Knocking on Heaven's Door - Lisa Randall [154]
One way to understand this is to imagine an analogous situation with a water sprinkler. Think about the water that emerges from this sprinkler. If the water spread only in our dimensions, its impact would depend on the amount of water emerging from the hose and how far it had to travel. But if there were additional dimensions to space, the water would spread throughout those dimensions as well after emerging from the end of the hose. We would experience much less water than we would otherwise at a given distance from the source because water would also spread throughout the dimensions we don’t observe. (This is illustrated schematically in Figure 65.)
[ FIGURE 65 ] The strengths of forces weaken more quickly with distance in a higher-dimensional space than in a lower-dimensional one. This is analogous to a higher-dimensional water sprinkler for which the water dilutes much more quickly with distance. The water spreads more in three dimensions than it spreads in two—in the picture, only the flower receiving water from the lower-dimensional sprinkler is adequately maintained.
If the extra dimensions were of finite size, the water would reach the boundaries of the extra dimensions and no longer spread out. But the amount of water anything would receive at any given place in the extra-dimensional space would be far less than if it had never spread out in those dimensions in the first place.
Similarly, gravity could spread into other dimensions. Even though the force wouldn’t spread out forever if the dimensions have finite size, large dimensions would dilute the gravitational force we would experience in our three-dimensional world. If the dimensions were sufficiently large, we would experience very weak gravity, even though the fundamental strength of higher-dimensional gravity could be quite big. Keep in mind, however, that for this idea to work, the extra dimensions have to be enormous compared to what theoretical considerations lead us to expect, since gravity indeed appears so weakly in a three-dimensional world.
Nonetheless, the LHC will subject this idea to experimental tests. Even though the idea now seems improbable, reality and not our ease in finding models is the final arbiter of what is right. If realized in the world, these models would lead to a distinctive characteristic signature. Because higher-dimensional gravity is strong at energies of about the weak scale—the energies that the LHC will generate—p articles would collide together and produce a higher-dimensional graviton—the particle that communicates the force of higher-dimensional gravity. But this graviton travels into the extra dimensions. The gravity we are familiar with is extremely weak—far too weak to produce a graviton if there are only three dimensions of space. But in this new scenario, higher-dimensional gravity would be sufficiently strong to produce a graviton at the energies reached by the LHC.
The consequence would be the production of particles known as Kaluza-Klein (KK) modes, which are the manifestation of the higher-dimensional gravitation in three-dimensional space. They are named after Theodor Kaluza and Oskar Klein, who first thought about extra dimensions in our universe. KK particles have interactions similar to those of the particles we know, but with heavier masses. These heavier masses are the result of their additional momentum in the direction of the extra dimension. If the KK mode is associated with the graviton—as the large extra dimensional scenario predicts—once produced, it would disappear from the detector. The evidence of its ephemeral visit would be the energy that would go missing. (See Figure 66, in which a KK particle is produced and takes away unseen energy and momentum.)
[ FIGURE 66 ] In the large extra-dimensional scenario, a Kaluza-Klein partner of the graviton with momentum in the extra dimensions