The Elegant Universe - Brian Greene [214]
3. Edwin Abbott, Flatland (Princeton: Princeton University Press, 1991).
4. A. Einstein in letter to T. Kaluza as quoted in Abraham Pais, "Subtle is the Lord": The Science and the Life of Albert Einstein (Oxford: Oxford University Press, 1982), p. 330.
5. A. Einstein in letter to T. Kaluza as quoted in D. Freedman and P. van Nieuwenhuizen, "The Hidden Dimensions of Spacetime," Scientific American 252 (1985), 62.
6. Ibid.
7. Physicists found that the most difficult feature of the standard model to incorporate through a higher-dimensional formulation is something known as chirality. So as not to overburden the discussion we have not covered this concept in the main text, but for readers who are interested we do so briefly here. Imagine that someone shows you a film of some particular scientific experiment and confronts you with the unusual challenge of determining whether the film shot the experiment directly or whether it shot the experiment by looking at its reflection in a mirror. As the cinematographer was quite expert, there are no telltale signs of a mirror being involved. Is this a challenge you can meet? In the mid-1950s, the theoretical insights of T. D. Lee and C. N. Yang, and the experimental results of C. S. Wu and collaborators, showed that you can meet the challenge, so long as an appropriate experiment had been filmed. Namely, their work established that the laws of the universe are not perfectly mirror symmetric in the sense that the mirror-reflected version of certain processes—those directly dependent on the weak force—cannot happen in our world, even though the original process can. And so, as you watch the film if you see one of these forbidden processes occur, you will know that you are watching a mirror-reflected image of the experiment, as opposed to the experiment itself. Since mirrors interchange left and right, the work of Lee, Yang, and Wu established that the universe is not perfectly left-right symmetric—in the language of the field, the universe is chiral. It is this feature of the standard model (the weak force, in particular) that physicists found nearly impossible to incorporate into a higher-dimensional supergravity framework. To avoid confusion, we note that in Chapter 10 we will discuss a concept in string theory known as "mirror symmetry," but the use of the word "mirror" in that context is completely different from its use here.
8. For the mathematically inclined reader, we note that a Calabi-Yau manifold is a complex Kähler manifold with vanishing first Chern class. In 1957 Calabi conjectured that every such manifold admits a Ricci-flat metric, and in 1977 Yau proved this to be true.
9. This illustration is courtesy of Andrew Hanson of Indiana University, and was made using the Mathematica 3-D graphing package.
10. For the mathematically inclined reader we note that this particular Calabi-Yau space is a real three-dimensional slice through the quintic hypersurface in complex projective four-space.
Chapter 9
1. Edward Witten, "Reflections on the Fate of Spacetime" Physics Today, April 1996, p. 24.
2. Interview with Edward Witten, May 11, 1998.
3. Sheldon Glashow and Paul Ginsparg, "Desperately Seeking Superstrings?" Physics Today, May 1986, p. 7.
4. Sheldon Glashow, in The Superworld I, ed. A. Zichichi (New York: Plenum, 1990), p. 250.
5. Sheldon Glashow, Interactions (New York: Warner Books, 1988), p. 335.
6. Richard Feynman, in Superstrings: A Theory of Everything? ed. Paul Davies and Julian Brown (Cambridge, Eng: Cambridge University Press, 1988).
7. Howard Georgi, in The New Physics, ed. Paul Davies (Cambridge: Cambridge University Press 1989), p. 446.
8. Interview with Edward Witten, March 4, 1998.
9. Interview with Cumrun Vafa, January 12, 1998.
10. Murray Gell-Mann, as quoted in Robert P. Crease and Charles C. Mann, The Second Creation (New Brunswick,