Neutrino98 said:
Can anyone here explain to me how does quantum loop gravity works?
It works first of all by focusing attention on geometric MEASUREMENT.
You know that the Einstein 1915 theory of gravity is actually a theory of
geometry. How geometry evolves and interacts with matter. How a concentration of matter will cause geometry to curve around it. So gravity = geometry.
Any modern theory of gravity must be a theory of geometry.
What is geometry? It's about
measuring things like areas, volumes, angles. And about relations among these measurements, which can change depending on when and what order you measure them. And about predictions concerning future measurements. On a cosmic scale geometry can be about the pattern of expanding distances people call "expanding universe" and all the stuff that goes along with that.
So Loop Gravity works first of all by setting up NETWORKS where each node corresponds to a volume measurement something might make, and the connections between nodes are labeled to indicate the AREA where those chunks of volume might touch. Another word for network is graph: something made up of a bunch of points (nodes) interconnected by lines (links). In this case it's a network of possible measurements and the nodes and links are labeled with volume and area numbers.
A network could have millions of nodes but to picture one of the simplest examples it might just be a square: four nodes at the corners, connected by 4 links which are the sides of the square.
So a network is an idealized STATE of the world's geometry representing the results of a bunch of interrelated measurements which some thing or somebody could be imagined making. (If matter measurements like particle detections are included, that means more labels on the network.)
Then, as a theory of dynamically evolving geometry, LOOP HAS TO SAY HOW THESE NETWORKS, these states of geometry, EVOLVE.
In a quantum theory the PROBABILITY of going from state A to state B is given by a complex number called an AMPLITUDE. So Loop has to say what the amplitude is of going from network state A to network state B.
At the current stage of development of the theory, the tool used to arrive at amplitudes is a kind of path leading from one network to the other. the path looks like a FOAM. To take a simple example, suppose both A and B are
squares as described earlier. A path between the two squares could be pictured as a CUBE with A on the bottom or "start" and B on the top or "finish". A hollow cube is all you need to make continuous connection between the two squares. It can even be open on the top and bottom. Such a cube might be one part of a much more elaborate foam.
Loop has a rule for calculating amplitudes from foams. Given a foam that runs from network A (say at the bottom) to network B (say at the top) there is a way to calculate the amplitude of that foam---the probability amplitude of that path of evolution being taken from A to B.
That's the theory. That's how it works.
It gives results like replacing the BigBang "singularity" (where the old theory broke down) by a bounce. The present theory applied to cosmology predicts that a collapsing universe will rebound and undergo a brief very rapid phase of re-expansion. It let's us extrapolate backwards in time to before the start of our own universe's expansion and suggests things to look for as traces of the bounce (as a way of testing.)
