Warped Passages by Lisa Randall Read Free Book Online

well as Central Park and most of the museums. Although such distinctions are blurred from far away, within the city they are very real.
    But now think about how people far away see New York. To them, it’s a dot on a map. An important dot, perhaps, a dot with a distinctive character; but from outside New York, a dot nonetheless. Even with all their variety, New Yorkers are in a single category when viewed from the Midwest or Kazakhstan, for example. When I mentioned this analogy to my cousin who lives downtown (in the West Village, to be precise), he confirmed my point by balking at the suggestion of grouping together New Yorkers living uptown and downtown. Nonetheless, as any non-New Yorker could tell him, the distinctions are too small to matter to people not living in their midst.
    It is common practice in physics to formalize this intuition, and organize categories in terms of the distance or energy that is relevant. Physicists accept this practice and have given it a name— effective theory . The effective theory concentrates on the particles and forcesthat have “effects” at the distance in question. Rather than describing particles and interactions in terms of unmeasurable parameters that describe ultra-high-energy behavior, we formulate observations in terms of the things that are actually relevant to the scales we might detect. The effective theory at any single distance scale doesn’t go into the details of an underlying short-distance physical theory; it only asks about things you could hope to measure or see. If something is beyond the resolution of the scales at which you are working, you don’t need its detailed structure. This practice is not scientific fraud, but a way of disregarding the clutter of superfluous information. It is an “effective” way to obtain accurate answers efficiently.
    Everyone, including physicists, is happy to return to a three-dimensional universe when higher-dimensional details are beyond our resolution. Just as physicists will often treat a wire as if it is one-dimensional, we will also describe a higher-dimensional universe in lower-dimensional terms when the extra dimensions are minuscule and higher-dimensional details are too tiny to matter. Such a lower-dimensional description would summarize the observable effects of all possible higher-dimensional theories in which the extra dimensions are too tiny to see. For many purposes, such a lower-dimensional description is adequate, independent of the number, size, and shape of the additional dimensions.
    The lower-dimensional quantities are not providing the fundamental description, but they are a convenient way of organizing observations and predictions. If you do know the short-distance details, or the microstructure, of a theory, you can use them to derive the quantities that appear in the low-energy description. Otherwise, those quantities are just unknowns to be experimentally determined.
    The following chapter elaborates these ideas and considers the consequences of tiny rolled-up extra dimensions. The dimensions we’ll consider first are minuscule, too tiny to make any difference at all. Later on, when we return to extra dimensions, we’ll explore both the large and the infinite dimensions that recently radically revised this picture.

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    Restricted Passages: Rolled-up Extra Dimensions
No way out
None whatsoever.
Jefferson Starship
    Athena awoke with a start. The previous day she had read Alice in Wonderland and Flatland in order to seek some inspiration about dimensions. But that night she had the strangest dream, which, when fully conscious, she recognized as the result of having read the two books on the same day. *
    Athena dreamed she had turned into Alice, slipped into a rabbit hole, and met the resident Rabbit, who had pushed her out into an unfamiliar world. Athena had thought it a rather rude way to convey a guest. Even so, she had eagerly looked forward to her upcoming adventure in Wonderland.
    Athena was in