Warped Passages (11 page)

Even if the universe does have many dimensions, if the particles and forces with which we are familiar are trapped on a brane that extends in three dimensions, they would still behave as if they lived in only three. Particles confined to branes would travel only along the brane.
And if light were also stuck to the brane, light rays would spread out only along the brane. In a three-dimensional brane, light would behave exactly as it would in a truly three-dimensional universe.

Furthermore, forces trapped on a brane influence only particles confined to this same brane. The material of which we are composed, such as nuclei and electrons, and the forces through which these building blocks interact, such as the electric force, might be confined on a three-dimensional brane. Brane-bound forces would spread out only along their brane, and brane-bound particles would be exchanged and would travel solely along the dimensions of the brane.

So if you lived in such a three-dimensional brane, you would be able to travel freely along its dimensions, much as you do in three dimensions now. Anything confined within a three-dimensional brane would look just the same as it would if the world were truly three-dimensional. The other dimensions would exist adjacent to the brane, but things stuck to a three-dimensional brane would never penetrate the higher-dimensional bulk.

But although forces and matter can be stuck on a brane, brane-worlds are interesting precisely because we know that not everything is confined to a single brane. Gravity, for example, is never confined to a brane. According to general relativity, gravity is woven into the framework of space and time. That means that gravity must be exerted throughout space and in every dimension. If it could be confined to a single brane, we would have to abandon general relativity.

Fortunately this is not the case. Even if branes exist, gravity will be felt everywhere, on and off branes. This is important because it means that braneworlds have to interact with the bulk, even if only via gravity. Because gravity extends into the bulk, and everything interacts via gravity, braneworlds will always be connected to the extra dimensions. Braneworlds do not exist in isolation: they are part of a larger whole with which they interact. In addition to gravity, there could conceivably exist other particles and forces in the bulk. If there are, such particles could also interact with particles confined to a brane and connect brane-bound particles to the higher-dimensional bulk.

The string theory branes that we will briefly consider later on have specific properties aside from the ones I have mentioned: they can carry particular charges, and they will respond in particular ways
when something pushes on them. However, I will rarely bring in such detailed properties later on when I talk about branes. It will be enough to know the properties we have considered in this chapter: branes are lower-dimensional surfaces that can house forces and particles, and they can be the boundaries of higher-dimensional space.

Braneworlds: Blueprints for a Jungle Gym of Branes

Because branes could trap most particles and forces, the universe we live in could conceivably be housed on a three-dimensional brane, floating in an extra-dimensional sea. Gravity would extend into the extra dimensions, but stars, planets, people, and everything else that we sense could be confined to a three-dimensional brane. We would then be living on a brane. A brane might be our habitat. The concept of braneworlds is based on this assumption (see Figure 28).

If there can be one brane suspended in a higher-dimensional spacetime, there is no denying the possibility of many more. Brane-world scenarios often involve more than a single brane. We don’t yet
know the number or types of branes that could be present in the cosmos.
Multiverse
is a name that is sometimes attached to theories with more than one brane (see Figure 29). People often use the word to describe a cosmos with non-interacting or only weakly interacting pieces.

Figure 28.
We could be living on a brane. That is, the matter we are made of, photons, and other Standard Model particles can all be on the brane. But gravity is always everywhere—on the brane and in the bulk, as is illustrated by the squiggly lines.

Figure 29.
The universe can contain multiple branes that interact only via gravity or don’t interact at all. Such set-ups are sometimes called multiverses.

I find the term “multiverse” a bit strange, since a universe is defined as the whole that is the unity of its parts. It is possible, however, to have different branes that are too far apart ever to communicate with one another, or that can communicate with one another only weakly, through mediating particles that travel between them. Particles on distant branes, then, would experience entirely different forces, and brane-bound particles would never have direct contact with particles bound on another brane. So when there is more than one brane with no force in common aside from gravity, I will sometimes refer to the universe housing them both as a multiverse.

Thinking about branes makes you aware of just how little we know about the space in which we live. The universe might be a magnificent composition linking intermittent branes. Even if we know the basic ingredients, in a multiverse populated by more than one brane, exotic new scenarios for the geometry of space are conceivable as well as myriad possibilities for how the particles we know and don’t know are distributed among them. A single deck of cards can yield many different hands. There are scores of possibilities.

Other branes might be parallel to ours and might house parallel worlds. But many other types of braneworld might exist too. Branes could intersect and particles could be trapped at the intersections. Branes could have different dimensionality. They could curve. They could move. They could wrap around unseen invisible dimensions. Let your imagination run wild and draw any picture you like. It is not impossible that such a geometry exists in the cosmos.

