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THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 15: Notes
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1. Interview with Edward Witten, March 4, 1998. Return to Text
2. Some theorists see a hint of this idea in the holographic principle, a concept originated by Susskind and the renowned Dutch physicist Gerard 't Hooft. Just as a hologram can reproduce a three-dimensional visual image from a specially designed two-dimensional film, Susskind and 't Hooft have suggested that all of the physical happenings we encounter may actually be encoded fully through equations defined in a lower-dimensional world. Although this may sound as strange as trying to draw someone's portrait by viewing only their shadow, we can get a sense of what it means, and understand part of Susskind's and 't Hooft's motivation, by thinking about black hole entropy as discussed in Chapter 13. Recall that the entropy of a black hole is determined by the surface area of its event horizon—and not by the total volume of space that the event horizon bounds. Therefore, the disorder of a black hole, and correspondingly the information it can embody, is encoded in the two-dimensional data of surface area. It is almost as if the event horizon of the black hole acts like a hologram by capturing all the information content of the black hole's three-dimensional interior. Susskind and 't Hooft have generalized this idea to the whole universe by suggesting that everything that occurs in the "interior" of the universe is merely a reflection of data and equations defined on a distant, bounding surface. Recently, work by the Harvard physicist Juan Maldacena, together with important subsequent work by Witten and of Princeton physicists Steven Gubser, Igor Klebanov, and Alexander Polyakov, has shown that, at least in certain cases, string theory embodies the holographic principle. In a manner that is currently being investigated vigorously, it appears that the physics of a universe governed by string theory has an equivalent description that involves only physics that takes place on such a bounding surface—a surface necessarily of lower dimensionality than the interior. Some string theorists have suggested that fully understanding the holographic principle and its role in string theory may well lead to the third superstring revolution. Return to Text
3. Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, trans. Motte and Cajori (Berkeley: University of California Press, 1962), Vol. I, p. 6. Return to Text
4. If you are familiar with linear algebra, one simple and relevant way of thinking about noncommutative geometry is to replace conventional Cartesian coordinates, which commute under multiplication, with matrices, which do not. Return to Text
5. Interview with Cumrun Vafa, January 12, 1998. Return to Text
6. Interview with Edward Witten, May 11, 1998. Return to Text
7. Quoted in Banesh Hoffman with Helen Dukas, Albert Einstein, Creator and Rebel (New York: Viking, 1972), p. 18. Return to Text
8. Martin J. Klein, "Einstein: The Life and Times, by R. W. Clark," (book review) Science 174, pp. 1315-16. Return to Text
9. Jacob Bronkowski, The Ascent of Man (Boston: Little, Brown, 1973), p. 20. Return to Text or
or2. Some theorists see a hint of this idea in the holographic principle, a concept originated by Susskind and the renowned Dutch physicist Gerard 't Hooft. Just as a hologram can reproduce a three-dimensional visual image from a specially designed two-dimensional film, Susskind and 't Hooft have suggested that all of the physical happenings we encounter may actually be encoded fully through equations defined in a lower-dimensional world. Although this may sound as strange as trying to draw someone's portrait by viewing only their shadow, we can get a sense of what it means, and understand part of Susskind's and 't Hooft's motivation, by thinking about black hole entropy as discussed in Chapter 13. Recall that the entropy of a black hole is determined by the surface area of its event horizon—and not by the total volume of space that the event horizon bounds. Therefore, the disorder of a black hole, and correspondingly the information it can embody, is encoded in the two-dimensional data of surface area. It is almost as if the event horizon of the black hole acts like a hologram by capturing all the information content of the black hole's three-dimensional interior. Susskind and 't Hooft have generalized this idea to the whole universe by suggesting that everything that occurs in the "interior" of the universe is merely a reflection of data and equations defined on a distant, bounding surface. Recently, work by the Harvard physicist Juan Maldacena, together with important subsequent work by Witten and of Princeton physicists Steven Gubser, Igor Klebanov, and Alexander Polyakov, has shown that, at least in certain cases, string theory embodies the holographic principle. In a manner that is currently being investigated vigorously, it appears that the physics of a universe governed by string theory has an equivalent description that involves only physics that takes place on such a bounding surface—a surface necessarily of lower dimensionality than the interior. Some string theorists have suggested that fully understanding the holographic principle and its role in string theory may well lead to the third superstring revolution. Return to Text
3. Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, trans. Motte and Cajori (Berkeley: University of California Press, 1962), Vol. I, p. 6. Return to Text
4. If you are familiar with linear algebra, one simple and relevant way of thinking about noncommutative geometry is to replace conventional Cartesian coordinates, which commute under multiplication, with matrices, which do not. Return to Text
5. Interview with Cumrun Vafa, January 12, 1998. Return to Text
6. Interview with Edward Witten, May 11, 1998. Return to Text
7. Quoted in Banesh Hoffman with Helen Dukas, Albert Einstein, Creator and Rebel (New York: Viking, 1972), p. 18. Return to Text
8. Martin J. Klein, "Einstein: The Life and Times, by R. W. Clark," (book review) Science 174, pp. 1315-16. Return to Text
9. Jacob Bronkowski, The Ascent of Man (Boston: Little, Brown, 1973), p. 20. Return to Text
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