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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 9: Notes
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1. Edward Witten, "Reflections on the Fate of Spacetime" Physics Today, April 1996, p. 24. Return to Text
2. Interview with Edward Witten, May 11, 1998. Return to Text
3. Sheldon Glashow and Paul Ginsparg, "Desperately Seeking Superstrings?" Physics Today, May 1986, p. 7. Return to Text
4. Sheldon Glashow, in The Superworld I, ed. A. Zichichi (New York: Plenum, 1990), p. 250. Return to Text
5. Sheldon Glashow, Interactions (New York: Warner Books, 1988), p. 335. Return to Text
6. Richard Feynman, in Superstrings: A Theory of Everything? ed. Paul Davies and Julian Brown (Cambridge, Eng: Cambridge University Press, 1988). Return to Text
7. Howard Georgi, in The New Physics, ed. Paul Davies (Cambridge: Cambridge University Press 1989), p. 446. Return to Text
8. Interview with Edward Witten, March 4, 1998. Return to Text
9. Interview with Cumrun Vafa, January 12, 1998. Return to Text
10. Murray Gell-Mann, as quoted in Robert P. Crease and Charles C. Mann, The Second Creation (New Brunswick, N.J.: Rutgers University Press), 1996, p. 414. Return to Text
11. Interview with Sheldon Glashow, December 28, 1997. Return to Text
12. Interview with Sheldon Glashow, December 28, 1997. Return to Text
13. Interview with Howard Georgi, December 28, 1997. During the interview, Georgi also noted that the experimental refutation of the prediction of proton decay that emerged from his and Glashow's first proposed grand unified theory (see Chapter 7) played a significant part in his reluctance to embrace superstring theory. He noted poignantly that his grand unified theory invoked a vastly higher energy realm than any theory previously considered, and when its prediction was proved wrong—when it resulted in his "being slapped down by nature"—his attitude toward studying extremely high energy physics abruptly changed. When I asked him whether experimental confirmation of his grand unified theory might have inspired him to lead the charge to the Planck scale, he responded, "Yes, it likely would have." Return to Text
14. David Gross, "Superstrings and Unification," in Proceedings of the XXIV International Conference on High Energy Physics, ed. R. Kotthaus and J. Kuhn (Berlin: Springer-Verlag, 1988), p. 329. Return to Text
15. Having said this, it's worth bearing in mind the long-shot possibility, pointed out in endnote 8 of Chapter 6, that strings just might be significantly longer than originally thought and therefore might be subject to direct experimental observation by accelerators within a few decades. Return to Text
16. For the mathematically inclined reader we note that the more precise mathematical statement is that the number of families is half the absolute value of the Euler number of the Calabi-Yau space. The Euler number itself is the alternating sum of the dimensions of the manifold's homology groups—the latter being what we loosely refer to as multidimensional holes. So, three families emerge from Calabi-Yau spaces whose Euler number is ±6. Return to Text
17. Interview with John Schwarz, December 23, 1997. Return to Text
18. For the mathematically inclined reader we note that we are referring to Calabi-Yau manifolds with a finite, nontrivial fundamental group, the order of which, in certain cases, determines the fractional charge denominators. Return to Text
19. Interview with Edward Witten, March 4, 1998. Return to Text
20. For the expert we note that some of these processes violate lepton number conservation as well as charge-parity-time (CPT) reversal symmetry. Return to Text or
or 2. Interview with Edward Witten, May 11, 1998. Return to Text
3. Sheldon Glashow and Paul Ginsparg, "Desperately Seeking Superstrings?" Physics Today, May 1986, p. 7. Return to Text
4. Sheldon Glashow, in The Superworld I, ed. A. Zichichi (New York: Plenum, 1990), p. 250. Return to Text
5. Sheldon Glashow, Interactions (New York: Warner Books, 1988), p. 335. Return to Text
6. Richard Feynman, in Superstrings: A Theory of Everything? ed. Paul Davies and Julian Brown (Cambridge, Eng: Cambridge University Press, 1988). Return to Text
7. Howard Georgi, in The New Physics, ed. Paul Davies (Cambridge: Cambridge University Press 1989), p. 446. Return to Text
8. Interview with Edward Witten, March 4, 1998. Return to Text
9. Interview with Cumrun Vafa, January 12, 1998. Return to Text
10. Murray Gell-Mann, as quoted in Robert P. Crease and Charles C. Mann, The Second Creation (New Brunswick, N.J.: Rutgers University Press), 1996, p. 414. Return to Text
11. Interview with Sheldon Glashow, December 28, 1997. Return to Text
12. Interview with Sheldon Glashow, December 28, 1997. Return to Text
13. Interview with Howard Georgi, December 28, 1997. During the interview, Georgi also noted that the experimental refutation of the prediction of proton decay that emerged from his and Glashow's first proposed grand unified theory (see Chapter 7) played a significant part in his reluctance to embrace superstring theory. He noted poignantly that his grand unified theory invoked a vastly higher energy realm than any theory previously considered, and when its prediction was proved wrong—when it resulted in his "being slapped down by nature"—his attitude toward studying extremely high energy physics abruptly changed. When I asked him whether experimental confirmation of his grand unified theory might have inspired him to lead the charge to the Planck scale, he responded, "Yes, it likely would have." Return to Text
14. David Gross, "Superstrings and Unification," in Proceedings of the XXIV International Conference on High Energy Physics, ed. R. Kotthaus and J. Kuhn (Berlin: Springer-Verlag, 1988), p. 329. Return to Text
15. Having said this, it's worth bearing in mind the long-shot possibility, pointed out in endnote 8 of Chapter 6, that strings just might be significantly longer than originally thought and therefore might be subject to direct experimental observation by accelerators within a few decades. Return to Text
16. For the mathematically inclined reader we note that the more precise mathematical statement is that the number of families is half the absolute value of the Euler number of the Calabi-Yau space. The Euler number itself is the alternating sum of the dimensions of the manifold's homology groups—the latter being what we loosely refer to as multidimensional holes. So, three families emerge from Calabi-Yau spaces whose Euler number is ±6. Return to Text
17. Interview with John Schwarz, December 23, 1997. Return to Text
18. For the mathematically inclined reader we note that we are referring to Calabi-Yau manifolds with a finite, nontrivial fundamental group, the order of which, in certain cases, determines the fractional charge denominators. Return to Text
19. Interview with Edward Witten, March 4, 1998. Return to Text
20. For the expert we note that some of these processes violate lepton number conservation as well as charge-parity-time (CPT) reversal symmetry. Return to Text
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