The Shape of Inner Space
String Theory and the Geometry of the Universe's Hidden Dimensions
by Shing-Tung Yau
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The Shape of Inner Space
A UNIVERSE IN THE MARGINS
The invention of the telescope, and its steady improvement over the years, helped confirm what has become a truism: There’s more to the universe than we can see. Indeed, the best available evidence suggests that nearly three fourths of all the stuff of the cosmos lies in a mysterious, invisible form called dark energy. Most of the rest—excluding only the 4 percent composed of ordinary matter that includes us—is called dark matter. And true to form, it too has proved “dark” in just about every respect: hard to see and equally hard to
fathom.
The portion of the cosmos we can see forms a sphere with a radius of about 13.7 billion light-years. This sphere is sometimes referred to as a Hubble volume, but no one believes that’s the full extent of the universe. According to the best current data, the universe appears to extend limitlessly, with straight lines literally stretching from here to eternity in every direction we can point. There’s a chance, however, that the universe is ultimately curved and bounded. But even if it is, the allowable curvature is so slight that, according to some analyses, the Hubble volume we see is just one out of at least one thousand
such volumes that must exist. And a recently launched space instrument, the Planck telescope, may reveal within a few years that there are at least one million Hubble volumes out there in the cosmos, only one of which we’ll ever have access to. I’m trusting the astrophysicists on this one, realizing that some may quarrel with the exact numbers cited above. One fact, however, appears to be unassailable: What we see is just the tip of iceberg.
At the other extreme, microscopes, particle accelerators, and various imaging devices continue to reveal the universe on a miniature scale, illuminating a previously inaccessible world of cells, molecules, atoms, and smaller entities. By now, none of this should be all that surprising. We fully expect our telescopes to probe ever deeper into space, just as our microscopes and other tools bring more of the invisible to light.
But in the last few decades—owing to developments in theoretical physics, plus some advances in geometry that I’ve been fortunate enough to participate in—there has been another realization that is even more startling: Not only is there more to the universe than we can see, but there may even be more dimensions, and possibly quite a few more than the three spatial dimensions we’re intimately acquainted with.
That’s a tough proposition to swallow, because if there’s one thing we know about our world—if there’s one thing our senses have told us from our first conscious moments and first groping explorations—it’s the number of dimensions. And that number is three. Not three, give or take a dimension or so, but exactly three.
From the book The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions by Shing-Tung Yau and Steve Nadis. Reprinted by arrangement with Basic Books, a member of The Perseus Books Group. Copyright © 2010.
The Shape of Inner Space
String theory says we live in a 10-dimensional universe, of which we see four. According to theorists, the missing six are curled up in structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau—the man who proved these structures could exist—argues that not only is geometry fundamental to string theory, it is also basic to the nature of the universe.
In accessible prose, Yau and Steve Nadis present ideas from geometry and physics needed to understand the defining features of Calabi-Yau manifolds. He reviews successes in geometric analysis, including advances in four-dimensional topology and the proof of the Poincaré conjecture, before coming to the conjecture first raised by Eugenio Calabi in 1953 that links the topology of complex space to geometry or curvature. Yau proved the Calabi conjecture in a set of papers published in 1977 and 1978.
Subsequently, string theorists (and later M-theorists) incorporated Calabi-Yau manifolds into their redefinition of the fabric of spacetime; if string theory is correct, at any point in four-dimensional spacetime there’s a hidden, six-dimensional, Calabi-Yau manifold. Its properties could determine everything we experience. As string theorist Joe Polchinski notes in the book, “All of the numbers we measure in nature...are derived from the geometry of the Calabi-Yau.”
Yau himself remains open on whether his creation underlies physical reality; owing to the manifolds’ complexity, the equations of string theory have myriad solutions, each implying a separate universe with different characteristics. Experimental proof eludes us for now, and possibly always.
The Shape of Inner Space explains ideas that alter how we view the universe on all scales.
“For more than twenty years, Shing-Tung Yau has played a pivotal role in the geometrical development of string theory.... [This] will have wide appeal to the science-reading public.” —Brian Greene, author of The Elegant Universe
Hardcover : 400 pages
Publisher: Basic Books Inc. ( September 07, 2010 )
Item #: 13-145752
ISBN: 9780465020232
Product Dimensions: 6.125 x 9.25 inches
Product Weight: 22.0 ounces (View shipping rates and policies)
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