## sabato 21 gennaio 2012

### "MT" vs "LQG". Beyond the last gravity frontier

The "Loop Quantum Gravity" (LQG), designed by Carlo Rovelli and Lee Smolin in 1990, based on the concept of "spin networks", designed in the early '70s by Roger Penrose, is one of the most fascinating and elegant theories of gravity.

In physics a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation often simplifies calculation because simple diagrams may be used to represent complicated functions. Roger Penrose is credited with the invention of spin networks in 1971, although similar diagrammatic techniques existed before that time.
Spin networks have been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin and others.

A spin network, as described by Penrose in 1971, is a kind of diagram in which each line segment represents the world line of a "unit" (either an elementary particle or a compound system of particles). Three line segments join at each vertex. A vertex may be interpreted as an event in which either a single unit splits into two or two units collide and join into a single unit. Diagrams whose line segments are all joined at vertices are called closed spin networks. Time may be viewed as going in one direction, such as from the bottom to the top of the diagram, but for closed spin networks the direction of time is irrelevant to calculations.
Each line segment is labeled with an integer called a spin number. A unit with spin number n is called an n-unit and has angular momentum nh/2л. For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd.
In loop quantum gravity (LQG), a spin network represents a "quantum state" of the gravitational field on a 3-dimensional hypersurface.
The loop quantum gravity is also known by terms of gravity loop quantum geometry and quantum canonical general relativity. It has been proposed as a quantum theory of spacetime which attempts to unify seemingly incompatible theories of quantum mechanics and general relativity. This theory is part of a family of theories called canonical quantum gravity. It is a quantum theory of gravity in which the real space in which happen all the other physical phenomena is quantized.
The LQG retains the basic aspects of general relativity, such as invariance to coordinate transformations, and at the same time, using the quantization of space and time at the Planck scale, feature of quantum mechanics. In this sense it combines general relativity and quantum mechanics. Critics of the LQG often refer to the fact that the theory doesen't predict the existence of extra dimensions of space-time, or supersymmetry. The response of the LQG proponents is that at present, despite repeated experimental researches, there is no experimental evidence or other dimensions or supersymmetric particles, so the additional dimensions of space and time, both supersymmetry must be considered speculative hypotheses found to run faster than they do on Earth.

Abstract from “on LQG” by Carlo Rovelli.