Warped Passages (68 page)

We named our scenario
locally localized gravity
because localization produces a graviton that communicates four-dimensional gravitational interactions only in a local region—the rest of space doesn’t look four-dimensional. A four-dimensional
^*
world exists only
on a gravitational “island.” The dimensionality you see depends on your location in the five-dimensional bulk.

Figure 90.
We could be living in a four-dimensional sinkhole in a higher-dimensional space.

To understand local localization, let’s return to our ducks in a pond. You might have disagreed when I said that the size of the pond doesn’t matter. If the pond were truly enormous, ducks on the opposite side of the pond wouldn’t congregate with the ducks on your side. In fact, it would be very strange if you could influence ducks that were very far away. The distant ducks wouldn’t notice your bread, and would obliviously paddle about in a remote part of the lake.

The basic idea underlying locally localized gravity is very similar. Localization of gravity on a brane shouldn’t necessarily depend on what is happening in distant regions of space. Although the model I studied with Raman had a graviton whose probability function decayed exponentially but was never quite zero—and that four-dimensional gravity would be experienced everywhere—gravity’s behavior far away should not be essential to determining whether four-dimensional gravity exists in the vicinity of the brane.

That is the essence of locally localized gravity. A graviton can be localized and generate a four-dimensional gravitational force in the
vicinity of a brane without affecting the gravitational force far away. Four-dimensional gravity can be a completely local phenomenon, relevant only to some portion of space.

Ironically, Andreas, who is an excellent physicist and a very nice guy, had first started thinking about the model that showed that this was possible while he was working on a research project with one of my former MIT colleagues, who had intended to challenge Raman’s and my work. (Happily for us, their collaboration did a beautiful job of showing that our work was right.) In the course of his project, Andreas identified a model that was closely related to the one Raman and I had developed, but which had some very peculiar properties. When Andreas visited Princeton, he came to talk to me about it. Eventually we figured out that this model has some startling implications. At first, Andreas and I collaborated via e-mail and on visits to each other’s institutions, and afterward, more easily, when I was back in Boston. And what we found was quite remarkable.

This model was very similar to the one I had studied with Raman; it had a single brane in five-dimensional warped space. But the difference in this case was that the brane was not exactly flat. This was because it carried a tiny amount of negative vacuum energy. In general relativity, as we have seen, not only relative energy but also the total amount of energy is meaningful. The total energy tells spacetime how to curve. For example, constant negative energy in five-dimensional spacetime gives rise to the warped spacetime that we have been discussing in the last few chapters. However, in that case the branes themselves were flat. Here, negative energy on the brane makes the brane itself slightly curved.

The negative energy on the brane leads to an even more interesting theory. However, we weren’t actually interested in the negative energy itself—if we live on a brane, our brane should actually have a tiny positive energy to agree with observations. Andreas and I decided to study this model solely because of its fascinating implications for dimensionality.

To understand what we found, let’s briefly return to a setup with two branes, with the understanding that afterward we will remove the second one. When the second brane was sufficiently far away, we
found that there were two
different
gravitons, one localized near each of the two branes. Each of the graviton probability functions peaked near one of the two branes, and decreased exponentially quickly as you left it.

Neither of the gravitons was responsible for four-dimensional gravity over the entire space. They produced four-dimensional gravity only in the region adjacent to the brane on which they were localized. The gravities experienced on the different branes were different. They could even have very different strengths. And objects on one brane didn’t interact gravitationally with objects on the other.

The setup with two widely separated branes can be compared to a situation in which someone on the opposite, very distant shore is also feeding ducks. Those ducks could even be of a different type; perhaps you are attracting mallards but, on the opposite shore, someone is attracting wood ducks. In that case, there would be a second concentration of ducks along the opposite shoreline, analogous to the second graviton probability function that is localized near a second brane.

The appearance of two different particles that both look like the four-dimensional graviton was a big surprise to us. General physical principles were supposed to ensure that there is only a single theory of gravity. And indeed, there is a single five-dimensional theory of gravity. However, five-dimensional spacetime turns out to contain two distinct particles that each communicate a gravitational force that acts as if it is four-dimensional, each in a distinct region of five-dimensional space. Different regions of space look like they both contain four-dimensional gravity, but the graviton communicating the four-dimensional gravitational force in those theories is different.

But there was a second surprise as well. According to general relativity, the graviton is massless. Like the photon, it should travel at the speed of light. But Andreas and I discovered that one of the two gravitons has a nonzero mass and didn’t travel at this speed. This was truly surprising—but also disturbing. The physics literature said that no graviton with mass would ever produce a gravitational force that matched all observations. In fact, just as we discussed in the case of a heavy gauge boson in Chapter 10, a graviton with mass would have
more polarizations than a massless one. And physicists demonstrated, by comparing different measured gravitational processes, that no effects of any extra graviton polarizations have ever been seen. This puzzled us for some time.

But the model outsmarted conventional wisdom. Once we had discovered this model, Massimo Porrati, a physicist at New York University, and Ian Kogan, Stavros Mousopoulos, and Antonios Papazouglou at Oxford University, found that in certain cases the graviton could in fact have mass and still yield correct gravitational predictions. They analyzed technicalities in the theory and demonstrated the loophole in the logic of why a graviton with mass should not agree with observed gravitational processes.

