Quantum Machian Time in Toy Models of Gravity

Understand

General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints.

• These constraints can be thought of as a way of imposing temporal and spatial relationalism.
• The same type of constraints can be used in non-relativistic particle models to produce relational theories that suffer from the same Problem of Time as that encountered in General Relativity.
• As a result, these simple toy models are well suited for studying the Problem of Time in quantum gravity.