Warped Passages (2 page)
Greg Elliott and Jonathan Flynn executed the beautiful pictures contained in this book, and I’m extraordinarily grateful for their important contribution. I thank Rob Meyer and Laura Van Wyk for helping me obtain permissions for the many quotes throughout the book. I have made every effort to properly credit sources. If you think you have not been credited properly, please let me know.
I also want to thank my collaborators on my research that I describe in this book, particularly Raman Sundrum and Andreas Karch, who were both great to work with. And I’d like to acknowledge the contributions of the many physicists who have thought about these and related ideas, including those that I didn’t have room to discuss.
I’d also like to express my appreciation to my Ecco Press editor, Dan Halpern, my Penguin editors, Stefan McGrath and Will Goodlad, and my copy editors in the U.S. and England, Lyman Lyons and John Woodruff, for their many helpful suggestions and for their support for this book. And I wish to thank my literary agent, John Brockman, as well as Katinka Matson, for their important commentary and advice, and for their invaluable help in getting this book launched. I’m also grateful to Harvard University and to the Radcliffe Institute for Advanced Study for providing some time to focus on this book, and to MIT, Princeton, Harvard, the National Science Foundation, the Department of Energy, and the Alfred P. Sloan Foundation for supporting my research.
Finally, I wish to thank my family: my parents, Richard Randall and Gladys Randall, and my sisters, Barbara Randall and Dana Randall, for backing my scientific career and for sharing their humor, thoughts, and encouragement over the years. Lynn Festa, Beth Lyman, Gene Lyman, and Jen Sacks were extremely supportive and I thank them all for their wonderful advice and suggestions along the way. And lastly, I’m so grateful to Stuart Hall for his insightful perspective, helpful comments, and unselfish support.
I thank you all and hope you find your contributions are repaid.
Lisa Randall
Cambridge,
MA
April 2005
Got to be good looking
’Cause he’s so hard to see.
The Beatles
The universe has its secrets. Extra dimensions of space might be one of them. If so, the universe has been hiding those dimensions, protecting them, keeping them coyly under wraps. From a casual glance, you would never suspect a thing.
The disinformation campaign began back in the crib, which first
introduced you to three spatial dimensions. Those were the two dimensions in which you crawled, plus the remaining one by which you climbed out. Since that time, physical laws—not to mention common sense—have bolstered the belief in three dimensions, quelling any suspicion that there might be more.
Figure 1.
A baby’s three-dimensional world.
But spacetime could be dramatically different from anything you’ve ever imagined. No physical theory we know of dictates that there should be only three dimensions of space. Dismissing the possibility of extra dimensions before even considering their existence might be very premature. Just as “up-down” is a different direction from “left-right” or “forward-backward,” other completely new dimensions could exist in our cosmos. Although we can’t see them with our eyes or feel them with our fingertips, additional dimensions of space are a logical possibility.
Such hypothetical unseen dimensions don’t yet have a name. But should they exist, they would be new directions along which something might travel. So when I need a name for an extra dimension, I’ll sometimes call it a
passage
. (And when I explicitly discuss extra dimensions, I’ll use chapter names with “passages” in the title.)
These passages could be flat, like the dimensions we are accustomed to. Or they could be warped, like reflections in a fun-house mirror. They might be tiny—far smaller than an atom—until recently, that’s what anyone who believed in extra dimensions assumed. But new work has shown that extradimensions might also be big, or even infinite in size, yet still be hard to see. Our senses register only three large dimensions, so an infinite extra dimension might sound incredible. But an infinite unseen dimension is one of many bizarre possibilities for what might exist in the cosmos, and in this book we’ll see why.
Research into extra dimensions has also led to other remarkable concepts—ones that might fulfill a science fiction aficionado’s fantasy—such as parallel universes, warped geometry, and three-dimensional sinkholes. I’m afraid such ideas might sound more like the province of novelists and lunatics than the focus of real scientific inquiry. But outlandish as they might seem at the moment, they are genuine scientific scenarios that could arise in an extra-dimensional world. (Don’t worry if you are not yet familiar with these words or ideas; we’ll introduce and investigate them later on.)
Why Consider Unseen Dimensions?
Even if physics with extra spatial dimensions permit these intriguing scenarios, you might still wonder why physicists concerned with making predictions about observable phenomena would bother to take them seriously. The answer is as dramatic as the idea of extra dimensions itself. Recent advances suggest that extra dimensions, not yet experienced and not yet entirely understood, might nonetheless resolve some of the most basic mysteries of our universe. Extra dimensions could have implications for the world we see, and ideas about them might ultimately reveal connections that we miss in three-dimensional space.
We wouldn’t understand why Inuit and Chinese people share physical features, either, if we failed to include the dimension of time that lets us recognize their common ancestry. Similarly, the connections that can occur with additional dimensions of space might illuminate perplexing aspects of particle physics, shedding light on decades-old mysteries. Relationships between particle properties and forces that seemed inexplicable when space was shackled to three dimensions seem to fit together elegantly in a world with more dimensions of space.
Do I believe in extra dimensions? I confess I do. In the past, I’ve mostly viewed speculations about physics beyond what’s been measured—including my own ideas—with fascination, but also with some degree of skepticism. I like to think this keeps me interested, but honest. Sometimes, however, an idea seems like it must contain a germ of truth. One day on my way to work about five years ago, as I was crossing the Charles River into Cambridge, I suddenly realized that I really believed that some form of extra dimensions must exist. I looked around and contemplated the many dimensions I couldn’t see. I had the same shock of surprise at my altered worldview that I experienced when I realized that I, a native New Yorker, was rooting for the Red Sox during a playoff game against the Yankees—something else I never anticipated I’d do.
