Loop Quantum Gravity - Key Concepts

Key Concepts

The general problem of quantum gravity is one of the major unsolved issues in fundamental physics. The standard quantization techniques that work for the Standard Model of particle physics do not work for gravity because they lead to a non-renormalizable quantum field theory, which is not predictive.

The deep origin of the problem is the fact that gravity is geometry. When the quantum properties of gravity are not disregarded, spacetime itself becomes a quantum object, and therefore the usual logic of conventional quantum field theory, which requires the existence of a well defined classical geometry, does not work anymore. This is the starting point of LQG. A quantum theory defined without assuming a classical spacetime is called background independent. LQG is essentially a technique for studying quantum field theory when there is no spacetime background. The quantum states of the theory, labelled by spin networks, should not be thought as living inside a physical space, but rather to define physical space themselves. This is the quantum version of the main property of Einstein's general relativity, where the solutions of the theory are not gravitational field living inside a spacetime, but are themselves defining spacetime.

The reformulation of general relativity introduced by Ashtekar, which goes under the name of Ashtekar variables represents the gravitational field using fields similar to the electric and magnetic fields. In the quantum version of the theory, the Faraday lines of these fields become the loops of LQG, and carry discrete quanta of geometry. A spin network can be seen as an ensemble of a finite number of (quantum) Faraday lines of gravity, which define a quantum space. These evolve in time in discrete steps.

Quantum matter is usually coupled to the quantum gravitational field as an independent field, in LQG. But there are also attempts to relate directly matter and geometry (by Renate Loll, Jan Ambjørn, Lee Smolin, Sundance Bilson-Thompson, Laurent Freidel, Mark B. Wise and others).

To date, the main successes of loop quantum gravity are:

1. It is a nonperturbative quantization of 3-space geometry, with quantized area and volume operators
2. It includes a calculation of the entropy of black holes
3. It replaces the Big Bang spacetime singularity with a Big Bounce

None of these results has so far received any direct empirical support. Therefore the theory must be considered only tentative for the moment, like all other tentative theories that go beyond the standard model, such as string theory or supersymmetry. The research community in fundamental theoretical physics is following different research directions, and this is of course a healthy situation. A lively critical and competitive attitude between groups following different research directions is also healthy, since science requires sharp critical thinking. Polemics between some partisans of the loop and string communities have been quite lively sometime ago.