This is how things stood in the world of extra dimensions until very recently. It was thought that extra dimensions might be present but that they would be extremely small. But our expectations changed dramatically after 1995, when Joe Polchinski, of the University of California at Santa Barbara, and other theorists recognized the importance of additional objects in string theory called branes. Branes are essentially membranes—lower-dimensional objects in a higher-dimensional space. (To picture this, think of a shower curtain, virtually a two-dimensional object in a three-dimensional space.) Branes are special, particularly in the context of string theory, because there’s a natural mechanism to confine particles to the brane; thus not everything need travel in the extra dimensions, even if those dimensions exist. Particles confined to the brane would have momentum and motion only along the brane, like water spots on the surface of your shower curtain.
Branes allow for an entirely new set of possibilities in the physics of extra dimensions, because particles confined to the brane would look more or less as they would in a three-plus-one-dimension world; they never venture beyond it. Protons, electrons, quarks, all sorts of fundamental particles could be stuck on the brane. In that case, you may wonder why we should care about extra dimensions at all, since despite their existence the particles that make up our world do not traverse them. However, although all known standard-model particles stick to the brane, this is not true of gravity. The mechanisms for confining particles and forces mediated by the photon or electrogauge proton to the brane do not apply to gravity. Gravity, according to the theory of general relativity, must necessarily exist in the full geometry of space. Furthermore, a consistent gravitational theory requires that the graviton, the particle that mediates gravity, has to couple to any source of energy, whether that source is confined to the brane or not. Therefore, the graviton would also have to be out there in the region encompassing the full geometry of higher dimensions—a region known as the bulk—because there might be sources of energy there. Finally, there’s a string-theory explanation of why the graviton is not stuck to any brane: The graviton is associated with the closed string, and only open strings can be anchored to a brane.
A scenario in which particles are confined to a brane and only gravity is sensitive to the additional dimensions permits extra dimensions that are considerably larger than previously thought. The reason is that gravity is not nearly as well tested as other forces, and if it’s only gravity that experiences extra dimensions, the constraints are much more permissive. We haven’t studied gravity as well as we’ve studied most other particles, because it’s an extremely weak force and therefore more difficult to precisely test. Physicists have showed that even dimensions almost as big as a millimeter would be permitted if it were only gravity out in the higher-dimensional bulk. This size is huge compared with the scales we’ve been talking about. It is a macroscopic, visible size! But because photons (which we see with) are stuck to the brane, too, the dimensions would not be visible to us, at least in the conventional ways.
Once branes are included in the picture, you can start talking about crazily large extra dimensions. If the extra dimensions are very large, that might explain why gravity is so weak. Gravity might not seem weak to you, but it’s the entire Earth that’s pulling you down; the result of coupling an individual graviton to an individual particle is quite small. From the point of view of particle physics, which looks at the interactions of individual particles, gravity is an extremely weak force. This weakness of gravity is a reformulation of the so-called hierarchy problem—that is, why the huge Planck mass suppressing gravitational interactions is 16 orders of magnitude bigger than the mass associated with particles we see. But if gravity is spread out over large extra dimensions, its force would indeed be diluted. The gravitational field would spread out in the extra dimensions and consequently be very weak on the brane—an idea recently proposed by theorists Nima Arkani Hamed, Savas Dimopoulos, and Gia Dvali. The problem with this scenario is the difficulty of explaining why the dimensions should be so large. The problem of the large ratio of masses is transmuted into the problem of the large size of curled-up dimensions.
Raman Sundrum, currently at Johns Hopkins University, and I recognized that a more natural explanation for the weakness of gravity could be the direct result of the gravitational attraction associated with the brane itself. In addition to trapping particles, branes carry energy. We showed that from the perspective of general relativity this means that the brane curves the space around it, changing gravity in its vicinity. When the energy in space is correlated with the energy on the brane so that a large flat three-dimensional brane sits in the higher-dimensional space, the graviton—the particle communicating the gravitational force—is highly attracted to the brane. Rather than spreading uniformly in an extra dimension, gravity stays localized, very close to the brane.
The high concentration of the graviton near the brane—let’s call the brane where gravity is localized the Planck brane—leads to a natural solution to the hierarchy problem in a universe with two branes. For the particular geometry that solves Einstein’s equations, when you go out some distance in an extra dimension, you see an exponentially suppressed gravitational force. This is remarkable, because it means that a huge separation of mass scales—16 orders of magnitude—can result from a relatively modest separation of branes. If we are living on the second brane—not the Planck brane—we would find that gravity was very weak. Such a moderate distance between branes is not difficult to achieve and is many orders of magnitude smaller than that necessary for the large-extra-dimensions scenario just discussed. A localized graviton plus a second brane separated from the brane on which the standard model of particle physics is housed provides a natural solution to the hierarchy problem—the problem of why gravity is so incredibly weak. The strength of gravity depends on location, and away from the Planck brane it is exponentially suppressed.