Greater familiarity with extra dimensions has only increased my confidence in their existence. Arguments against them have too many holes to be reliable, and physical theories without them leave too
many questions unanswered. Furthermore, as we’ve explored extra dimensions in the last few years, we’ve expanded the range of possible extra-dimensional universes that can mimic our own, suggesting that we’ve identified only the tip of the iceberg. Even if extra dimensions don’t conform precisely to the pictures I will present, I think they are very likely to be there, in one form or another, and their implications are bound to be surprising and remarkable.
You might be intrigued to know that there could be a vestige of extra dimensions hidden in your kitchen cabinet—on a nonstick frying pan coated with
quasicrystals
. Quasicrystals are fascinating structures whose underlying order is revealed only with extra dimensions. A crystal is a highly symmetric latticework of atoms and molecules with one basic element repeated many times. In three dimensions we know what structures crystals can form, and which patterns are possible. However, the arrangement of atoms and molecules in quasicrystals does not conform to any of these patterns.
An example of a quasicrystalline pattern is shown in Figure 2. It lacks the precise regularity you would see in a true crystal, which would look more like the kind of grid you would see on a piece of graph paper. The most elegant way of explaining the pattern of molecules in these strange
materials is with a projection—a sort of three-dimensional shadow—of a higher-dimensional crystalline pattern, which reveals the symmetry of the pattern in a higher-dimensional space. What looked like a completely inexplicable pattern in three dimensions reflects an ordered structure in a higher-dimensional world. The nonstick frying pans that are coated with quasicrystals exploit the structural differences between the projections of higher-dimensional crystals in the pan’s coating and the more mundane structure of ordinary three-dimensional food. The different arrangements of atoms, which keeps them from binding to each other, is a tantalizing suggestion that extra dimensions exist and explain some observable physical phenomena.
Figure 2.
This is a “Penrose tiling.” It is a projection of a five-dimensional crystalline structure onto two dimensions.
Overview
Just as extra dimensions help us understand the confusing arrangement of molecules in a quasicrystal, physicists today speculate that theories of extra dimensions also will illuminate connections in particle physics and cosmology—connections that are difficult to understand with only three dimensions.
For thirty years, physicists have relied on a theory called the Standard Model of particle physics, which tells us about the fundamental nature of matter and the forces through which elementary constituents interact.
*
Physicists have tested the Standard Model by creating particles that have not been present in our world since the earliest seconds of the universe, and they’ve found that the Standard Model describes many of their properties extremely well. Yet the Standard Model leaves some fundamental questions unanswered—questions so basic that their resolution promises new insight into the building blocks of our world and their interactions.
This book tells about how I and others searched for answers to Standard Model puzzles and found ourselves in extra-dimensional worlds. The new developments with extra dimensions will ultimately take center stage, but I’ll first introduce the supporting players—the revolutionary physics advances of the twentieth century. The recent
ideas that I discuss later are grounded in these stupendous breakthroughs.
The review topics we’ll encounter will, broadly, divide into three categories: early-twentieth-century physics, particle physics, and string theory. We’ll investigate the key ideas of relativity and quantum mechanics, as well as the current state of particle physics and the problems that extra dimensions might address. We’ll also consider the concepts that underlie string theory, which many physicists think is the leading contender for a theory that incorporates both quantum mechanics and gravity. String theory, which postulates that the most basic units in nature are not particles but fundamental, oscilllating strings, has provided much of the impetus for studying extra dimensions, because it requires more than three dimensions of space. And I will also describe the role of branes, membrane-like objects within string theory, which are as essential to the theory as strings themselves. We’ll consider both the successes of these theories and the questions they leave open—the ones that motivate current research.
One of the chief mysteries is why gravity is so much weaker than the other known forces. Gravity might not feel weak when you’re hiking up a mountain, but that’s because the entire Earth is pulling on you. A tiny magnet can lift a paper clip, even though all the mass of the Earth is pulling it in the opposite direction. Why is gravity so defenseless against the small tug of a tiny magnet? In standard three-dimensional particle physics, the weakness of gravity is a huge puzzle. But extra dimensions might provide an answer. In 1998, my collaborator Raman Sundrum and I showed one reason this might be so.
Our proposal is based on warped geometry, a notion that arises in Einstein’s theory of general relativity. According to this theory, space and time are integrated into a single spacetime fabric that gets distorted, or warped, by matter and energy. Raman and I applied this theory in a new, extra-dimensional context. We found a configuration in which spacetime warps so severely that even if gravity is strong in one region of space, it is feeble everywhere else.
And we found something even more remarkable. Although physicists have assumed for eighty years that extra dimensions must be tiny in order to explain why we haven’t seen them, in 1999 Raman and I discovered that not only can warped space explain gravity’s feebleness,
but also that an invisible extra dimension can stretch out to infinity, provided it is suitably distorted in a curved spacetime. An extra dimension can be infinite in size–but nonetheless be hidden. (Not all physicists immediately accepted our proposal. But my non-physicist friends were more quickly convinced I was on to something—not because they fully grasped the physics, but because when I attended a conference banquet after speaking about my work, Stephen Hawking saved me a seat.)
