Loop Quantum Gravity

Loop Quantum Gravity (LQG), rival of string theory in the quest to unite quantum mechanics with general relativity, does not suffer from certain mathematical "infinities" (corresponding to ephemeral, but numerous, alternatives in the way that interactions take place in spacetime), a new study shows. This clears up some doubts as to the theory's usefulness.

What is LQG, and why has it been so difficult to quantize gravity? To address this question, return to classical (pre-1900) physics, a regime in which space was fixed. Then the relativity and quantum revolutions changed everything utterly. With the advent of general relativity, space was combined with time in an integrated, but deformable, spacetime. Meanwhile, in quantum mechanics spacetime remains fixed but matter becomes fuzzy; the whereabouts of particles can only be expressed in terms of probability clouds. In a theory that would combine quantum and gravity features, spacetime would then have to be both deformable and fuzzy, and this has been difficult to do. In string theory, the merger is accomplished by imagining that matter ultimately consists of tiny strings. In loop theory, the merger is attempted by imagining that space itself consists of moveable tiny loops.

Carlo Rovelli (Center for Theoretical Physics, Marseilles, rovelli@cpt.univ-mrs.fr, 33-0491-269644; also University of Pittsburgh) argues that loop theory does not have to import the extra commodities (additional dimensions and particles) needed by string theory and that it offers, in principle, more testable predictions, such as the idea of quantized surface areas (that is, regions of space would come in discrete chunks and there would be a minimum possible size scale) and the notion that quantized spacetime might manifest itself as a minute difference in the speed of light for different colors. The new version of loop gravity studied by Rovelli and his colleagues pictures spacetime as being foamy: points in space sometimes grow into bubbles. The bubbles are not "in" space but constitute space itself. The infinities pondered in the present paper represent not difficulties posed by the reality of particles within particles (a necessary complexity dealt with in Richard Feynman's quantum electrodynamics theory) but rather, analogously, to those potentially corresponding to interactions occurring on spacetime loops within loops. (Crane et al., Physical Review Letters, 29 October 2001.)