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The Essential New Feature

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  • The Essential New Feature

    Table of Contents
    .......The Elegant Universe
    THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
    ```(annotated and with added bold highlights by Epsilon=One)
    Chapter 10 - Quantum Geometry
    The Essential New Feature
    We do not have to search far to find the essential new string physics. A point particle moving in this two-dimensional universe can execute the kinds of motion illustrated in Figure 10.2: It can move along the extended dimension of the Garden-hose, it can move along the curled-up part of the Garden-hose, or any combination of the two. A loop of string can undergo similar motion, with one difference being that it oscillates as it moves around on the surface, as shown in Figure 10.3(a). This is a distinction we have already discussed in some detail: The oscillations of the string imbue it with characteristics such as mass and force charges. Although a crucial aspect of string theory, this is not our present focus, since we already understand its physical implications.

    ......
    Figure 10.2 Point particles moving on a cylinder.
    Figure 10.3 Strings can move on a cylinder in two different ways—in "unwrapped" or "wrapped" configurations.
    Instead, our present interest is in another difference between point-particle and string motion, a difference directly dependent on the shape of the space through which the string is moving. Since the string is an extended object, there is another possible configuration beyond those already mentioned: It can wrap around—lasso, so to speak—the circular part of the Garden-hose universe, as shown in Figure 10.3(b). 1 The string will continue to slide around and oscillate, but it will do so in this extended configuration. In fact, the string can wrap around the circular part of the space any number of times, as also shown in Figure 10.3(b), and again will execute oscillatory motion as it slides around. When a string is in such a wrapped configuration, we say that it is in a winding mode of motion. Clearly, being in a winding mode is a possibility inherent to strings. There is no point-particle counterpart. We now seek to understand the implications of this qualitatively new kind of string motion on the string itself as well as on the geometrical properties of the dimension it wraps.
    Table of Contents
    .......The Elegant Universe
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