Warped Passages (57 page)

Figure 75.
Schematic drawing of the ADD braneworld. The universe’s extra dimensions are rolled up (and large). We live on a brane (the dotted line along the cylinder), so only gravity experiences the extra dimensions.

One question ADD wanted to address with their setup was how large extra dimensions could still be hidden if all particles of the Standard Model were trapped on a brane and the only force in the higher-dimensional bulk was gravity. The answer they found surprised most physicists. As opposed to the size of one-hundredth of a thousandth of a trillionth of a centimeter that we considered in the previous chapter, these extra curled-up dimensions could be as large as a millimeter. (Actually, it’s a little tricky to give the precise number now because, as we’ll discuss further later in the chapter, physicists at the University of Washington have since looked for millimeter-size extra dimensions experimentally and they didn’t find them. Based on their results, we now know that extra dimensions must be smaller than about a tenth of a millimeter, or else they would be ruled out. Nonetheless, dimensions that are even one-tenth of a millimeter in size would still be rather shocking.)

You might have thought that if dimensions were as big as a millimeter (or even ten times smaller), we would surely know about them already. After all, anyone who can’t see a millimeter-size object needs new glasses. On the scales of particle physics, a millimeter is enormous.

To get an idea of how extraordinary extra dimensions a millimeter—or even one a tenth of a millimeter—in size would be, let us recap the sorts of length scale we have discussed so far. The Planck scale length, well out of any experimental reach, is 10
^-33
cm. The TeV scale, which experiments currently explore, is about 10
^-17
cm; physicists have tested electromagnetism down to distances as small as 10
^-17
cm. The sizes ADD were talking about are huge in comparison. In the absence of branes, millimeter-size extra dimensions would be an absurdity that would have been ruled out.

However, branes make far larger extra dimensions conceivable. Branes can trap quarks, leptons, and gauge bosons so that
only
gravity experiences the full higher dimensionality of space. In the ADD scenario, which assumes that everything other than gravity is confined to a brane, everything that doesn’t involve gravity would look exactly the same as it would without the extra dimensions, even if the extra dimensions were extremely large.

For example, everything you see would look four-dimensional. Your eye detects photons, and photons in the ADD model are trapped
on a brane. Therefore all objects you see would look as if there were only three spatial dimensions. If photons are trapped on a brane, then no matter how strong your glasses you could never see any evidence of extra dimensions directly.

In fact, you could hope to see evidence of millimeter-size dimensions in the ADD scenario only with an extremely sensitive gravity probe. All of the usual particle physics processes, such as interactions mediated by the electromagnetic force, electron-positron pair creation, and the binding of the nucleus through the strong force, occur only on the four-dimensional brane and would be exactly the same as in a purely four-dimensional universe.

Charged KK particles would not be a problem either. The previous chapter explained that extra dimensions cannot be very big when all particles are in the bulk, because if they were, we would already have seen the KK partners of Standard Model particles. But this is not true in the ADD scenario because all Standard Model particles—the electron, for example—are bound to a brane. So the Standard Model particles, which don’t travel in the higher-dimensional bulk, wouldn’t carry extra-dimensional momenta. Standard Model particles, which are confined to a brane, therefore wouldn’t have KK partners. And since there would be no KK partners, the constraints based on KK particles such as the ones considered in the last chapter wouldn’t apply.

In fact, in the ADD model, the only particle that must have KK partners is the graviton, which we know must travel in the higher-dimensional bulk. However, the graviton’s KK partners interact far more weakly than the Standard Model KK partners. Whereas Standard Model KK partners interact via electromagnetism, the weak force, and the strong force, the KK partners of the graviton interact only with gravitational strength—as weakly as the graviton itself. The graviton’s KK partners would therefore be much harder to produce and detect than the KK partners of Standard Model particles. After all, no one has ever directly seen the graviton. Its KK partners, which interact as weakly as the graviton itself, should be no easier to find.

ADD realized that if the only constraints on extra dimensions came from gravity, the size of the extra dimension in their scenario where
Standard Model particles are stuck to a brane could be much larger than the previous chapter suggests. The reason is that gravity is very feeble, and is therefore extremely difficult to investigate experimentally. For light objects at close distances, gravity is so weak that its effects are readily overwhelmed by other forces.

For example, the gravitational force between two electrons is 10
⁴³
times weaker than the electromagnetic force. The gravitational force of the Earth dominates only because its net charge is zero. On small scales, not only the net charge matters, but also the way charges are distributed. To test the gravitational force law between small objects, the pull of gravity must be shielded from even the tiniest consequences of the other forces. Although the planets orbiting the Sun, the Moon orbiting the Earth, and the evolution of the universe itself tell us about the form of gravity at very large distances, gravity is hard to test at short distances. We know a lot less about it than we do about the other forces. So if gravity is the only force in the bulk, the existence of surprisingly large extra dimensions would not contradict any experimental results. Dimensions with brane-bound particles are hard to observe.

In 1996, when ADD wrote their paper, Newton’ inverse square law had been tested down to distances of only about a millimeter. That meant that extra dimensions could be as large as a millimeter and no one would have seen any evidence of them. As ADD said in their paper, “Our interpretation of
M
_Pl
[the Planck energy] as a fundamental energy scale [where gravitational interactions become strong] is then based on the assumption that gravity is unmodified over the 33 orders of magnitude between where it is measured…down to the Planck length 10
^-33
cm.”
^*
In other words, in 1998 nothing was known about gravity from experiments at distances smaller than about a millimeter. At separations less than that, the gravitational force law could behave differently, with gravitational attraction increasing much more rapidly as objects approached each other, for example—yet no one would have known.

