The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [193]
3. The discovery of superstring theory spawned other, closely related, theoretical approaches seeking a unified theory of nature’s forces. In particular, supersymmetric quantum field theory, and its gravitational extension supergravity, have been vigorously pursued since the mid-1970s. Supersymmetric quantum field theory and supergravity are based on the new principle of supersymmetry, which was discovered within superstring theory, but these approaches incorporate supersymmetry in conventional point-particle theories. We will briefly discuss supersymmetry later in the chapter, but for the mathematically inclined reader, I’ll note here that supersymmetry is the last available symmetry (beyond rotational symmetry, translational symmetry, Lorentz symmetry, and, more generally, Poincaré symmetry) of a nontrivial theory of elementary particles. It relates particles of different quantum mechanical spin, establishing a deep mathematical kinship between particles that communicate forces and the particles making up matter. Supergravity is an extension of supersymmetry that includes the gravitational force. In the early days of string theory research, scientists realized that the frameworks of supersymmetry and supergravity emerged from a low-energy analysis of string theory. At low energies, the extended nature of a string generally cannot be discerned, so it appears to be a point particle. Correspondingly, as we will discuss in this chapter, when applied to low energy processes, the mathematics of string theory transforms into that of quantum field theory. Scientists found that because both supersymmetry and gravity survive the transformation, low energy string theory gives rise to supersymmetric quantum field theory and to supergravity. In more recent times, as we will discuss in Chapter 9, the link between supersymmetric field theory and string theory has grown yet more profound.
4. The informed reader may take exception to my statement that every field is associated to a particle. So, more precisely, the small fluctuations of a field about a local minimum of its potential are generally interpretable as particle excitations. That’s all we need for the discussion at hand. Additionally, the informed reader will note that localizing a particle at a point is itself an idealization, because it would take—from the uncertainty principle—infinite momentum and energy to do so. Again, the essence is that in quantum field theory there is, in principle, no limit to how finally localized a particle can be.
5. Historically speaking, a mathematical technique known as renormalization was developed to grapple with the quantitative implications of severe, small-scale (high-energy) quantum field jitters. When applied to the quantum field theories of the three nongravitational forces, renormalization cured the infinite quantities that had emerged in various calculations, allowing physicists to generate fantastically accurate predictions. However, when renormalization was brought to bear on the quantum jitters of the gravitational field, it proved ineffective: the method failed to cure infinities that arose in performing quantum calculations involving gravity.
From a more modern vantage point, these infinities are now viewed rather differently. Physicists have come to realize that en route to an ever-deeper understanding of nature’s laws, a sensible attitude to take is that any given proposal is provisional, and—if relevant at all—is likely capable of describing physics only down to some particular length scale (or only up to some particular energy scale). Beyond that are phenomena that lie outside the reach of the given proposal. Adopting this perspective, it would be foolhardy to extend the theory to distances smaller