The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [212]
For the mathematically inclined reader, the more precise statement of Maldacena’s result is the following. Let N be the number of three-branes in the brane stack, and let g be the value of the coupling constant in the Type IIB string theory. When gN is a small number, much less than one, the physics is well described by low-energy strings moving on the brane stack. In turn, such strings are well described by a particular four-dimensional supersymmetric conformally invariant quantum field theory. But when gN is a large number, this field theory is strongly coupled, making its analytical treatment difficult. However, in this regime, Maldacena’s result is that we can use the description of strings moving on the near horizon geometry of the brane stack, which is AdS5 × S5 (anti-de Sitter five-space times the five sphere). The radius of these spaces is controlled by gN (specifically, the radius is proportional to (gN)¼), and thus for large gN, the curvature of AdS5 × S5 is small, ensuring that string theory calculations are tractable (in particular, they are well approximated by calculations in a particular modification of Einsteinian gravity). Therefore, as the value of gN varies from small to large values, the physics morphs from being described by four-dimensional supersymmetric conformally invariant quantum field theory to being described by ten-dimensional string theory on AdS5 × S5. This is the so-called AdS/CFT (anti-de Sitter space/conformal field theory) correspondence.
16. Although a full proof of Maldacena’s argument remains beyond reach, in recent years the link between the bulk and boundary descriptions has become increasingly well understood. For example, a class of calculations has been identified whose results are accurate for any value of the coupling constant. The results can therefore be explicitly tracked from small to large values. This provides a window onto the “morphing” process by which a description of physics from the bulk perspective transforms into a description in the boundary perspective, and vice versa. Such calculations have shown, for instance, how chains of interacting particles from the boundary perspective can transform into strings in the bulk perspective—a particularly convincing interpolation between the two descriptions.
17. More precisely, this is a variation on Maldacena’s result, modified so that the quantum field theory on the boundary is not the one that originally arose in his investigations, but instead closely approximates quantum chromodynamics. This variation also entails parallel modifications to the bulk theory. Specifically, following the work of Witten, the high temperature of the boundary theory translates into a black hole in the interior description. In turn, the dictionary between the two descriptions shows that the difficult viscosity calculations of the quark-gluon plasma translate into the response of the black hole’s event horizon to particular deformations—a technical but tractable calculation.
18. Another approach to providing a full definition of string theory emerged from earlier work in an area called Matrix theory (another possible meaning of the “M” in M-theory), developed by Tom Banks, Willy Fischler, Steve Shenker, and Leonard Susskind.
Chapter 10: Universes, Computers, and Mathematical Reality
1. The number I quoted, 1055 grams, accounts for the contents of the observable universe today, but at ever-earlier times, the temperature of these constituents would be larger and so they would contain higher energy. The number 1065 grams is a better estimate of what you’d need to gather into a tiny speck to recapitulate the evolution of our universe from when it was roughly one second old.
2. You might think that because your speed is constrained to be less than the speed of light, your kinetic energy will also be limited. But that’s not the case. As your speed gets ever closer to that of light, your energy grows ever larger; according to special relativity, it has