Large Dimensions and the Hierarchy Problem

The possibility of large extra dimensions was an important observation. But ADD didn’t study large extra dimensions simply to explore abstract possibilities. Their true interest was particle physics, and the hierarchy problem in particular.

As was explained in Chapter 12, the hierarchy problem concerns the large ratio of the weak scale mass and the Planck scale mass, the masses that we associate with particle physics and gravity. Until recently, the main question that particle physicists asked was why the weak scale mass is so small, despite the large (Planck-scale-mass-size)
^*
virtual contributions to the Higgs particle’s mass that tend to make it larger. Until physicists started thinking about extra dimensions, all attempts to address the hierarchy problem involved enhancing the Standard Model in the hope of finding a more comprehensive underlying particle physics theory that would explain why the weak scale mass is so much smaller than the Planck scale mass.

But the hierarchy problem involves a large disparity between two numbers. The conundrum is why the Planck scale and the weak scale are so different. So the hierarchy problem can be phrased another way: why is the Planck scale mass so large when the weak scale mass is so small—or, equivalently, why is the strength of gravity acting on elementary particles so weak? Put this way, the hierarchy problem raises the question of whether gravity, and not particle physics, is different from what physicists have assumed.

ADD pursued this train of logic and suggested that attempts at solving the hierarchy problem through extensions of the Standard Model were on the wrong track. They observed that sufficiently large extra dimensions could equally well solve the problem. They proposed that the fundamental mass scale that determines gravity’s strength is not the Planck scale mass, but a much smaller mass scale, close to a TeV.

However, ADD were then left with the question of why gravity
should be so weak. After all, the reason that the Planck scale mass is so big is that gravity is weak—gravity’s strength is inversely proportional to this scale. A much smaller fundamental mass scale for gravity would make gravitational interactions far too strong.

But this problem wasn’t insurmountable. ADD pointed out that it was only higher-dimensional gravity that was necessarily strong. They reasoned that large extra dimensions could dilute the strength of gravity so much that although the gravitational force would be very strong in higher dimensions, gravity in the lower-dimensional effective theory would be very feeble. In their picture, gravity appears feeble to us because it gets diluted in a very large extra-dimensional space. The electromagnetic, strong, and weak forces, on the other hand, would not be feeble because those forces would be confined to a brane and would not be diluted at all. Large dimensions and a brane could therefore conceivably explain why gravity is so much feebler than the other forces.

Nima told me that the turning point in their research was when he and his collaborators understood the precise relationship between the strengths of higher-and lower-dimensional gravity. This relationship was not new. String theorists, for example, always used it to relate the four-dimensional gravitational scale to the ten-dimensional one. And, as I briefly explained in Chapter 16, Hořava and Witten used the relationship between the strengths of ten-and eleven-dimensional gravity when they observed that gravity can be unified with other forces: a large eleventh dimension permits the higher-dimensional gravitational scale, and hence the string scale, to be as low as the GUT scale. But no one before had recognized that higher-dimensional gravity could be sufficiently strong to address the hierarchy problem so long as extra dimensions are large enough to adequately dilute it. After Nima, Savas, and Gia had thought about extra dimensions for a while and learned how to relate higher-and lower-dimensional gravity, they understood this extraordinary implication.

Relating Higher-and Lower-Dimensional Gravity

In Chapter 2 we saw that when you explore only those distances that are larger than the size of curled-up extra dimensions, the extra dimensions are imperceptible. However, that doesn’t necessarily mean that additional dimensions don’t have physical consequences; even though we don’t see them, they can still influence the values of quantities we do see. Chapter 17 gave an example of this phenomenon. In the sequestering model of supersymmetry breaking, in which supersymmetry breaking occurred on a distant brane and the graviton communicated the breaking to the supersymmetric partners of Standard Model particles, the values of superpartner masses reflected the extra-dimensional origin of supersymmetry breaking and its communication via gravity.

We’ll now consider another example in which extra dimensions influence the values of measurable quantities. The sizes of the compactified dimensions determine the relationship between the strength of four-dimensional gravity (that is, the one we observe) and the strength of the higher-dimensional gravity from which it derives. Gravity is diluted in extra dimensions and is weaker when curled-up extra dimensions enclose a larger volume.

To see how this works, let’s return to the example of Chapter 2, where we considered the three-dimensional garden-hose universe as an analogy for a bulk three-dimensional space bounded by branes. If water were to enter the hose through a pinhole (see Figure 23, Chapter 2), it would initially spurt out from the hole and spread in all three dimensions. However, once the water reached the width of the hose, it would spread only along the hose’s length—which is why the hose appears to be one-dimensional when we measure the gravitational force law at distances greater than the extra dimensions’ size.

But even though the water travels only along the single dimension of the hose, its pressure depends on the size of the cross-section. One way to understand this is by imagining what would happen if the width of the hose increased. The water that entered through the pinhole would then spread out over a larger region, and the pressure of the water exiting the hose would be weaker.

If the pressure of water represents gravitational force lines, and the water entering the hose through the pinhole represents the field lines emerging from a massive object, then the force lines from this massive object would initially spread in all three directions, just like the water in the previous example. And when the force lines reach the walls of the universe (the branes), they would bend and run solely along the single large dimension. With the hose, we found that the wider the nozzle, the weaker the water pressure. Similarly, the area of extra dimensions in our toy garden-hose universe would determine how dilute the field lines will be in the lower-dimensional world. The larger the area of the extra dimensions, the weaker the gravitational field strength in the effective lower-dimensional universe would be.