Warped Passages (3 page)
I will explain the physical principles underlying these and other theoretical developments and the new notions about space that make them conceivable. And later on, we’ll also encounter an even weirder possibility, which the physicist Andreas Karch and I discovered a year later: we could be living in a three-dimensional pocket of space, even though the rest of the universe behaves as if it is higher-dimensional. This result opens a host of new possibilities for the fabric of spacetime, which could consist of distinct regions, each appearing to contain a different number of dimensions. Not only are we not in the center of the universe, as Copernicus shocked the world by suggesting five hundred years ago, but we just might be living in an isolated neighborhood with three spatial dimensions that’s part of a higher-dimensional cosmos.
The newly-studied membrane-like objects called branes are important components of the rich higher-dimensional landscapes. If extra dimensions are a physicist’s playground, then
braneworlds
—hypothesized universes in which we live on a brane—are the tantalizing, multi-layered, multi-faceted jungle gyms.
*
This book will take you to braneworlds and universes with curled-up, warped, large, and infinite dimensions, some of which contain a single brane and others of which have multiple branes housing unseen worlds. All of these are within the realm of possibility.
The Excitement of the Unknown
The postulated braneworlds are a theoretical leap of faith, and the ideas they contain are speculative. However, as with the stock market, riskier ventures might fail but they could also reward you with greater returns.
Imagine the sight of the snow under a ski chairlift on the first sunny day after a storm, when untracked powder tempts you from below. You know that no matter what, once you hit the snow, it’s going to be a great day. Some runs will be steep and full of bumps, some will be easy cruisers, and some will be tricky routes through trees. But even if you take the occasional wrong turn, most of the day will be wonderfully rewarding.
For me, model building—which is what physicists call the search for theories that might underlie current observations—has this same irresistible appeal. Model building is adventure travel through concepts and ideas. Sometimes new ideas are obvious, and sometimes they are tricky to find and negotiate. However, even when we don’t know where they’re heading, interesting new models often explore untouched, delightful terrain.
We will not know right away which of the theories gets it right about our place in the universe. For some of them, we might never know. But, incredibly, that is not true for all extra-dimensional theories. The most exciting feature of any extra-dimensional theory that explains the weakness of gravity is that if it is correct, we will soon find out. Experiments that study very energetic particles could discover evidence supporting these proposals and the extra dimensions they contain within the next five years—as soon as the Large Hadron Collider (LHC), a very high energy
particle collider
near Geneva, is up and running.
This collider, which turns on in 2007, will bang together tremendously energetic particles that could turn into new types of matter we have never seen before. If any of these extra-dimensional theories is right, it could leave visible signs at the LHC. The evidence would include particles called
Kaluza-Klein modes
, which travel in the extra dimensions yet leave traces of their existence here in the familiar three dimensions. Kaluza-Klein modes would be fingerprints of extra dimensions in our three-dimensional world. And if we’re very lucky, experiments will register other clues as well, perhaps even higher-dimensional black holes.
The detectors that will record these objects will be large and impressive—so much so that working on them will require climbing gear like harnesses and helmets. In fact, I once took advantage of this gear when I went glacier hiking in Switzerland close to the European
Organization for Particle Research (CERN), the physics center that will house the LHC. These enormous detectors will record particle properties that physicists will use to reconstruct what passed through.
Admittedly, the evidence for extra dimensions will be somewhat indirect, and we will have to piece together various clues. But that is true of almost all recent physics discoveries. As physics evolved in the twentieth century, it moved away from things that can be directly observed with the naked eye to things that can be “seen” only through measurements coupled with a theoretical train of logic. For example, quarks, components of the proton and neutron familiar from high-school physics, never appear in isolation; we find them by following the trail of evidence they leave behind them as they influence other particles. It’s the same with the intriguing kinds of stuff known as dark energy and dark matter. We don’t know where most of the energy in the universe comes from or the nature of most of the matter that the universe contains. Yet we know that dark matter and dark energy exist in the universe, not because we’ve detected them directly, but because they have noticeable effects on matter that surrounds them. Like quarks or dark matter and dark energy, whose existence we only indirectly ascertain, extra dimensions will not appear to us directly. Nonetheless, signatures of extra dimensions, even when indirect, could ultimately reveal their existence.
Let me say at the outset that obviously not all new ideas prove correct, and that many physicists are skeptical about any new theories. The theories I present here are no exception. But speculation is the only way to make progress in our understanding. Even if it turns out that the details don’t all align with reality, a new theoretical idea can still illuminate physical principles at work in the true theory of the cosmos. I’m fairly certain that the ideas about extra dimensions we’ll encounter in this book contain more than a germ of truth.
When engaging with the unknown and working with speculative ideas, I find it comforting to recall that the discovery of fundamental structure has always come as a surprise and been met with skepticism and resistance. Oddly enough, not just the general populace, but sometimes even the very people who suggest underlying structures have been reluctant to believe in them at first.
James Clerk Maxwell, for example, who developed the classical
theory of electricity and magnetism, didn’t believe in the existence of fundamental units of charge such as electrons. George Stoney, who at the end of the nineteenth century proposed the electron as a fundamental unit of charge, didn’t believe that scientists would ever isolate electrons from the atoms of which they are components. (In fact, all it takes is heat or an electric field.) Dmitri Mendeleev, creator of the periodic table, resisted the notion of valence, which his table encoded. Max Planck, who proposed that the energy carried by light was discontinuous, didn’t believe in the reality of the light quanta that were implicit in his own idea. Albert Einstein, who suggested these quanta of light, didn’t know that their mechanical properties would permit them to be identified as particles—the photons we now know them to be. Not everyone with correct new ideas has denied their connection to reality, however. Many ideas, whether believed-in or mistrusted, have turned out to be true.
