Once Before Time - Martin Bojowald [47]
In 1990, Carlo Rovelli and Lee Smolin conceived the idea of loops of gravity, giving the name to the field of loop quantum gravity.1 The concept of loops itself was not entirely new; for a long time, it had successfully been used in quantum theories of forces such as the electromagnetic one. In those theories, loops arise not as fundamental concepts but rather as useful ways of approximation. Instead of considering a quantity, such as the magnetic field, at all points in space, one would take into account only its cumulative effect over the whole extension of a curve.2 As when approximating a complex curve by several short straight lines, the mathematical description can simplify the picture considerably, and be more amenable to computer-aided solutions.
The idea of loops was not new, but in the hands of Rovelli and Smolin it became truly revolutionary. When used for gravity, loops are not approximations but provide a complete description; they become fundamental. The key for this realization is general covariance, the basic concept behind general relativity, which holds that there is no absolute position in space, but only relations between different objects matter. Changing the positions of loops has no effect when they describe gravity, while it would change the state if they are used to describe other forces. What matters is only the relationships between different loops, such as the way they may be knotted or interlinked. A complex but elegant picture arises in which space is woven from one-dimensional objects mathematically described by Rovelli and Smolin’s loops.
After this realization, Rovelli and Smolin quickly derived further consequences. The area and volume of spatial regions cannot be stretched to arbitrary values, as in traditional geometry, but only assigned those in certain discrete sets. The allowed values for areas or volumes form grids, or spectra, in the set of all numbers, and only values at the nodes of the grid can be realized. In this way, the atomic nature of space is established mathematically: Regions can grow only by adding spatial atoms of specific predetermined sizes. Adding up the different atomic volumes leads to the lattice sets computed by Rovelli and Smolin. A region growing dynamically, such as part of an expanding universe, is subject to specific laws determining how the atomic interactions take place. Rovelli and Smolin also formulated an early version of these rules for changing atoms of space, which was exceedingly complicated but seemed workable.
When they started to look at possible realizations of these rules by solving the underlying mathematical equations, enthusiasm rose. While not many specific solutions for space-times in general relativity are known, Rovelli and Smolin were quickly able to find infinitely many solutions to the atomic rules they had laid down. That would indeed be exciting; it might suggest that the quantum theory of space and time, despite all expectations, could be simpler than the classical analog. Alas, this was one of the misguided yet crucial excitements that often characterize an emerging field. All the solutions they found, it turned out, described spaces of vanishing volume (but nonzero areas), none of which could possibly describe anything in the real world.
Nonetheless, with these initial strokes, Rovelli and Smolin considerably extended the previous frontiers of quantum gravity. They were driven mainly by intuition