Quantum Loop Gravity

Basic idea

Background-independent quantum gravity built from spin networks (graphs labeled by SU(2) representations). Space is not continuous; areas and volumes come in discrete Planck-scale chunks.

Key formulas

• Wheeler-DeWitt equation: $\hat H \Psi = 0$
• Ashtekar variables: connection $A^i_a$ and densitised triad $E^a_i$
• Area spectrum: $A = 8\pi\gamma\ell_P^2 \sum_i \sqrt{j_i(j_i+1)}$
• Planck length: $\ell_P \approx 1.616 \times 10^{-35}$ m