Quantum Spacetime, Noncommutative Geometry and Quantum Observers

Since the dynamical variable of general relativity is spacetime itself, it is natural to think that a quantization of gravity requires a quantization of spacetime, possibly described by a noncommutative geometry. Such a quantum spacetime requires quantum symmetries, and a quantization of observers/references frames. I will introduce the necessity for a quantum spacetime, and describe some instances for which symmetries and observers are likewise quantized.