Knocking on Heaven's Door (50 page)

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 can be produced. If so, it will disappear from the detector, leaving as evidence missing energy and momentum.

Of course, missing energy is also characteristic of supersymmetric models. The signals could even appear so similar that even if a discovery is made, people from both extra-dimensional and supersymmetry camps are likely to interpret the data as supporting their expectations—at least initially. But with detailed understanding of the consequences and predictions of both types of models, we will be able to determine which idea—if either—is correct. One of our goals in building models is to match experimental signatures and details to their true implications. Once we have characterized different possibilities, we know the rate and features of the signatures that follow, and we can use subtle features to distinguish among them.

In any case, at this point, along with most of my colleagues, I doubt that the large-extra-dimensional scenario is truly the solution to the hierarchy problem, though we will soon see a very different extra-dimensional example that seems much more promising. For one thing, we don’t expect extra dimensions to be so large. It turns out that the extra dimensions would have to be enormous relative to the other scales posed in the problem. Even though the hierarchy between the weak scale and the gravity scale is in principle eliminated, a new hierarchy involving the new dimensions’ size gets introduced in this scenario.

Even more worrisome is that in this scenario, we would expect the evolution of the universe to be very different from what has been observed. The problem is that these very large dimensions would expand along with the rest of the universe until the temperatures are very low. For a model to be a potential candidate for reality, the evolution of the universe it predicts would have to mimic that which has been observed that is consistent with only three dimensions of space. That poses a difficult challenge for scenarios with such large additional dimensions.

These challenges are not enough to definitively rule out the idea. Clever enough model builders can find solutions to most problems. But the models tend to become overly complicated and convoluted in order to agree with all observations. Most physicists are skeptical about such ideas on aesthetic grounds. Many have therefore turned to more promising extra-dimensional ideas such as the ones described in the following section. Even so, only experiments will tell us for certain whether models with large extra dimensions apply to the real world or not.

A WARPED EXTRA DIMENSION

Large extra dimensions are not the only potential solution to the hierarchy problem, even in the context of an extra-dimensional universe. Once the door was opened to extra-dimensional ideas, Raman Sundrum and I identified what seems to be a better solution
⁶⁶
—one that most physicists would agree is much more likely to exist in nature. Mind you, that doesn’t mean that most physicists think it is likely to be true. Many suspect that anyone would be lucky to correctly predict what the LHC will reveal or to get a model completely correct without further experimental clues. But it’s an idea that probably stands as good a chance as any of being right, and—like most good models—presents clear search strategies so that theorists and experimenters can more fully exploit all the LHC’s capabilities—and maybe even discover evidence that the proposal is true.

The solution that Raman and I proposed involves only a single extra dimension, and that dimension need not be large. No new hierarchy involving the dimension’s size is necessary. And—as opposed to large-extra-dimensional scenarios—the universe’s evolution automatically agrees with late time cosmological observations.

Although our focus is the single new dimension, additional dimensions of space might exist as well—but in this scenario they won’t play any discernible role in explaining particle properties. Therefore, we can justifiably ignore them when investigating the hierarchy solution—in accordance with the effective theory approach—and concentrate on the consequences of the single extra dimension.

[
FIGURE 67
]
The Randall-Sundrum setup contains two branes that bound a fourth dimension of space (a fifth dimension of spacetime). In this space, the graviton wavefunction (which tells the probability of finding the graviton at any point in space) decreases exponentially from the Gravitybrane to the Weakbrane.

If the idea that Raman and I had is right, the LHC will soon teach us fascinating properties about the nature of space. It turns out that the universe we suggested is dramatically curved, in accordance with what Einstein taught us about spacetime in the presence of matter and energy. In technical terminology, the geometry we derived from Einstein’s equations is “warped” (that really was the pre-existing technical term). What that means is that space and time vary along the single additional dimension of interest. It does so in such a way that space and time, as well as masses and energy, are all rescaled as you move from one place in extra-dimensional space to another, as we will soon get to and is illustrated in Figure 68.

One important consequence of this warped spacetime geometry is that whereas the Higgs particle would have been heavy in some other location in extra-dimensional space, it will have weak scale mass—exactly as should be the case—in the location where we reside. This might sound somewhat arbitrary, but it is not. According to our scenario, there is a brane on which we live—the Weakbrane—and a second brane where gravity is concentrated, known as the Gravitybrane—or among physicists, the Planck brane. This brane would contain another universe that is separated from us in an extra dimension. (See Figure 67.) In this scenario, the second brane would in fact be right next door—separated by an infinitesimal distance, a million trillion trillion times smaller than a centimeter.

The remarkable property that follows from the warped geometry (illustrated in the Figure 67), is that the
graviton
, the particle that communicates the force of gravity, is far more heavily weighted on the other brane than on ours. That would make gravity strong elsewhere in the other dimension, but very weak where we live. In fact, Raman and I found that gravity should be exponentially weaker in our vicinity than on the other brane, thereby giving a natural explanation for the weakness of gravity.

An alternative way of interpreting the consequences of this setup is through the geometry of spacetime, schematically illustrated in Figure 68. The scale of spacetime depends on location in the fourth spatial dimension. Masses get exponentially rescaled too—and they do so in a way that the Higgs boson mass is what it needs to be. Although one can debate the assumptions our model relies on—namely, two large flat branes bounding an extra-dimensional universe—the geometry itself follows directly from Einstein’s theory of gravity once you postulate the energy carried by the branes and by the extra-dimensional space known as the bulk. Raman and I solved the equations of general relativity. And when we did, we found the geometry I just described—namely, the curved warped space in which masses get rescaled in the way required to solve the hierarchy problem.

[
FIGURE 68
]
Another way to understand why warped geometry solves the hierarchy problem is in terms of the geometry itself. Space, time, energy, and mass all are rescaled exponentially as you go from one brane to the next. In this scenario, it would be very natural to find that the Higgs mass is exponentially smaller than the Planck mass.

Unlike the large extra-dimensional models, the models based on the warped geometry don’t replace the old enigma of the hierarchy problem by a new one (why are the extra dimensions so large?). In the warped geometry, the extra dimension is not large. The large numbers arise from an exponential rescaling of space and time. The exponential rescaling makes the ratio of sizes—and masses—of objects enormous, even when those objects are separated only modestly in extra-dimensional space.

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.