The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena

Understand

This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle.

• The Problem of Time is that `time' in GR and `time' in ordinary quantum theory are mutually incompatible notions, which is problematic in trying to put these two theories together to form a theory of Quantum Gravity.
• Four frontiers to this resolution in full GR are identified, alongside three further directions not yet conquered even for the relational triangle.
• This article is also the definitive review on relational particle models originally due to Barbour (2003: dynamics of pure shape) and Barbour and Bertotti (1982: dynamics of shape and scale).