Knocking on Heaven's Door - Lisa Randall [157]
The exponential function isn’t made up. It arises from the unique solution to Einstein’s equations in the scenario we proposed. Raman and I calculated that in the warped geometry, the ratio of the strength of gravity and the weak force is the exponential of the distance between the two branes. If the separation between the two branes has a reasonable value—a few dozens or so in terms of the scale set by gravity—the right hierarchy between masses and the strength of forces naturally emerges.
In the warped geometry, the gravity we experience is weak—not because it is diluted throughout large extra dimensions—but instead because it is concentrated somewhere else: on the other brane. Our gravity arises only as the tail end of what in other regions of the extra-dimensional world feels like a very intense force.
We don’t see the other universe on the other brane because the lone shared force is gravity, and gravity is too weak in our vicinity to communicate readily observable signals. In fact, this scenario can be thought of as one example of a multiverse, in which the stuff and elements of our world interact very weakly, or in some cases not at all, with the stuff in another world. Most such speculations cannot be tested and will be left to the realm of imagination. After all, if matter is so far distant that light couldn’t reach us in the lifetime of the universe, we can’t detect it. The “multiverse” scenario that Raman and I proposed is unusual in that the shared gravitational force leads to experimentally testable consequences. We don’t directly access the other universe. But particles that travel in the higher-dimensional bulk can come to us.
The most obvious effect of the extra-dimensional world—in the absence of detailed searches such as those at the LHC—would be the explanation for the hierarchy of mass scales that particle physics theories need in order to successfully explain observed phenomena. This of course is not sufficient for us to know if the explanation is the one operational in the world, since it doesn’t distinguish among proposed solutions.
However, the higher energy that will be achieved at the LHC should help us discover whether an extra dimension of space is just an outlandish idea or an actual fact about the universe. If our theory is correct, we would expect the LHC to produce Kaluza-Klein modes. Because of the connection to the hierarchy problem, the right energy scale to look for KK modes in this scenario is the one that will be probed at the LHC. They should have mass of about a TeV—the weak mass scale. Once the energy achieved is high enough, these heavy particles might be produced. The discovery of these KK particles would provide the key confirmation that gives us insight into a greatly expanded world.
In fact, the KK modes of the warped geometry have an important and distinctive feature. Whereas the graviton itself has extraordinarily feeble interaction strength—after all, it communicates the extremely weak gravitational force—the KK modes of the graviton interact far more strongly, almost as strongly as the force called the weak force, which is in actuality trillions of times stronger than gravity.
The reason for the KK gravitons’ surprisingly strong interaction strength is the warped geometry they travel in. Owing to spacetime’s dramatic curvature, the interactions of KK gravitons have far greater strength than those of the graviton that communicates the gravitational force we experience. In the warped geometry, not only do masses get rescaled, but gravitational interactions do as well. Calculations demonstrate that in the warped geometry, KK gravitons have interactions comparable to that of weak scale particles.
This means that unlike supersymmetric models, and unlike large extra-dimensional ones, the experimental evidence for this scenario will not be missing energy where the interesting particle escapes unseen. Instead, it will be a much cleaner, and easier to identify, signature, consisting of the particle decaying inside the detector into Standard Model particles that leave