3.2 Loop Quantum Gravity

summary

General relativity and quantum theory together suggest that space itself is discrete.

General relativity says that space and time are aspects of a field that can be influenced by matter and transmit information and energy.
Quantum theory says that fields, like the electromagnetic field, are granular and not continuous.
Each of these theories functions extraordinarily well at describing the universe, general relativity at the macroscopic scale and quantum theory at the microscopic scale.
The implication of our two best theories of physics is that the spacetime field should also be discretized, just like all of the other fields. To truly synthesize quantum theory and general relativity, we need a quantum theory of gravity that describes the granular nature of the gravitational field.

Finding the quanta of spacetime

Quantum gravity is primarily relevant at extremely small scales. The scale at which the quantum structure of spacetime is expected to become apparent is about 10^-33cm (the Planck scale).
One potentially confusing aspect of the quanta of spacetime is that they are not immersed in spacetime, the way photons are – they constitute spacetime itself.
In the theory of loop quantum gravity (LQG), the quanta of spacetime “know” when they are next to one another. These interactions can be conceived of as interconnected loops, in which quanta of spacetime are all mutually connected to their neighboring quanta.

The granular structure of spacetime in LQG is called a spin network.

The term “spin” arises from the mathematics of quantum mechanics. In LCG, Spins are half-integer quantum numbers associated with the geometry of two interacting quanta of spacetime.
When two quanta of spacetime are adjacent to each other, there is an area between them along the surface of their interaction.
The size of these areas cannot take on any arbitrary value, which is true for any parameter in quantum theory. Rather, there is a discretized spectrum of possible geometries, and these geometries are the titular spin states.
Spin networks are also called spin foams because the three-dimensional structure resembles suds or foam.

The equations of loop quantum gravity do not include a time variable.

Spin networks function very similarly to the way Feynman diagrams do for quantum interactions of photons. However, Feynman diagrams take place within spacetime while spin foams represent the interactions of spacetime itself.
Just as there are equations associated with Feynman diagrams that can be used to calculate probabilities of future outcomes, so too there are equations associated with spin foams.
The equations of loop quantum gravity provide a way of computing how individual quanta of spacetime evolve.