Is there more waiting to be discovered? For the answer to that question, I turn to the all-too-mortal words of George Gamow, the prominent nuclear physicist and science popularizer. In 1945 he wrote, “Instead of a rather large number of ‘indivisible atoms’ of classical physics, we are now left with only three essentially different entities; nucleons, electrons, and neutrinos…Thus it seems that we have actually hit the bottom in our search for the basic elements from which matter is formed.” When Gamow wrote this, he had no idea that the nucleons are composites of quarks, which would be discovered within thirty years!
Wouldn’t it be strange if we turn out to be the first people for whom the search for further underlying structure ceased to be fruitful? So strange, in fact, that it seems hardly credible? Inconsistencies in existing theories tell us they can’t be the final word. Earlier generations had neither the tools nor the motivations of today’s physicists for exploring the extra-dimensional arenas that this book will describe. Extra dimensions, or whatever underlies the Standard Model of particle physics, would be a discovery of major importance.
When it comes to the world around us, is there any choice but to explore?
Entryway Passages: Demystifying Dimensions
You can go your own way.
Go your own way.
Fleetwood Mac
“Ike, I’m not so sure about this story I’m writing. I’m considering adding more dimensions. What do you think of that idea?”
“Athena, your big brother knows very little about fixing stories. But odds are it won’t hurt to add new dimensions. Do you plan to add new characters, or flesh out your current ones some more?”
“Neither; that’s not what I meant. I plan to introduce new dimensions—as in new dimensions of space.”
“You’re kidding, right? You’re going to write about alternative realities—like places where people have alternative spiritual experiences or where they go when they die, or when they have near-death experiences?
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I didn’t think you went in for that sort of thing.”
“Come on, Ike. You know I don’t. I’m talking about different spatial dimensions—not different spiritual planes!”
“But how can different spatial dimensions change anything? Why would using paper with different dimensions—11"
×
8" instead of 12"
×
9"
,
for example—make any difference at all?”
“Stop teasing. That’s not what I’m talking about either. I’m really planning to introduce new dimensions of space, just like the dimensions we see, but along entirely new directions.”
“Dimensions we don’t see? I thought three dimensions is all there are.”
“Hang on, Ike. We’ll soon see about that.”
The word “dimension,” like so many words that describe space or motion through it, has many interpretations—and by now I think I’ve heard them all. Because we see things in spatial pictures we tend to describe many concepts, including time and thought, in spatial terms. This means that many words that apply to space have multiple meanings. And when we employ such words for technical purposes, the alternative uses of the words can make their definitions sound confusing.
The phrase “extra dimensions” is especially baffling because even when we apply those words to space, that space is beyond our sensory experience. Things that are difficult to visualize are generally harder to describe. We’re just not physiologically designed to process more than three dimensions of space. Light, gravity, and all our tools for making observations present a world that appears to contain only three dimensions of space.
Because we don’t directly perceive extra dimensions—even if they exist—some people fear that trying to grasp them will make their head hurt. At least, that’s what a BBC newscaster once said to me during an interview. However, it’s not thinking about extra dimensions but trying to picture them that threatens to be unsettling. Trying to draw a higher-dimensional world inevitably leads to complications.
Thinking about extra dimensions is another thing altogether. We are perfectly capable of considering their existence. And when my colleagues and I use the words “dimensions,” and “extra dimensions,” we have precise ideas in mind. So before taking another step forward or exploring how new ideas fit into our picture of the universe—note the spatial phrases—I will explain the words “dimensions” and “extra dimensions” and what I will mean when I use them later on.
We’ll soon see that when there are more than three dimensions, words (and equations) can be worth a thousand pictures.
What Are Dimensions?
Working with spaces that have many dimensions is actually something everyone does every day, although admittedly most of us don’t think of it that way. But consider all the dimensions that enter into your calculations when you make an important decision, like buying a house. You might consider the size, the schools nearby, the proximity to places of interest, the architecture, the noise level—and the list goes on. You need to optimize in a multidimensional context, enumerating all your desires and needs.
The number of dimensions is the number of quantities you need to know to completely pin down a point in a space. The multidimensional space might be an abstract one, such as the space of features you are looking for in a house, or it might be concrete, like the real physical space we will soon consider. But when buying a house, you can think of the number of dimensions as the number of quantities you would record in each entry in a database—the number of quantities you find worth investigating.
A more frivolous example applies dimensions to people. When you peg someone as one-dimensional, you actually have something rather specific in mind: you mean that the person has only a single interest. For example, Sam, who does nothing but sit at home watching sports, can be described with just one piece of information. If you felt so inclined, you could picture this information as a dot on a one-dimensional graph: Sam’s proclivity to watch sports, for example. In drawing this graph you need to specify your units so that someone else can understand what the distance along this single axis means. Figure 3 shows a plot with Sam as a point along a horizontal axis. This plot represents the number of hours Sam spends per week watching sports on TV. (Fortunately, Sam won’t be insulted by this
example; he is not among the multidimensional readers of this book.)
