The Elegant Universe - Brian Greene [212]
8. Based upon insights gleaned from the second superstring revolution (discussed in Chapter 12), Witten and, most notably, Joe Lykken of the Fermi National Accelerator Laboratory have identified a subtle, yet possible, loophole in this conclusion. Lykken, exploiting this realization, has suggested that it might be possible for strings to be under far less tension, and therefore be substantially larger in size, than originally thought. So large, in fact, that they might be observable by the next generation of particle accelerators. If this long-shot possibility turns out to be the case, there is the exciting prospect that many of the remarkable implications of string theory discussed in this and the following chapters will be verifiable experimentally within the next decade. But even in the more "conventional" scenario espoused by string theorists, in which strings are typically on the order of 10-33 centimeters in length, there are indirect ways to search for them experimentally, as we will discuss in Chapter 9.
9. The expert reader will recognize that the photon produced in a collision between an electron and a positron is a virtual photon and therefore must shortly relinquish its energy by dissociating into a particle-antiparticle pair.
10. Of course, a camera works by collecting photons that bounce off the object of interest and recording them on a piece of photographic film. Our use of a camera in this example is symbolic, since we are not imagining bouncing photons off of the colliding strings. Rather, we simply want to record in Figure 6.7(c) the whole history of the interaction. Having said that, we should point out one further subtle point that the discussion in the text glosses over. We learned in Chapter 4 that we can formulate quantum mechanics using Feynman's sum-over-paths method, in which we analyze the motion of objects by combining contributions from all possible trajectories that lead from some chosen starting point to some chosen destination (with each trajectory contributing with a statistical weight determined by Feynman). In Figures 6.6 and 6.7 we show one of the infinite number of possible trajectories followed by point particles (Figure 6.6) or by strings (Figure 6.7) taking them from their initial positions to their final destinations. The discussion in this section, however, applies equally well to any of the other possible trajectories and therefore applies to the whole quantum-mechanical process itself. (Feynman's formulation of point-particle quantum mechanics in the sum-over-paths framework was generalized to string theory through the work of Stanley Mandelstam of the University of California at Berkeley and by the Russian physicist Alexander Polyakov, who is now on the faculty of the physics department of Princeton University.)
Chapter 7
1. Albert Einstein, as quoted in R. Clark, Einstein: The Life and Times (New York: Avon Books, 1984), p. 287.
2. More precisely, spin-1/2 means that the angular momentum of the electron from its spin is /2.
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.
4. For the mathematically