Warped Passages - Lisa Randall [216]
After all, the speed of light is finite, and our universe has existed for only a finite amount of time. That means that we can only possibly know about the surrounding region of space within the distance that light could have traveled since the universe’s inception. That is not infinitely far away. It defines a region known as the horizon, the dividing line between information that is and is not accessible to us.
Beyond the horizon, we don’t know anything. Space needn’t look like ours. The Copernican Revolution is repeatedly updated and revised as we see further into the universe and realize not everywhere is necessarily the same as what we see. Even if the laws of physics are the same everywhere, that doesn’t mean that the stage on which they are played out is the same. It could be that nearby branes induce a different gravitational force law in our vicinity than would be seen elsewhere.
How can we claim to know the dimension of the universe outside our purview? There would be no contradiction if the universe beyond exhibited more dimensions—maybe five, maybe ten, maybe more. By thinking about the bare essentials, rather than assuming that everywhere, even inaccessible regions, is made up of spacetime that looks like ours, we can deduce what is really fundamental and what is ultimately conceivable and legitimate.
All we know is that the space we experience appears to be four-dimensional. It might be overstepping the mark to assume that all other regions of the universe must be four-dimensional as well. Why should a world extremely far from ours, which might not interact with us at all—or perhaps only via extremely weak gravitational signals—have to see gravity and space the way we do? Why can’t it have a different type of gravity?
The marvelous thing is that it can. Our braneworld could experience three-plus-one dimensions, while outside regions do not. To our amazement, in 2000, Andreas Karch and I developed a theory in which space looks four-dimensional on or near the brane, but most of the space far from the brane appears higher-dimensional. This idea is schematically illustrated in Figure 90.
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