Warped Passages - Lisa Randall [218]
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