To some “loop quantum gravity is an attempt to define a quantization of gravity paying special attention to the conceptual lessons of general relativity”, while to others it does not have to be about the quantization of gravity but should be “at least conceivable that such a theory marries a classical understanding of gravity with a quantum understanding of matter”
The term ‘loop’ comes from the solution written for every line closed on itself on the proposed structure of quanta’s interactions. John Archibald Wheeler was one of the pioneers in constructing a representation of space which had a granular structure on a very small scale. Together with Bryce DeWitt they produced a mathematical formula known as Wheeler-DeWitt equation, “an equation which should determine the probability of one or another curved space”. The starting point was spacetime of general relativity having “loop-like states”. Having a quantum approach to gravity on closed loops, which are threads of the Faraday lines of the quantum field, constitutes a gravitational field which looks like a spiderweb. A solution could be written for every line closed on itself. Moreover, every line determining a solution of the Wheeler-DeWitt equation describes one of the threads of the spiderweb created by Faraday force lines of the quantum field which are the threads with which the space is woven. The physical Hilbert space as the space of all quantum states of the theory solves all the constraints and thus ought to be considered as the physical states. This implies that the physical Hilbert space of Loop Quantum Gravity is not yet known. The larger space of states which satisfy the first two families of constraints is often termed the kinematical Hilbert space. The one constraint that has so far resisted resolution is the Hamiltonian constraint equation with the seemingly simple form Hˆ|ψ⟩ = 0, the Wheeler-DeWitt equation, where Hˆ is the Hamiltonian operator usually interpreted to generate the dynamical evolution and |ψ⟩ is a quantum state in the kinematical Hilbert space. Of course, the Hamiltonian operator Hˆ is a complicated function(al) of the basic operators corresponding to the basic canonical variables. In fact, the very functional form of Hˆ is debated as several inequivalent candidates are on the table. Insofar as the physical Hilbert space has thus not yet been constructed, Loop Quantum Gravity remains incomplete.
Space, then, is defined based on the nodes on this spiderweb, which is called a spin network, and time, which already lost its fundamental status with special and general relativity, vanishes from the picture of the universe altogether.
Loop quantum gravity combines the dynamic spacetime approach of general relativity with quanta nature of gravity fields. Accordingly, space that bends and stretches are made up of very small particles which are called quanta of space. If one had eyes capable zooming into the space and seeing magnetic fields and quanta, then, by observing the space, one would first witness the quantum field, and then would end up seeing quanta which are extremely small and granular.