This theory has exciting experimental implications, since it applies to a particle physics scale—namely, the TeV scale. In this theory’s highly curved geometry, Kaluza-Klein particles—those particles with momentum in the extra dimensions—would have mass of about a TeV; thus there is a real possibility of producing them at colliders in the near future. They would be created like any other particle and they would decay in much the same way. Experiments could then look at their decay products and reconstruct the mass and spin that is their distinguishing property. The graviton is the only particle we know about that has spin-2. The many Kaluza-Klein particles associated with the graviton would also have spin-2 and could therefore be readily identified. Observation of these particles would be strong evidence of the existence of additional dimensions and would suggest that this theory is correct.
As exciting as this explanation of the existence of very different mass scales is, Raman and I discovered something perhaps even more surprising. Conventionally, it was thought that extra dimensions must be curled up or bounded between two branes, or else we would observe higher-dimensional gravity. The aforementioned second brane appeared to serve two purposes: It explained the hierarchy problem because of the small probability for the graviton to be there, and it was also responsible for bounding the extra dimension so that at long distances, bigger than the dimension’s size, only three dimensions are seen.
The concentration of the graviton near the Planck brane can, however, have an entirely different implication. If we forget the hierarchy problem for the moment, the second brane is unnecessary. That is, even if there’s an infinite extra dimension and we live on the Planck brane in this infinite dimension, we wouldn’t know about it. In this “warped geometry,” as the space with exponentially decreasing graviton amplitude is known, we would see things as if this dimension did not exist and the world were only three-dimensional.
Because the graviton has such a small probability of being located away from the Planck brane, anything going on far away from the Planck brane should be irrelevant to physics on or near it.
The physics far away is in fact so entirely irrelevant that the extra dimension can be infinite, with absolutely no problem from a three-dimensional vantage point. Because the graviton makes only infrequent excursions into the bulk, a second brane or a curled-up dimension isn’t necessary to get a theory that describes our three-dimensional world, as had previously been thought. We might live on the Planck brane and address the hierarchy problem in some other manner—or we might live on a second brane out in the bulk, but this brane would not be the boundary of the now infinite space. It doesn’t matter that the graviton occasionally leaks away from the Planck brane; it’s so highly localized there that the Planck brane essentially mimics a world of three dimensions, as though an extra dimension didn’t exist at all. A four-spatial-dimensions world, say, would look almost identical to one with three spatial dimensions. Thus all the evidence we have for three spatial dimensions could equally well be evidence for a theory in which there are four spatial dimensions of infinite extent.
It’s an exciting but frustrating game. We used to think the easiest thing to rule out would be large extra dimensions, because large extra dimensions would be associated with low energies, which are more readily accessible. Now, however, because of the curvature of space, there is a theory permitting an infinite fourth dimension of space in a configuration that so closely mimics three dimensions that the two worlds are virtually indistinguishable.
If there are differences, they will be subtle. It might turn out that black holes in the two worlds would behave differently. Energy can leak off the brane, so when a black hole decays it might spit out particles into the extra dimension and thus decay much more quickly. Physicists are now doing some interesting work on what black holes would look like if this extra-dimensional theory with the highly concentrated graviton on the brane is true; however, initial inquiries suggest that black holes, like everything else, would look too similar to distinguish the four- and three-dimensional theories. With extra dimensions, there are an enormous number of possibilities for the overall structure of space. There can be different numbers of dimensions and there might be arbitrary numbers of branes contained within. Branes don’t even all have to be three-plus-one-dimensional; maybe there are other dimensions of branes in addition to those that look like ours and are parallel to ours. This presents an interesting question about the global structure of space, since how space evolves with time would be different in the context of the presence of many branes. It’s possible that there are all sorts of forces and particles we don’t know about that are concentrated on branes and can affect cosmology.
In the above example, physics everywhere—on the brane and in the bulk—looks three-dimensional. Even away from the Planck brane, physics appears to be three-dimensional, albeit with weaker gravitational coupling. Working with Andreas Karch (now at the University of Washington), I discovered an even more amazing possibility: Not only can there be an infinite extra dimension but physics in different locations can reflect different dimensionality. Gravity is localized near us in such a way that it’s only the region near us that looks three-dimensional; regions far away reflect a higher-dimensional space. It may be that we see three spatial dimensions not because there really are only three spatial dimensions but because we’re stuck to this brane and gravity is concentrated near it, while the surrounding space is oblivious to our lower-dimensional island. There are also some possibilities that matter can move in and out of this isolated four-dimensional region, seeming to appear and disappear as it enters and leaves our domain. These are very hard phenomena to detect in practice, but theoretically there are all sorts of interesting questions about how such a construct all fits together.