In a world in which branes are embedded in a higher-dimensional bulk, there could be some particles that explore the higher dimensions and others that stay trapped on branes. If the bulk separates one brane from another, some particles can be on the first brane, some on the other, and some in the middle. Theories tell us about many ways in which particles and forces might be distributed among different branes and the bulk. Even for branes derived from string theory, we don’t yet know why string theory should single out any particular allocation of particles and forces. Braneworlds introduce new physical scenarios that might describe both the world we think we know and other worlds we don’t know on other branes we don’t know, separated from our world in unseen dimensions.

New forces confined to distant branes might exist. New particles with which we will never directly interact might propagate on such other branes. Additional stuff accounting for dark matter and dark energy—the matter and energy that we surmise from their gravitational effects but whose identity is a mystery—might be distributed among different branes, or even in both the bulk and on other branes. And gravity might even influence particles differently as you go from one brane to the next.

If there is life on another brane, those beings, imprisoned in an entirely different environment, most likely experience entirely different forces that are detected by different senses. Our senses are attuned to the chemistry, light, and sound surrounding us. Because fundamental forces and particles are likely to be different, the creatures of other branes, should they exist, are unlikely to bear much resemblance to the life of our brane. The other branes will probably be nothing like our own. The only necessarily shared force is gravity, and even gravity’s influence can vary.

The consequences of a braneworld will depend on the number and
types of branes, and where they are located. Unfortunately for the curious, particles and forces confined to distant branes are not required to influence us very strongly. They might merely determine what travels in the bulk, and emit weak signals which might never even reach us. Therefore many conceivable braneworlds will be very difficult to detect, even if they do exist. After all, gravity is the only interaction that we know for sure is shared between the stuff on our brane and the stuff on any other brane, and gravity is an extremely weak force. Without direct evidence, other branes will remain cloistered in the realm of theory and conjecture.

But some of the braneworlds I will present could lead to detectable signals. The detectable braneworlds are the ones that have implications for the physical features of our world. Even though the proliferation of possible braneworlds is in some respects frustrating, it is really quite exciting. Not only might branes help resolve long-standing problems in particle physics, but if we’re lucky, and one of the scenarios that I will describe is correct, evidence for braneworlds should appear in experiments with elementary particle physics very soon. We might really be living on a brane—and we might actually know it within a decade.

As of now, we do not know which, if any, of the many possibilities is the true description of the universe. I will therefore keep all options open, so as not to omit anything interesting. Whatever scenario turns out to describe our world, the ones I will present introduce new and fascinating ideas that no one would previously have thought possible.

4

Approaches to Theoretical Physics

She’s a model and she’s looking good.

Kraftwerk

“Hey, Athena, is that
Casablanca
you’re watching?”

“Sure is. Want to join me? This is such a great scene.”

You must remember this,

A kiss is just a kiss.

A sigh is just a sigh.

The fundamental things apply as time goes by.

“Hang on, Ike. Don’t you think that last line’s a little weird? It’s supposed to be so romantic, but it almost sounds as if it’s about physics.”

“Athena, if you think that’s strange, you’ve got to hear the opening verse of the original:”

This day and age we’re living in

Give cause for apprehension,

With speed and new invention.

And things like fourth dimension,

Yet we get a trifle weary

With Mr. Einstein’s theory…

“Ike, you don’t really expect me to believe that, do you? Next thing I know you’ll tell me Rick and Ilsa escape into the seventh dimension! Why don’t we forget I ever said anything and just sit back and watch the movie?”

Einstein introduced general relativity in the early twentieth century, and by 1931 Rudy Vallee had recorded Ike’s (true) version of Herman Hupfeld’s song. However, by the time Sam played the tune in
Casablanca
, the omitted lyrics—as well as the science of spacetime—were all but forgotten in popular culture. And although Theodor Kaluza introduced the idea of an extra dimension back in 1919,
^*
physicists didn’t take the idea all that seriously until very recently.

Now that we’ve seen
what
dimensions are and
how
dimensions could escape our notice, we are almost set to ask what triggered this renewed interest in extra dimensions.
Why
should physicists believe that they might actually exist in the real physical world? That will require a far longer explanation—one that involves some of the most significant physics developments of the past century. In the next few chapters, before launching into a description of possible extra-dimensional universes, I will review these developments and why they serve as precursors for more recent theories. We will look at the major paradigm shifts that happened in the early twentieth century (quantum mechanics, general relativity), the essence of particle physics today (the Standard Model, symmetry, symmetry breaking, the hierarchy problem), and new ideas for approaching currently unresolved problems (supersymmetry, string theory, extra dimensions, and branes).