# Lie Theory suffices for Local Classical Resolution of Problem of Time. 1. Closure, as implemented by Lie brackets and Lie’s Algorithm, is Central.

Abstract

The Problem of Time is due to conceptual gaps between General Relativity and the other observationally-confirmed theories of Physics. It is a fundamental issue in Quantum Gravity. A key point in resolving the Problem of Time turns out to be that Algebra rapidly takes centre stage. The first algebraic aspect encountered is that constraints must close, as must spacetime generators. This Closure aspect is assessed by the generalized Lie Algorithm. Dirac’s Algorithm is the constrained canonical perspective’s subcase of this. Such algorithms have the capacity to shut down trial sets of generators for being inconsistent. Thus they constitute a type of selection principle. Those sets of generators which survive form Lie algebras or Lie algebroids. Examples include the Lie algebra of spacetime diffeomorphisms and the Dirac algebroid of constraints in GR. Around 3/4 of Problem of Time aspects revolve around brackets algebraic structures. Observables and Constructability join Closure in this regard, while Relationalism is distinct. Moreover, Closure’s centrality has been under-represented in the literature to date. The current series justifies this centrality both algebraically and graph-theoretically. We furthermore proceed to compensate for previous literature’s under-representation of this point.