We shouldn’t avoid anything. We should try to do our best to use the simplest explanations possible, or what proves simplest, and if something falls into your hands as an explanation of why the cosmological constant vacuum energy is so small, and you decide not to accept it for ideological reasons, this is very much what we had in Russia long ago. That ideology told me which type of physics was right and which type of physics was wrong. We should not proceed this way. Once you have multiple possibilities, then you can have scientific premises for anthropic considerations, not just philosophical talk about “other worlds.” Now we have a consistent picture of the multiverse, so now we can say, “This is physics. This is something serious.”
When you look at our own part of the universe, you have a galaxy to the right of you, you have a set of galaxies to the left of you. Could it be that our universe was formed differently? Is there a chance that me, my copy, might live somewhere far away from me? How far away from me? Why my exact copy? Well, because quantum fluctuations produce different universes over and over again. Alex Vilenkin has this description of “many worlds in one.” He wrote a book about it. The question is, how many of these different types of universes can you produce? And “different types of universes” does not just mean vacuum states but different distributions of matter. The distribution of matter in our part of the universe, the distribution of galaxies, is determined by quantum fluctuations, which were produced during inflation.
For example, you may have a scalar field that rolls down slowly, which is how inflation ends, but then quantum fluctuations push it, locally, up just a little. Then in these places the energy of the universe will locally increase. Then it becomes very, very big, and at this part you’ll see a galaxy in the place where you live. If the jump is down, then in this place you will see no galaxies. When this happens during inflation over and over again at different scales, then you check: How many different jumps, or kinds of configurations of jumps, have there been?
These jumps produce what later looks like different classical universes—a galaxy here, a void there. How many possibilities are there? And the answer—and this is purely a combinatorial answer—is that if n is the number of times the size of the universe doubled during inflation, and you take 23n, this will show you the volume of the universe after inflation. Where the volume grows by 23n, the total number of possible configurations that can occur there because of these quantum jumps will be also proportional to 23n. This will give you the total number of possible configurations of matter that you can produce during inflation, and this number typically is much, much greater than 10500.
Of course, during eternal inflation, inflation goes on forever, so you could even expect that this number is infinite. However, during eternal inflation each jump can be repeated; it can repeat itself. A scalar field jumps again to the state where it jumps again, to a state where it jumps again, and eventually it starts producing identical configurations of matter.
Think about it this way: Previously we thought our universe was like a spherical balloon. In the new picture, it’s like a balloon producing balloons producing balloons. This is a big fractal. The Greeks thought of our universe as an ideal sphere because this was the best image they had at their disposal. The 20th-century idea is a fractal, the beauty of a fractal. Now you have these fractals. We ask, How many different types of these elements of fractals are there which are irreducible to each other? And the number will be exponentially large. In the simplest models, it’s about 10 to the degree 10, to the degree 10, to the degree 7. It actually may be much more than that, even though nobody can see all of these universes at once.
Soon after Alan Guth proposed his version of inflationary theory, he famously exclaimed that the universe is an ultimate free lunch. Indeed, in inflationary theory the whole universe emerges from almost nothing. A year later, in the proceedings of the first conference on inflation, in Cambridge, I expanded his statement by saying that the universe is not just a free lunch, it is an eternal feast where all possible dishes are served. But at that time I could not even imagine that the menu of all possible universes could be so incredibly large.
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Theories of the Brane
Lisa Randall
Theoretical physicist, Frank B. Baird, Jr., Professor of Science, Harvard University; author, Higgs Discovery: The Power of Empty Space
Particle physics has contributed to our understanding of many phenomena, ranging from the inner workings of the proton to the evolution of the observed universe. Nonetheless, fundamental questions remain unresolved, motivating speculations beyond what is already known. These mysteries include the perplexing masses of elementary particles; the nature of the dark matter and dark energy that constitute the bulk of the universe; and what predictions string theory, the best candidate for a theory incorporating both quantum mechanics and general relativity, makes about our observed world. Such questions, along with basic curiosity, have prompted my excursions into theories that might underlie currently established knowledge. Some of my most recent work has been on the physics of extra dimensions of space and has proved rewarding beyond expectation.
Particle physics addresses questions about the forces we understand—the electromagnetic force, the weak forces associated with nuclear decay, and the strong force that binds quarks together into protons and neutrons—but we still have to understand how gravity fits into the picture. String theory is the leading contender, but we don’t yet know how string theory reproduces all the particles and physical laws we actually see. How do we go from this pristine, beautiful theory existing in ten dimensions to the world surrounding us, which has only four—three spatial dimensions plus time? What has become of string theory’s superfluous particles and dimensions?
