearing from nowhere, for example, as 4D objects intrude.

Go back to the 2D analogy. We don't intervene in any 2D worlds, because we haven't found any. Geometrically, this may mean that we are isolated on a membrane ("brane theory") and can't reach down to a 2D world. We're tightly bound to our brane by forces at the particle level. Our effects can't reach the lesser world of 2D.

Similarly, 4D spaces may not be able to reach into ours. When we know more about the forces keeping us in our 3D universe, maybe we'll discover a way to venture into both 2D and 4D universes.

Or maybe we don't recognize the signs of intrusion? In our 3D world, two 2D planes can intersect, meeting along a line---like the two opposite pages of a book. Similarly, two 3D spaces can intersect, meeting only in a plane.

Clear evidence that somebody is tinkering from 4D would be the sudden appearance of a plane slanting across our space, extending to infinity, mottled with passing images. When you approach the plane you can feel the objects in it. Though you flatten yourself against the plane, you cannot fully enter the other realm, because you can only insert a slice of yourself at a time.

Nobody sees such things in everyday life, of course. But maybe we're not making allowances for how utterly different a 4D world might be. Objects that appear only on a plane would be mysterious images without solid manifestations. We would see them moving, but not find any hard evidence.

This sounds oddly like the many UFO sightings that never yield solid proof. (Or like ghosts, too.) What if, for reasons we do not fathom, 4D beings appear only in our skies, not on the ground? Then they might seem to be cruising forms, ships, glowing lights---then gone, vanished into other 4D realms we do not know.

This is just a speculation, but it shows how little we truly know about the possibilities of 4D, or more-D. As theories mount, we should remember that a mind-wrenching notion like higher dimensions will have ramifications far beyond the conventional.

They may be hard to recognize. The most valuable tool in the scientist's kit is the ability to be surprised.

*     *     *

But it takes data to do that. So the experiments to see sprays of mini-black holes in our upper atmosphere may give us the first clue to the lurking extra dimensions. Not as shocking as a sudden apparition from 4D, maybe, but solid.

Suppose the detectors now being assembled do find jets of energetic particles zooming along horizontal paths in our atmosphere---the signature of black hole evaporation. We could use these to study black holes, learning far more than we ever could by looking for distant holes in the galaxy.

Beyond opening a whole new window on the laws of our universe, what use could we make of the spray of particles that signify black holes?

Could we enhance the mass of the tiny holes until they could survive? To do that, they would have to ingest a lot more matter and build up their masses. It looks impossible, even if the particle shower occurs right next to a sheet of lead.

If this proves so, too bad---because tiny holes could be both disposal sites and energy sources. So far, all speculations about how to utilize black holes have focused on holes with the mass of stars, but the basic processes work on any scale.

Throw garbage down a hole and it is gone forever. But in the last instant before vanishing down gravity's gullet, the heated mass radiates back out to us high energy jets of virulent light. Roger Penrose noticed this possibility in his early papers on black hole geometry. Harnessing this effect might be possible, making a genuinely pollution-swallowing energy source.

So it's conceivable that as arcane an idea as extra dimensions could have

engineering implications. The day may come when civil engineers will need to know not mere differential and integral calculus, but hypergeometric surfaces, 4D projection, and other rarefied arts.

Knowing this material could do worlds of good (literally). But as a professor who teaches mechanics to engineers now, that's one course I hope I won't have to teach.

===THE END===


copyright © 2002 Abbenford Associates

Gregory Benford is a professor of physics at the University of California, Irvine. Comments on this column welcome at gbenford@uci.edu, or Physics Dept., Univ. Calif., Irvine, CA 92717


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