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The Physical Implications of Extra Dimensions

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  • The Physical Implications of Extra Dimensions

    Table of Contents
    .......The Elegant Universe
    THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
    ```(annotated and with added bold highlights by Epsilon=One)
    Chapter 8 - More Dimensions Than Meet the Eye
    The Physical Implications of Extra Dimensions
    Years of research, dating back to Kaluza's original paper, have shown that even though any extra dimensions that physicists propose must be smaller than we or our equipment can directly "see" (since we haven't seen them), they do have important indirect effects on the physics that we observe. In string theory, this connection between the microscopic properties of space and the physics we observe is particularly transparent.

    To understand this, you need to recall that masses and charges of particles in string theory are determined by the possible resonant vibrational string patterns. Picture a tiny string as it moves and oscillates, and you will realize that the resonant patterns are influenced by its spatial surroundings. Think, for example, of ocean waves. Out in the grand expanse of the open ocean, isolated wave patterns are relatively free to form and travel this way or that. This is much like the vibrational patterns of a string as it moves through large, extended spatial dimensions. As in Chapter 6, such a string is equally free to oscillate in any of the extended directions at any moment. But if an ocean wave passes through a more cramped spatial environment, the detailed form of its wave motion will surely be affected by, for example, the depth of the water, the placement and shape of the rocks encountered, the canals through which the water is channeled, and so on. Or, think of an organ pipe or a French horn. The sounds that each of these instruments can produce are a direct consequence of the resonant patterns of vibrating air streams in their interior; these are determined by the precise size and shape of the spatial surroundings within the instrument through which the air streams are channeled. Curled-up spatial dimensions have a similar impact on the possible vibrational patterns of a string. Since tiny strings vibrate through all of the spatial dimensions, the precise way in which the extra dimensions are twisted up and curled back on each other strongly influences and tightly constrains the possible resonant vibrational patterns. These patterns, largely determined by the extradimensional geometry, constitute the array of possible particle properties observed in the familiar extended dimensions. This means that extradimensional geometry determines fundamental physical attributes like particle masses and charges that we observe in the usual three large space dimensions of common experience.

    This is such a deep and important point that we say it once again, with feeling. According to string theory, the universe is made up of tiny strings whose resonant patterns of vibration are the microscopic origin of particle masses and force charges. String theory also requires extra space dimensions that must be curled up to a very small size to be consistent with our never having seen them. But a tiny string can probe a tiny space. As a string moves about, oscillating as it travels, the geometrical form of the extra dimensions plays a critical role in determining resonant patterns of vibration. Because the patterns of string vibrations appear to us as the masses and charges of the elementary particles, we conclude that these fundamental properties of the universe are determined, in large measure, by the geometrical size and shape of the extra dimensions. That's one of the most far-reaching insights of string theory.

    Since the extra dimensions so profoundly influence basic physical properties of the universe, we should now seek—with unbridled vigor—an understanding of what these curled-up dimensions look like.
    Table of Contents
    .......The Elegant Universe
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