And the model has even weirder implications. Let’s think now about what happens when we eliminate the second brane. Physical laws will then still appear to be four-dimensional on the remaining brane, the Gravitybrane, despite the infinite extra dimension. Gravity near the Gravitybrane is virtually identical to that in the RS2 model. For things on the Gravitybrane, the single graviton communicates the force of gravity, and gravity appears to be four-dimensional.

However, there is an important distinction between this model and RS2. In this model, which is different only because of the negative energy on the brane, the graviton that is localized near the brane does not dominate the gravitational force over the entire space. The graviton does not interact with objects anywhere in the space; it yields four-dimensional gravity only on or near the brane. Far from the brane, gravity no longer looks four-dimensional!
³⁸

This might seem to contradict what I said earlier, that gravity must exist everywhere in the higher-dimensional bulk. This is not a false statement; five-dimensional gravity is everywhere. However, unlike the other extra-dimensional theories we have so far considered, in which physics always has a four-dimensional interpretation, this theory looks four-dimensional only for things that are on or near the brane. Newton’s gravitational force law applies only on or near the brane. Everywhere else, the gravitational force is five-dimensional.

In this setup, four-dimensional gravity is a completely local phenomenon, experienced only in the vicinity of the brane. The
dimensionality you would deduce from the behavior of gravity would depend on where you are in the fifth dimension. If this model is correct, we would have to live on the brane to experience four-dimensional gravity. If we were anywhere else, gravity would look five-dimensional. The brane is a four-dimensional gravity sinkhole—a four-dimensional gravitational island.

Of course, we don’t yet know whether locally localized gravity applies in the real world. We don’t even know whether extra dimensions exist or—if they do—what has become of them. However, if string theory is right, there are extra dimensions. And if so, they could be hidden by either compactification or localization (or local localization) or by some combination of the two. Many string theorists continue to believe that compactification is the answer, but because there are so many puzzles about the gravity that emerges from string theory, no one can be sure. I view localization as a new option. When gravity is localized, physical laws behave as if the dimensions weren’t there, just as with rolled-up dimensions. Localized gravity therefore supplements our model building toolkit and increases the chances of discovering a realization of string theory that agrees with observations.

I like the way locally localized gravity concentrates on what we can explicitly verify. It says only that the universe has to look four-dimensional where we can test it—not that it has to
be
four-dimensional. Our three spatial dimensions could be a mere accident of our location. This idea has yet to be fully explored. But it is not out of the question that different regions of space could appear to have different numbers of dimensions. After all, new physics is revealed each time we probe shorter distances beyond what had previously been seen. Maybe the same thing is true about large distances: if we live on a brane, who knows what lies beyond?

What’s New

• Localized gravity is a local phenomenon. It doesn’t depend on distant regions of spacetime.
  
• Gravity can behave as if the world has different dimensions in different regions, since a localized graviton does not necessarily extend over all of space.
  
• We could be living in an isolated pocket of space that appears to be four-dimensional.
  

24

Extra Dimensions: Are You In or Out?

But I still haven’t found what I’m looking for.

U
₂

Athena’s dreams about OneDLand, branes, and five dimensions were passed down for generations. When Ike XLII heard them, he wanted to check whether there was any truth to her stories. So he took out his Alicxvr and went down to a very small scale—not so small that strings would appear, but sufficiently small to check whether there was a fifth dimension. The Alicxvr answered Ike’s question by sending him off to a five-dimensional world.

But Ike was not completely satisfied. He remembered the bizarre things that had happened earlier on when he had fooled around with the hyperdrive option. So he once again cranked up the hyperdrive lever—and once again, everything changed drastically. Ike couldn’t identify a single familiar object. He could tell only one thing: the fifth dimension had disappeared.

Ike was mystified, so he searched the spacernet to see what it could tell him about “dimensions.” He waded through numerous sites that he recognized from his more embarrassing spam, but soon realized that he’d have to refine his search. When he still couldn’t find anything definitive, he conceded that he wouldn’t know the fundamental origin of dimensions any time soon. So he decided to turn his attention to time travel instead.

Physics has entered a remarkable era. Ideas that were once the realm of science fiction are now entering our theoretical—and maybe even
experimental—grasp. Brand-new theoretical discoveries about extra dimensions have irreversibly changed how particle physicists, astrophysicists, and cosmologists now think about the world. The sheer number and pace of discoveries tells us that we’ve most likely only scratched the surface of the wondrous possibilities that lie in store. Ideas have taken on a life of their own.

Nonetheless, many questions have yet to be fully answered, and our journey is far from over. Particle physicists still want to know why we see the particular forces we see, and are there any more. What is the origin of the masses and properties of familiar particles? We also want to know whether string theory is right. And if it is, how does it connect to our world?

Recent observations of the cosmos point to even more mysteries we want to address. What composes most of the energy and matter in the universe? Was there a brief phase of explosive expansion early on in the universe’s evolution, and if so, what caused it? And everyone wants to know what the universe looked like when it started.