Sometimes a fruitful approach to the big, seemingly intractable problems is to ask questions whose possible answers will be subject to experimental test. These questions generally address physical laws and processes we’ve already seen. Any new insights will almost certainly have implications for even more fundamental questions. For example, we still don’t know what gives rise to the masses of the fundamental particles—the quarks, leptons (the electron, for example), and electroweak gauge bosons—or why these masses are so much less than the mass associated with quantum gravity. The discrepancy is not small: The two mass scales are separated by 16 orders of magnitude! Only theories that explain this huge ratio are likely candidates for theories underlying the standard model. We don’t yet know what that theory is, but much of current particle physics research, including that involving extra dimensions of space, attempts to discover it. Such speculations will soon be explored at the Large Hadron Collider in Geneva, which will operate at the TeV energies relevant to particle physics. The results of experiments to be performed there should select among the various proposals for the underlying physical description in concrete and immediate ways. If the underlying theory turns out to be either supersymmetry or one of the extra-dimension theories I will go on to describe, it will have deep and lasting implications for our conception of the universe.
Right now, I’m investigating the physics of the TeV scale. Particle physicists measure energy in units of electron volts. “TeV” means “a trillion electron volts.” This is a very high energy and challenges the limits of current technology, but it’s low from the perspective of quantum gravity, whose consequences are likely to show up only at energies 16 orders of magnitude higher. This energy scale is interesting, because we know that the as-yet-undiscovered part of the theory associated with giving elementary particles their masses should be found there.
Most of us, however, suspect that a prerequisite for progress will be a worked-out theory that relates gravity to the microworld. Back at the very beginning, the entire universe could have been squeezed to the size of an elementary particle. Quantum fluctuations could shake the entire universe, and there would be an essential link between cosmology and the microworld. Of course, string theory and M-theory are the most ambitious
and currently fashionable attempts to do that. When we have that theory, we at least ought to be able to formulate some physics for the very beginning of the universe. One question, of course, is whether we’ll find that space and time are so complicated and screwed up that we can’t really talk about a beginning in time. We’ve got to accept that we will have to jettison more and more of our commonsense concepts as we go to these extreme conditions.
The main stumbling block at the moment is that the mathematics involved in these theories is so difficult that it’s not possible to relate the complexity of this ten- or eleven-dimensional space to anything we can actually observe. In addition, although these theories may appear aesthetically attractive, and although they give us a natural interpretation of gravity, they don’t yet tell us why our three-dimensional world contains the types of particles that physicists study. We hope that one day this theory, which already deepens our insight into gravity, will gain credibility by explaining some of the features of the microworld that the current standard model of particle physics does not.
Although Roger Penrose can probably manage four dimensions, I don’t think any of these theorists can in any intuitive way imagine the extra dimensions. They can, however, envision them as mathematical constructs, and certainly the mathematics can be written down and studied. The one thing that’s rather unusual about string theory from the viewpoint of the sociology and history of science is that it’s one of the few instances where physics has been held up by a lack of the relevant mathematics. In the past, physicists have generally taken fairly old-fashioned mathematics off the shelf. Einstein used 19th-century non-Euclidean geometry, and the pioneers in quantum theory used group theory and differential equations that had essentially been worked out long beforehand. But string theory poses mathematical problems that aren’t yet solved, and has actually brought math and physics closer together.
String theory is the dominant approach right now, and it has some successes already, but the question is whether it will develop to the stage where we can actually solve problems that can be tested observationally. If we can’t bridge the gap between this ten-dimensional theory and anything that we can observe, it will grind to a halt. In most versions of string theory, the extra dimensions above the normal three are all wrapped up very tightly, so that each point in our ordinary space is like a tightly wrapped origami in six dimensions. We see just three dimensions; the rest are invisible to us because they are wrapped up very tightly. If you look at a needle, it looks like a one-dimensional line from a long distance, but really it’s three-dimensional. Likewise, the extra dimensions could be seen if you looked at things very closely. Space on a very tiny scale is grainy and complicated—its smoothness is an illusion of the large scale. That’s the conventional view in these string theories.
An idea which has become popular in the last two or three years is that not all the extra dimensions are wrapped up—that there might be at least one extra dimension that exists on a large scale. Raman Sundrum and I have developed this idea in our work on branes. According to this theory, there could be other universes, perhaps separated from ours by just a microscopic distance; however, that distance is measured in some fourth spatial dimension, of which we are not aware. Because we are imprisoned in our three dimensions, we can’t directly detect these other universes. It’s rather like a whole lot of bugs crawling around on a big two-dimensional sheet of paper, who would be unaware of another set of bugs that might be crawling around on another sheet of paper that could be only a short distance away in the third dimension. In a different way, this concept features in a rather neat model that Paul Steinhardt and Neil Turok have discussed, which allows a perpetual and cyclic universe. These ideas, again, may lead to new insights. They make some not-yet-testable predictions about the fluctuation of gravitational waves, but the key question is whether they have the ring of truth about them. We may know that when they’ve been developed in more detail.
