Warped Passages - Lisa Randall [182]
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 1043 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 MPl [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