Relativity and the Quantum / Elementary Tour part 4: Loop quantum gravity

From the point of view of Einstein´s theory, it comes as no surprise that all attempts to treat gravity simply like one more quantum force (on par with electromagnetism and the nuclear forces) have failed. According to Einstein, gravity is not a force – it is a property of spacetime itself. Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein´s geometrical formulation.

This approach is hard to explain in detail without resorting to the language of mathematics. Part of the problem is a still-unanswered question: Although this approach leads to a quantum formulation for gravity, researchers are still busy trying to work out how a universe like ours – which obeys the classical (i.e. non-quantum) general theory of relativity – can arise from such a quantum foundation.

One aspect of the loop models, though, is easy to grasp. Space, in general relativity, is a continuum. In every part of it, one can define regions of arbitrarily small volume, and every little region can be divided further into yet smaller regions, ad infinitum. In the loop models, the basic structure of spacetime turns out to be discrete. In such discrete spacetimes, there are smallest values for volumes and areas that are not divisible any farther – just as one cannot build a structure smaller than the smallest block in a Lego set. The fabric of space is called a spin network with lines and nodes, as pictured here:

spin network sketch

spin network sketch

Nodes can carry numerical values; depending on the number, they stand for volume building blocks of different size. The smallest possible volume is that of a region containing only a single node with the lowest possible value. As you add further nodes and/or make the values associated with existing nodes larger, the volume grows.

Thus, space acquires a grainy, discrete structure – and so does time. In simplified models used for cosmological explorations, it turns out that within loop quantum gravity, there is no big bang singularity; instead, the universe´s history can be traced infinitely far into the past, step by step.