Once Before Time - Martin Bojowald [51]
Later, though, around 2002, Hanno Sahlmann, at that time still a student of Thiemann’s at the Max Planck Institute for Gravitational Physics in Potsdam, Germany, realized that the quantum rules of loop gravity, like those of string theory, could also be proven unique in a mathematically rigorous way. Formulating this proof in all its details took longer, but the proof was eventually published in 2005 by Sahlmann, together with Jerzy Lewandowski, Andrzej Okolow, and Thiemann, as well as independently by Christian Fleischhack. (In jest, Ashtekar called the proof the LOST result, from the authors’ initials but also to indicate the apparent loss during the long years before its publication.)
Much earlier, Rovelli and Smolin had gone ahead to determine the first exciting consequences of their bold discovery. As mentioned, they were quickly led to conclude that Wilson loops represent, in an utterly and unapologetically abstract way, the creation and changing dynamics of atoms of space. Loops lead naturally to a discrete picture of spatial geometry, as generally expected from theories of quantum gravity: Spatial distances, areas, and volumes are generated when the loops build up some kind of lattice structure not only supporting but literally making space. The area of a surface is determined by the loops that intersect with it, as illustrated in figure 11. The volume of space depends on mutual intersections of loops. Loops are like atoms of space, endowing space with geometry such as length, area, and volume. This picture is entirely different from that usually referred to in general relativity: The fabric of space is not made of rubber, but woven from threads. (Applied to space-time, such a fine-structured picture was introduced by John Wheeler even before loop quantum gravity was devised, and dubbed “space-time foam.”)
One can view the space of loop quantum gravity as some kind of woven structure, but this is a visualization of mathematical objects and not a direct, tangible image: Where there is no loop, there is nothing. Loops must build space in which light could propagate to show us the spatial structure. A single loop could not be seen even with the mightiest microscope, since no signal could travel through the emptiness surrounding it. At most, indirect hints based on what happens on larger scales are conceivable, as we will see in the next chapter.
A large space such as the current universe must contain numerous loops, given that each one of them contributes just a tiny value to the volume. Loops also can intersect or partially overlap, and even those not doing so are typically knotted to an abstruse fabric as in figure 12. Seen from afar, this weave can indeed appear like a continuous space, as assumed in general relativity.
To see how these discrete spaces appear in an actual dynamic process of change, not adding or removing loops by hand but having them interact to produce new ones or possibly self-destruct, one needs to use the atomic evolution equations. Such equations and their solutions must, first of all, explain why the individualistic attitude of space, broken into tiniest chunks, gives rise to the familiar smooth classical rubber-band structure on the larger scales we have so far probed by observations. How does this wide, pervasive fabric we have come to call space-time “emerge” from the local tête-à-tête interplay of elementary quanta? With the work by Rovelli, Smolin, Ashtekar, and their collaborators at hand, loop quantum gravity was in an excellent position to address such questions.
11. A loop generates area when it intersects a surface (left). For several overlapping loops, the induced area is increased proportionally (right).
12. View of a sample fabric determining the quantum geometrical excitations of space-time by its links. The denser it is, the more continuous space appears to be. The gray scale indicates excitation levels of loops.
Deriving laws for the temporal change of a quantum gravitational universe was not supposed to have taken that long. The electromagnetic force