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Chapter 14: Notes

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  • Chapter 14: Notes

    Table of Contents
    .......The Elegant Universe
    THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
    ```(annotated and with added bold highlights by Epsilon=One)

    Chapter 14: Notes
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    1. More precisely, the universe should be filled with photons conforming to the radiation thermally emitted by a perfectly absorbent body—a "black-body" in the language of thermodynamics—with the stated temperature range. This is the same radiation spectrum emitted quantum mechanically by black holes, as explained by Hawking, and by a hot oven, as explained by Planck. Return to Text

    2. The discussion conveys the spirit of the issues involved although we are glossing over some subtle features having to do with the motion of light in an expanding universe that affect the detailed numerics. In particular, although special relativity declares that nothing can travel faster than the speed of light, this does not preclude two photons carried along on the expanding spatial fabric from receeding from one another at a speed exceeding that of light. For example, at the time the universe first became transparent, about 300,000 years ATB, locations in the heavens that were about 900,000 light-years apart would have been able to have influenced each other, even though the distance between them exceeds 300,000 light-years. The extra factor of three comes from the expansion of the spatial fabric. This means that as we run the cosmic film backward in time, by the time we get to 300,000 years ATB, two points in the heavens need only be less than 900,000 light-years apart to have had a chance to influence each other's temperature. These detailed numerics do not change the qualitative features of the issues discussed. Return to Text

    3. For a detailed and lively discussion of the discovery of the inflationary cosmological model and the problems it resolves, see Alan Guth, The Inflationary Universe (Reading, Mass: Addison-Wesley, 1997). Return to Text

    4. For the mathematically inclined reader, we note that the idea underlying this conclusion is the following: If the sum of the spacetime dimensions of the paths swept out by each of two objects is greater than or equal to the spacetime dimension of the arena through which they are moving then they will generically intersect. For instance, point particles sweep out one-dimensional spacetime paths—the sum of the spacetime dimensions for two such particle paths is therefore two. The spacetime dimension of Lineland is also two, and hence their paths will generally intersect (assuming their velocities have not been finely tuned to be exactly equal). Similarly, strings sweep out two-dimensional spacetime paths (their world-sheets); for two strings the sum in question is therefore four. This means that strings moving in four spacetime dimensions (three space and one time) will generally intersect. Return to Text

    5. With the discovery of M-theory and the recognition of an eleventh dimension, string theorists have begun studying ways of curling up all seven extra dimensions in a manner that puts them all on more or less equal footing. The possible choices for such seven-dimensional manifolds are known as Joyce manifolds, after Domenic Joyce of Oxford University, who is credited with finding the first techniques for their mathematical construction. Return to Text

    6. Interview with Cumrun Vafa, January 12, 1998. Return to Text

    7. The expert reader will note that our description is taking place in the so-called string frame of reference, in which increasing curvature during the pre—big bang arises from (a dilaton-driven) increase in the strength of the gravitational force. In the so-called Einstein frame, the evolution would be described as an accelerating contraction phase. Return to Text

    8. Interview with Gabriele Veneziano, May 19, 1998. Return to Text

    9. Smolin's ideas are discussed in his book The Life of the Cosmos (New York: Oxford University Press, 1997). Return to Text

    10. Within string theory, for example, this evolution could be driven by small changes to the shapc of the curled-up dimensions from one universe to its offspring. From our results on space-tearing conifold transitions, we know that a sufficiently long sequence of such small changes can take us from one Calabi-Yau to any other, allowing the multiverse to sample the reproductive efficiency of all universes based on strings. After the multiverse has passed through sufficiently many stages of reproduction, Smolin's hypothesis would lead us to expect that the typical universe will have a Calabi-Yau component that is optimized for fertility. Return to Text
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    Table of Contents
    .......The Elegant Universe
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