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.

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This rests the previous preprint – on Packing Theory applied to Social Distancing – on solid Graph Theory foundations that describe its topological-level structure. Further theoretical description of its metric and real-plane-embedded flat-geometric levels of structure are left for another occasion.

packing-1

April-v3

Diff-Geom-Intro-to-Ruled-Surfaces

Diff-Geom-Gauss-Bonnet-Overview

Diff-Geom-and-PoD-Intro-to-2nd-Variation-of-Arc

Diff-Geom-Types of Laplacian

Diff-Geom-Gauss-Codazzi-Ricci

Diff-Geom-Bel-Split-ito-Reps

Intro-To-Topological-Manifolds

Second-Course-in-Fibre-Bundles-Lecture-1

Differential-Geometry-Orbifold-Charts