Once Before Time - Martin Bojowald [45]
Ambition is closely connected with belief, and it is not always easy to say which comes first. The dominant ambition of string theory is unification, a decidedly monotheistic belief. All particles and forces moving and acting on a given space-time are reduced to vibrations and ruminations of a single object, the eponymous string. Since one of the forces is gravity and string theory is a quantum theory, this approach must ultimately lead to a quantum theory of the gravitational force. But the structure of space-time, though indirectly brought in contact with the quantum world, is left largely untouched. As far as space-time is concerned, string theory does not go much beyond general relativity. Only loop quantum gravity treats space-time and matter on an equal, though not completely unified, footing. Here, the concepts of quantum theory are directly applied to space and time, resulting in an atomic structure analogous to that of matter. Even space-time, the stage on which matter moves, is constructed within the theory of loop quantum gravity, while much of it is presupposed in string theory (figure 10). If string theory is monotheistic, loop quantum gravity is pantheistic. Everything—space, time, and matter—is a fluctuating discrete mesh whose internal relations are what we perceive as change.
The mathematical underpinning of each theory is equally challenging and sophisticated, yet strikingly different. Both are geometric, which is characteristic of modern physics. But string theory uses continuous versions of geometry, while loop quantum gravity is based on the discrete version it rapidly developed in its first years. Both make extensive use of quantum field theory, the universal language not only of particle physics but also of condensed matter physics, but different versions of them in accordance with their distinct viewpoints on space-time: quantum field theory on space-time in string theory, but quantum field theory of space-time in loop quantum gravity. Several exactly treatable models are known in both cases, theoretical highlights that always provide an elevated degree of mathematical access and sharpen concepts as well as expectations. But they all refer to different situations, and so do not provide easy comparisons of the approaches.
10. Many theories of quantum gravity describe properties of space-time by one-dimensional objects such as the strings of string theory or the loops of loop quantum gravity. But they differ considerably in their concepts as well as in the meaning of the one-dimensional objects. In string theory, strings provide excitations of matter or gravitational waves on a given space-time, as symbolized by the white rock on the right around which a thread is winding. Loop quantum gravity, by contrast, attempts to build up everything, including space-time itself, from one-dimensional loops (left)—a much more complex undertaking. (Sculpture by Gianni Caravaggio: Catturatore di volumi [Volume Catcher]), 2005. Photograph: Paolo Mussat Sartor.)
Most important is the difference in extra baggage between the theories, the institutionalization of beliefs and ambitions not directly serving the stated aim. Loop quantum gravity is applied directly to space-time as it is known in general relativity, just endowed with quantum laws. This combination has several