Warped Passages Read Free Page A

differences between the projections of higher-dimensional crystals in the pan’s coating and the more mundane structure of ordinary three-dimensional food. The different arrangements of atoms, which keeps them from binding to each other, is a tantalizing suggestion that extra dimensions exist and explain some observable physical phenomena.

Figure 2. This is a “Penrose tiling.” It is a projection of a five-dimensional crystalline structure onto two dimensions.
    Overview
    Just as extra dimensions help us understand the confusing arrangement of molecules in a quasicrystal, physicists today speculate that theories of extra dimensions also will illuminate connections in particle physics and cosmology—connections that are difficult to understand with only three dimensions.
    For thirty years, physicists have relied on a theory called the Standard Model of particle physics, which tells us about the fundamental nature of matter and the forces through which elementary constituents interact. * Physicists have tested the Standard Model by creating particles that have not been present in our world since the earliest seconds of the universe, and they’ve found that the Standard Model describes many of their properties extremely well. Yet the Standard Model leaves some fundamental questions unanswered—questions so basic that their resolution promises new insight into the building blocks of our world and their interactions.
    This book tells about how I and others searched for answers to Standard Model puzzles and found ourselves in extra-dimensional worlds. The new developments with extra dimensions will ultimately take center stage, but I’ll first introduce the supporting players—the revolutionary physics advances of the twentieth century. The recentideas that I discuss later are grounded in these stupendous breakthroughs.
    The review topics we’ll encounter will, broadly, divide into three categories: early-twentieth-century physics, particle physics, and string theory. We’ll investigate the key ideas of relativity and quantum mechanics, as well as the current state of particle physics and the problems that extra dimensions might address. We’ll also consider the concepts that underlie string theory, which many physicists think is the leading contender for a theory that incorporates both quantum mechanics and gravity. String theory, which postulates that the most basic units in nature are not particles but fundamental, oscilllating strings, has provided much of the impetus for studying extra dimensions, because it requires more than three dimensions of space. And I will also describe the role of branes, membrane-like objects within string theory, which are as essential to the theory as strings themselves. We’ll consider both the successes of these theories and the questions they leave open—the ones that motivate current research.
    One of the chief mysteries is why gravity is so much weaker than the other known forces. Gravity might not feel weak when you’re hiking up a mountain, but that’s because the entire Earth is pulling on you. A tiny magnet can lift a paper clip, even though all the mass of the Earth is pulling it in the opposite direction. Why is gravity so defenseless against the small tug of a tiny magnet? In standard three-dimensional particle physics, the weakness of gravity is a huge puzzle. But extra dimensions might provide an answer. In 1998, my collaborator Raman Sundrum and I showed one reason this might be so.
    Our proposal is based on warped geometry, a notion that arises in Einstein’s theory of general relativity. According to this theory, space and time are integrated into a single spacetime fabric that gets distorted, or warped, by matter and energy. Raman and I applied this theory in a new, extra-dimensional context. We found a configuration in which spacetime warps so severely that even if gravity is strong in one region of space, it is feeble everywhere else.
    And we found something even