Warped Passages - Lisa Randall [207]
Figure 86. Infinite warped spacetime with a single brane. There is a single four-dimensional brane in a five-dimensional universe. The Standard Model resides on this single brane.
In this scenario, the graviton, the particle that communicates gravity, is localized near a brane, which is the Brane of Athena’s story, but which I’ll call the Gravitybrane from now on. Athena’s dream took her to this warped five-dimensional space, in which the Gravitybrane so radically alters the nature of spacetime that space appears to be four-dimensional, even though it is in reality five-dimensional. Remarkably, a warped higher dimension can have infinite extent, yet nonetheless be hidden, while the three flat infinite dimensions reproduce the physics of our world.
The Localized Graviton
You might recall that when I first introduced branes, I distinguished reluctance to explore distant regions from genuine confinement, which explicitly forbids foreign travel beyond the place where someone or something is confined. Although you’ve probably never visited Greenland, no law forbids you from going there. But some places are just too much trouble to get to. Even if travel to such places is permitted, and even if they are no further away than some other places you’ve been, you still might just never go there.
Or imagine someone who has broken his leg. In principle, he could leave the house whenever he likes, but he’s much more likely to be found inside the house than outside, even when no bars or locks are keeping him there.
Similarly, the localized graviton has unrestricted access to an infinite fifth dimension. But it is nonetheless highly concentrated in the vicinity of a brane, and has very low probability of being found far away. According to general relativity, everything—including the graviton—is subject to the gravitational force. The graviton is not at all impaired, but it behaves as if it is gravitationally attracted to the brane and therefore remains close by. And because the graviton only rarely travels outside a limited region, the extra dimension can be infinite without giving rise to any dangerous effects that would rule the theory out.
In our work, Raman and I concentrated on gravity in a five-dimensional spacetime with only a single extra dimension of space. We could thereby concentrate on the localization mechanism we are about to discuss, which keeps gravity in a small region of the five-dimensional spacetime. I’ll assume that if the universe has ten or more dimensions, some mixture of localization and curling them up hides the rest. Such additional hidden dimensions wouldn’t affect the localization phenomenon I’m about to describe, so we’ll ignore them and focus on the five dimensions that are critical to our discussion.
In our model a single brane sits at one end of the fifth spacetime dimension. It is reflective, as were the two branes I described in Chapter 20. Things that hit the brane simply bounce back, so nothing loses energy when it hits this brane. Because the model we are now considering contains only this single brane, we’ll assume that the Standard Model particles are confined there; note the distinction from the model I discussed in the previous chapter, in which the Standard Model particles were on the Weakbrane, which no longer exists. The location of the Standard Model particles is not relevant to the spacetime geometry, but it does of course have implications for particle physics.
Although in this chapter we are interested in the single-brane theory, the first clue Raman and I had that an infinite fifth dimension might be legitimate was a curious feature of the warped geometry with two branes. We initially assumed that the second brane served two functions. One was to confine the Standard Model particles; the second was to make the fifth dimension finite. As with flat extra dimensions, a finite fifth dimension guaranteed that at sufficiently large distance, gravity would be that of four-dimensional spacetime.
However, a peculiar fact