Warped Passages - Lisa Randall [210]
Because I will use the duck analogy again in the next chapter, I’ll explain the same thing in terms of counting ducks attracted to the shore where someone has sprinkled crumbs. If you were to first count nearby ducks, and then count ones a little further out, your duck counting would quickly become almost futile. By the time you get a little way away from shore, there would be very few ducks left to count. You don’t need to keep counting ducks far from the shore because you’ve already counted essentially all of them by focusing on the region near the shore (see Figure 88).
The graviton’s probability function is simply so small beyond the second brane that a second brane’s location would make only a negligible difference to the interaction strength of the four-dimensional graviton. In other words, the extent of the fifth dimension is immaterial to the apparent strength of four-dimensional gravity in this theory, in which the gravitational field is localized near the Gravitybrane.37 Even if there’s no second brane and the fifth dimension is infinite, gravity still looks four-dimensional.
Raman and I called our scenario localized gravity. That is because the graviton’s probability function is localized near a brane. Although, strictly speaking, gravity can leak out into the fifth dimension because the fifth dimension is indeed infinite, in reality it does not because of the low probability of the graviton being found far away. Space is not truncated, yet everything remains in a concentrated region in the vicinity of the brane. A faraway brane makes no difference to physical processes on the Gravitybrane since very little from the Gravitybrane ventures far away. Anything produced on or near the Gravitybrane remains nearby, in a localized region.
Sometimes physicists refer to this model of localized gravity as RS2. The RS stands for Randall and Sundrum, but the 2 is misleading—it refers to the fact that this was the second paper we wrote on warped geometry, not the fact that there are two branes. The scenario with two branes, which addresses the hierarchy problem, is known as RS1. (The names would be less confusing if we had written the papers in the opposite order.) Unlike RS1, the scenario in this chapter is not necessarily relevant to the hierarchy problem, though you can introduce a second brane and solve the hierarchy as well, as we briefly considered towards the end of Chapter 20. But whether or not there is a second brane inside the space to address the hierarchy problem, localized gravity is a radical possibility with important theoretical implications that contradicts the long-held assumption that extra dimensions must be compact.
Kaluza-Klein Partners of the Graviton
The previous section discussed the graviton’s probability function, which is heavily concentrated on the Gravitybrane. The particle I was talking about plays the role of the four-dimensional graviton because it travels almost exclusively along the brane and has only a tiny probability of leaking out into the fifth dimension. From the graviton’s perspective, space looks as if the fifth dimension is only 10-33 cm in size (a size set by the curvature, which is in turn set by the energy in the bulk and on the brane) rather than of infinite extent.
But although Raman and I were rather excited by our discovery, we weren’t sure that we had completely solved the problem. Was the localized graviton by itself sufficient to generate a four-dimensional effective theory in which gravity behaved as it would in four dimensions? The potential problem was that Kaluza-Klein partners of the graviton could also contribute to the gravitational force, and could thereby significantly modify gravity.
The reason this seemed so dangerous was that, generally, the larger the size of the extra dimension, the smaller the mass of the lightest KK