Examining the Conservation of Angular Momentum in Quantum Mechanics, General Relativity, and Loop Quantum Gravity

While quantum mechanics and general relativity are both wildly successful theories describing quantum behavior and gravity, respectively, the two theories are incompatible due to conservation discrepancies, differences in background dependency, and the fact that general relativity does not support the existence of a gravitational gauge boson (graviton). Attempts to reconcile the two are widely referred to as quantum gravity theories. The loop quantum gravity theory introduces quantum-scale "loops" with intrinsic spin that accrete to form a spin foam, which produces macroscopic geometry and gravitational effects at the classical limit. A crucial test for the validity of a quantum gravity theory is whether or not it can preserve the conservation laws intrinsic to the quantum scale, which requires a time-independent expectation value of a quantity, and the classical scale, which requires a time-independent value of the quantity. This paper aims to examine the descriptions of the conservation of angular momentum between quantum mechanics and general relativity and to examine how loop quantum gravity reconciles the discreteness of quantum mechanics with the continuity of general relativity.