Two of the potential explanations for the huge disparity in energy scales are supersymmetry and the physics of extra dimensions. Supersymmetry, until very recently, was thought to be the only way to explain physics at the TeV scale. It is a symmetry that relates the properties of bosons to those of their partner fermions—bosons and fermions being two types of particles distinguished by quantum mechanics. Bosons have integral spin and fermions have half-integral spin, where spin is an internal quantum number. Without supersymmetry, one would expect these two particle types to be unrelated. But given supersymmetry, properties like mass and the interaction strength between a particle and its supersymmetric partner are closely aligned. It would imply for an electron, for example, the existence of a corresponding superparticle—called a selectron in this case—with the same mass and charge.
There was and still is a big hope that we will find signatures of supersymmetry in the next generation of colliders. The discovery of supersymmetry would be a stunning achievement. It would be the first extension of symmetries associated with space and time since Einstein constructed his theory of general relativity in the early 20th century. And if supersymmetry is right, it’s likely to solve other mysteries, such as the existence of dark matter. String theories that have the potential to encompass the standard model seem to require supersymmetry, so the search for supersymmetry is also important to string theorists. Both for these theoretical reasons and for its potential experimental testability, supersymmetry is a very exciting theory.
However, like many theories, supersymmetry looks fine in the abstract but leaves many questions unresolved when you get down to the concrete details of how it connects to the world we actually see. At some energy, supersymmetry must break down, because we haven’t yet seen any “superpartners.” This means that the two particle partners—for example, the electron and the selectron—cannot have exactly the same mass; if they did, we would see both. The unseen partner must have a bigger mass if it has so far eluded detection. We want to know how this could happen in a way consistent with all known properties of elementary particles. The problem for most theories incorporating supersymmetry breaking is that all sorts of other interactions and decays are predicted which experiment has already ruled out. The most obvious candidates for breaking supersymmetry permit the various kinds of quarks to mix together, and particles would have a poorly defined identity. The absence of this mixing, and the retention of the various quark identities, is a stringent constraint on the content of the physical theory associated with supersymmetry breaking, and is one important reason that people were not completely satisfied with supersymmetry as an explanation of the TeV scale. To find a consistent theory of supersymmetry requires introducing physics that gives masses to the supersymmetric partners of all the particles we know to exist, without introducing interactions we don’t want. So it’s reasonable to look around for other theories that might explain why particle masses are associated with the TeV energy scale and not one that’s 16 orders of magnitude higher.
There was a lot of excitement when it was first suggested that extra dimensions provide alternative ways to address the origin of the TeV energy scale. Additional spatial dimensions may seem like a wild and crazy idea at first, but there are powerful reasons to believe that there really are extra dimensions of space. One reason resides in string theory, in which it’s postulated that the particles are not themselves fundamental but are oscillation modes of a fundamental string. The consistent incorporation of quantum gravity is the major victory of string theory. But string theory also requires nine spatial dimensions, which, in our observable universe, is obviously six too many. The question of what happened to the six unseen dimensions is an important issue in string theory. But if you’re coming at it from the point of view of the relatively low-energy questions, you can also ask whether extra dimensions could have interesting implications in our observable particle physics or in the particle physics that should be observable in the near future. Can extra dimensions help answer some of the unsolved problems of three-dimensiona
l particle physics?
People entertained the idea of extra dimensions before string theory came along, although such speculations were soon forgotten or ignored. It’s natural to ask what would happen if there were different dimensions of space; after all, the fact that we see only three spatial dimensions doesn’t necessarily mean that only three exist, and Einstein’s general relativity doesn’t treat a three-dimensional universe preferentially. There could be many unseen ingredients to the universe. However, it was first believed that if additional dimensions existed they would have to be very small in order to have escaped our notice. The standard supposition in string theory was that the extra dimensions were curled up into incredibly tiny scales—10-33 centimeters, the so-called Planck length and the scale associated with quantum effects becoming relevant. In that sense, this scale is the obvious candidate: If there are extra dimensions, which are obviously important to gravitational structure, they’d be characterized by this particular distance scale. But if so, there would be very few implications for our world. Such dimensions would have no impact whatsoever on anything we see or experience.
From an experimental point of view, though, you can ask whether extra dimensions really must be this ridiculously small. How large could they be and still have escaped our notice? Without any new assumptions, it turns out that extra dimensions could be about 17 orders of magnitude larger than 10-33 cm. To understand this limit requires more fully understanding the implications of extra dimensions for particle physics.
If there are extra dimensions, the messengers that potentially herald their existence are particles known as Kaluza-Klein modes. These KK particles have the same charges as the particles we know, but they have momentum in the extra dimensions. They would thus appear to us as heavy particles with a characteristic mass spectrum determined by the extra dimensions’ size and shape. Each particle we know of would have these KK partners, and we would expect to find them if the extra dimensions were large. The fact that we have not yet seen KK particles in the energy regimes we’ve explored experimentally puts a bound on the extra dimensions’ size. As I mentioned, the TeV energy scale of 10-16 cm has been explored experimentally. Since we haven’t yet seen KK modes and 10-16 cm would yield KK particles of about a TeV in mass, that means all sizes up to 10-16 are permissible for the possible extra dimensions. That’s a lot larger than 10-33 cm, but it’s still too small to be significant.
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