  A hyperlink is a finite set of non-intersecting simple closed curves in
$\mathbb{R}^4 \equiv \mathbb{R} \times \mathbb{R}^3$, each curve is either a
matter or geometric loop. We consider an equivalence class of such hyperlinks,
up to time-like isotopy, preserving time-ordering. Using an equivalence class
and after coloring each matter component loop with an irreducible
representation of $\mathfrak{su}(2) \times \mathfrak{su}(2)$, we can define its
Wilson Loop observable using an Einstein-Hilbert action, which is now thought
of as a functional acting on the set containing equivalence classes of
hyperlink. Construct a vector space using these functionals, which we now term
as quantum states. To make it into a Hilbert space, we need to define a
counting probability measure on the space containing equivalence classes of
hyperlinks. In our previous work, we defined area, volume and curvature
operators, corresponding to given geometric objects like surface and a compact
solid spatial region. These operators act on the quantum states and by
deliberate construction of the Hilbert space, are self-adjoint and possibly
unbounded operators. Using these operators and Einstein's field equations, we
can proceed to construct a quantized stress operator and also a Hamiltonian
constraint operator for the quantum system. We will also use the area operator
to derive the Bekenstein entropy of a black hole. In the concluding section, we
will explain how Loop Quantum Gravity predicts the existence of gravitons,
implies causality and locality in quantum gravity, and formulate the principle
of equivalence mathematically in its framework.
