Knocking on Heaven's Door - Lisa Randall [153]
String theory’s extra dimensions might have physical import for the observable world and so too might three-dimensional branes. Perhaps the most important reason to consider extra dimensions is that they might affect visible phenomena, and, in particular, address outstanding puzzles such as the hierarchy problem of particle physics. Extra dimensions and branes could be the key to resolving this question—addressing the issue of why gravity is so weak.
[ FIGURE 64 ] Standard Model particles and forces can be stuck on a braneworld that lives in higher-dimensional space. In that case, my cousin Matt, the matter and stars we know, forces such as electromagnetism, and our galaxy and universe all live in its three spatial dimensions. Gravity, on the other hand, can always spread throughout all of space. (Photo courtesy of Marty Rosenberg)
Which brings us to what is perhaps the best reason right now to think about extra dimensions of space. They can have consequences for phenomena we are now trying to understand, and if so, we might see evidence in the imminent future.
Recall that we can phrase the hierarchy problem in two different ways. We can say it is the question of why the Higgs mass—and hence the weak scale—is so much smaller than the Planck mass. This is the question we considered when thinking about supersymmetry and technicolor. But we can also ask an equivalent question: Why is gravity so weak compared to the other known fundamental forces? The strength of gravity depends on the Planck mass scale, the enormous mass ten thousand trillion times greater than the weak scale. The bigger the Planck mass, the weaker the force of gravity. Only when masses are at or near the Planck scale is gravity strong. As long as particles are a good deal lighter than the scale set by the Planck mass, as they are in our world, the force of gravity is extremely weak.
The puzzle of why gravity is so weak is in fact equivalent to the hierarchy problem—the solution of one solves the other. But even though the problems are equivalent, phrasing the hierarchy problem in terms of gravity helps guide our thinking toward extra-dimensional solutions. We’ll now delve into a couple of the leading suggestions.
LARGE EXTRA DIMENSIONS AND THE HIERARCHY
Ever since people first started thinking about the hierarchy problem, physicists thought the resolution must involve modified particle interactions at the weak energy scale of about a TeV. With only Standard Model particles, the quantum contributions to the Higgs particle mass are simply too enormous. Something has to kick in to tame the large quantum mechanical contributions to the Higgs particle mass.
Supersymmetry and technicolor are two examples in which new heavy particles might participate in high-energy interactions and cancel the contributions or prevent them from arising in the first place. Until the 1990s, all proposed solutions to the hierarchy problem could be categorized similarly, with new particles and forces and even new symmetries emerging at the weak energy scale.
In 1998, Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali65 proposed an alternative way of addressing the problem. They pointed out that since the problem involves not just the weak energy scale alone, but its ratio to the Planck energy scale associated with gravity, perhaps the problem lay in an incorrect understanding of the basic nature of gravity itself.
They suggested that there is in fact no hierarchy in masses at all—at least with respect to the fundamental scale of gravity compared to the weak scale. Maybe gravity is instead much stronger in the extra-dimensional universe, but is only measured to be so feeble in our three-plus-one-dimensional world because it is diluted throughout all the dimensions that we don’t see. Their hypothesis was that the mass scale at which gravity becomes strong in the extra-dimensional