Loop Quantum Gravity: Fasciantion With Background Independance.

(Third post in the loop quantum gravity series.)

For centuries after Newton, physics was formulated where objects moved through space and time.  Space and time was something in which the dynamical quantities we measure, like protons and forces, move through. 

However, Einstein discovered that gravity isn't moving through space and time: gravity was space and time.  Gravity is just a manifestation of how space and time or spacetime is bent and curved by mass.  (See figure.)  General relativity is a theory of gravity that is background independent in that gravity is not moving in some separate spacetime.  It is the same thing.

This leads to a critique of string theory raised by many in the loop quantum gravity camp: String theorists are trying to combine general relativity and quantum mechanics by removing the idea that gravity doesn't propagate through spacetime but in fact is the spacetime.  (I'm sure real string theorists will debate this critique, but right now I am giving the LQG side of the argument.)

Requiring spacetime to be something that emerges from gravity through quantized loops, as opposed to gravity moving through space, has a few consequences:

1.  Excitations of the gravitation field give rise to the notion of length, are and volume ie.. spacetime. (Just like excitations of other quantum fields give rise to things like particles.)
2. Space and time is composed of little "quanta" that, in the literature I read, is described as really small grains of spacetime.
3. The loop quantization of gauge fields discussed in the last post in a continuous background gives rise to infinities that plague many quantum theories.  However, when spacetime is quantized into discrete packets, these infinities go away since these loops no longer are bunched together in a continuum. (The continuum gives rise to the infinity.)
4. (Repeating myself for emphasis.) What is space and time?: it emerges from the excitations of the gravitational field that is quantized trough loop operators.  These loop operators do not exist in space and time but give rise to the existence of spacetime.
5. Since these are loops quantizing the field, they give rise in a technical sense, to the notion of spin networks.  These spin networks have "world histories" described by what is called a spin foam. (See figure on the left.)

I'll leave of this post with another figure to the right that, assuming loop quantum gravity is correct, helps picture what is going on: Gravity is quantized through loop operators.  This quantum field of gravity does not move through or exist in spacetime.  Spacetime emerges as excitations of this gravitational field.