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

Chapter 7: Notes
1. Albert Einstein, as quoted in R. Clark, Einstein: The Life and Times (New York: Avon Books, 1984), p. 287. Return to Text

2. More precisely, spin-1/2 means that the angular momentum of the electron from its spin is /2. Return to Text

3. The discovery and development of supersymmetry has a complicated history. In addition to those cited in the text, essential early contributions were made by R. Haag, M. Sohnius, J. T. Lopuszanski, Y. A. Gol'fand, E. P. Lichtman, J. L. Gervais, B. Sakita, V. P. Akulov, D. V. Volkov, and V. A. Soroka, among many others. Some of their work is documented in Rosanne Di Stefano, Notes on the Conceptual Development of Supersymmetry, Institute for Theoretical Physics, State University of New York at Stony Brook, preprint ITP-SB-8878. Return to Text

4. For the mathematically inclined reader we note that this extension involves augmenting the familiar Cartesian coordinates of spacetime with new quantum coordinates, say u and v, that are anticommuting: u X v = X u. Supersymmetry can then be thought of as translations in this quantum-mechanically augmented form of spacetime. Return to Text

5. For the reader interested in more details of this technical issue we note the following. In note 6 of Chapter 6 we mentioned that the standard model invokes a "mass-giving particle"—the Higgs boson—to endow the particles of Tables 1.1 and 1.2 with their observed masses. For this procedure to work, the Higgs particle itself cannot be too heavy; studies show that its mass should certainly be no greater than about 1,000 times the mass of a proton. But it turns out that quantum fluctuations tend to contribute substantially to the mass of the Higgs particle, potentially driving its mass all the way to the Planck scale. Theorists have found, however, that this outcome, which would uncover a major defect in the standard model, can be avoided if certain parameters in the standard model (most notably, the so-called bare mass of the Higgs particle) are finely tuned to better than 1 part in 10^15 to cancel the effects of these quantum fluctuations on the Higgs particle's mass. Return to Text

6. One subtle point to note about Figure 7.1 is that the strength of the weak force is shown to be between that of the strong and electromagnetic forces, whereas we have previously said that it is weaker than both. The reason for this lies in Table 1.2, in which we see that the messenger particles of the weak force are quite massive, whereas those of the strong and electromagnetic forces are massless. Intrinsically, the strength of the weak force (as measured by its coupling constant—an idea we will come upon in Chapter 12) is as shown in Figure 7.1, but its massive messenger particles are sluggish conveyers of its influence and diminish its effects. In Chapter 14 we will see how the gravitational force fits into Figure 7.1. Return to Text

7. Edward Witten, lecture at the Heinz Pagels Memorial Lecture Series, Aspen, Colorado, 1997. Return to Text

8. For an in-depth discussion of these and related ideas, see Steven Weinberg, Dreams of a Final Theory.Return to Text
Table of Contents
.......The Elegant Universe