Warped Passages by Lisa Randall Read Free Book Online Page A

for a disappointment, however. The resident Rabbit, who was fond of puns, had sent her instead to OneDLand, a strange, not so wonderful, one-dimensional world. Athena looked around—or, I should say, to her left and right—and discovered that all she could see were two points—one to her left and another to her right (but in a prettier color, she thought).
    In OneDLand, all the one-dimensional people with their one-dimensional possessions were lined up along this single dimension like long, thin beads strung out along a thread. But even with her limited purview, Athena knew there must be more to OneDLand than met her eyes because of the outrageous din that met her ears. A Red Queen was well hidden behind a dot, but Athena couldn’t miss her strident yells: “This is the most ridiculous chess game I have ever seen! I can’t move any pieces, not even to castle!” Athena was relieved when she realized her one-dimensional existence shielded her from the wrath of the Red Queen.
    But Athena’s cozy universe did not last long. Slipping through a gap in OneDLand, she returned to the dreamworld’s rabbit hole, which had an elevator that could take her to hypothetical, other-dimensional universes. Almost immediately, the Rabbit announced, “Next stop: TwoDLand—a two-dimensional world.” Athena didn’t think “TwoDLand” a very nice name, but she cautiously entered all the same.
    Athena needn’t have been so hesitant. Almost everything in TwoDLand looked the same as in OneDLand. She did notice one difference—a vial labeled “Drink me.” Bored with one dimension, Athena promptly obeyed. She quickly shrank to a tiny size, and as she became smaller, a second dimension came into view. This second dimension was not very big—it was wrapped around in a fairly small circle. Her surroundings now resembled the surface of an extremely long tube. A Dodo was racing around this circular dimension, but he wanted to stop. So he kindly offered Athena, who looked rather hungry, some cake.
    When Athena ate a morsel of the Dodo’s dreamcake, she started to grow. After only a few bites (she was quite sure of this, as she was still rather hungry), the cake very nearly disappeared; all that remained was a very tiny crumb. At least Athena thought there was a crumb, but she could see it only when she squinted very hard. And the cake wasn’t the only thing that had vanished from view: when Athena returned to her usual size, the entire second dimension had disappeared.
    She thought to herself, “TwoDLand is very odd indeed. I’d best be getting home.” Her return journey was not without further adventures, but those will be kept for another time.
     

    Even if we don’t know why three spatial dimensions are special, we can ask how . How is it possible that the universe could appear to have only three dimensions of space if the fundamental underlying spacetime contains more? If Athena is in a two-dimensional world, why does she sometimes see only one? If string theory is the correct description of nature, and there are nine dimensions of space (plus one of time), what has become of the missing six spatial dimensions? Why aren’t they visible? Do they have any discernible impact on the world we see?
    The last three questions are central to this book. However, the first order of business is to determine whether there is any way in which the evidence of extra dimensions can be hidden so that Athena’s two-dimensional world would appear as one-dimensional, or a universe with extra dimensions would appear to have the three-spatial-dimensional structure we observe around us. If we’re to accept the idea of a world with extra dimensions, whatever theory they come from, there must be a good explanation for why we have not yet detected even the slightest trace of their existence.
    This chapter is about extremely small compactified , or rolled-up, dimensions. They don’t extend for ever, like the three familiar dimensions; instead, they