Whether or not these theories are right will not necessarily be answered experimentally but could be argued for theoretically, if one or more of them ties into a more fundamental theory. We’ve used the basic elements found in string theory—namely, the existence of branes and extra dimensions—but we would really like to know if there is a true brane construction. Could you take the very specific branes given by string theory and produce a universe with a brane that localizes gravity? Whether you can actually derive this from string theory or some more fundamental theory is important. The fact that we haven’t done it yet isn’t evidence that it’s not true, and Andreas and I have made good headway into realizing our scenario in string theory. But it can be very, very hard to solve these complicated geometrical set-ups. In general, the problems that get solved, although they seem very complicated, are in many ways simple problems. There’s much more work to be done; exciting discoveries await, and they will have implications for other fields.
In cosmology, for instance. Alan Guth’s mechanism whereby exponential expansion smooths out the universe works very well, but another possibility has been suggested: a cyclic universe, Paul Steinhardt’s idea, wherein a smaller amount of exponential expansion happens many times. Such a theory prompts you to ask questions. First of all, is it really consistent with what we see? The jury’s out on that. Does it really have a new mechanism in it? In some sense, the cyclic idea still uses inflation to smooth out the universe. Sometimes it’s almost too easy to come up with theories. What grounds your theories? What ties them down? What restricts you from just doing anything? Is there really a new idea there? Do we really have a new mechanism at work? Does it connect to some other, more fundamental theoretical idea? Does it help make that work? Recently I have been exploring the implications of extra dimensions for cosmology. It seems that inflation with extra dimensions works even better than without! What’s so nice about this theory is that one can reliably calculate the effect of the extra dimension; no ad-hoc assumptions are required. Furthermore, the theory has definite implications for cosmology experiments. All along, I’ve been emphasizing what we actually see. It’s my hope that time and experiments will distinguish among the possibilities.
6
The Cyclic Universe
Neil Turok
Theoretical physicist, director, and Mike and Ophelia Lazardis Neils Bohr Chair in Theoretical Physics, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; coauthor (with Paul Steinhardt), Endless Universe: Beyond the Big Bang
For the last ten years, I have mainly been working on the question of how the universe began—or didn’t begin. What happened at the Big Bang? To me, this seems like one of the most fundamental questions in science, because everything we know of emerged from the Big Bang. Whether it’s particles or planets or stars or, ultimately, even life itself.
In recent years, the search for the fundamental laws of nature has forced us to think about the Big Bang much more deeply. According to our best theories, string theory and M-theory, all of the details of the laws of physics are determined by the structure of the universe—specifically, by the arrangement of tiny, curled-up extra dimensions of space. This is a very beautiful picture: Particle physics itself is now just another aspect of cosmology. But if you want to understand why the extra dimensions are arranged as they are, you have to understand the Big Bang, because that’s where everything came from.
Somehow, until quite recently, fundamental physics had gotten along without really tackling that problem. Even back in the 1920s, Einstein, Friedmann, and Lemaître, the founders of modern cosmology, realized there was a singularity at the Big Bang. That somehow, when you trace the universe back, everything went wrong about 14 billion years ago. By “go wrong,” I mean all the laws of physics break down: They give infinities and meaningless results. Einstein himself didn’t interpret this as the beginning of time; he just said, “Well, my theory fails.” Most theories fail in some regime, and then you need a better theory. Isaac Newton’s theory fails when particles go very fast; it fails to describe that. You need relativity. Likewise, Einstein said we need a better theory of gravity than mine.
But in the 1960s, when the observational evidence for the Big Bang became very strong, physicists somehow leapt to the conclusion that it must have been the beginning of time.
I’m not sure why they did so, but perhaps it was due to Fred Hoyle, the main proponent of the rival Steady State theory, who seems to have successfully ridiculed the Big Bang theory by saying it didn’t make sense because it implied a beginning of time and that sounded nonsensical.
Then the Big Bang was confirmed by observation. And I think everyone just bought Hoyle’s argument and said, “Oh, well, the Big Bang is true, OK, so time must have begun.” So we slipped into this way of thinking—that somehow time “began,” and that the process, or event, whereby it began is not describable by physics. That’s very sad. Everything we see around us rests completely on that event, and yet that’s the event we can’t describe. That’s basically where things stood in cosmology, and people just worried about other questions for the next twenty years.
And then in the 1980s there was a merging of particle physics and cosmology, when the theory of inflation was invented. Inflationary theory also didn’t deal with the beginning of the universe, but it took us back further toward it. People said, “Let’s just assume the universe began somehow, but we’re going to assume that when it began it was full of a weird sort of energy called inflationary energy. This energy is repulsive—its gravitational field is not attractive, like ordinary matter—and the main property of that energy is that it causes the universe to expand, hugely fast. Literally like dynamite, it blows up the universe.”
The Universe_Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos Page 8
