A Local Resolution of the Problem of Time. I. Introduction and Temporal Relationalism

This Series of Articles provides a local resolution of this major longstanding foundational problem between QM and GR, or, more generally, between Background Dependent and Background Independent Physics. We focus on the classical version; the concepts we use are moreover universal enough to admit quantum counterparts. This requires a series of articles to lay out because the Problem of Time is multi-faceted and is largely about interferences between facets, with traditional solutions to individual facets breaking down in attempted joint resolutions of facets. [98] already covered this at both the classical and semiclassical quantum levels. This Series serves, firstly, to isolate this resolution from [98]'s introductory and field-wide comparative material, passing from an 84-part work down to just a 14-part one. Secondly, to clarify that, at the usual differential-geometric level of structure used in physical theories, our classical local resolution is entirely catered for by Lie's mathematics. This renders our local classical part of the Problem of Time understandable by a very large proportion of Theoretical Physics or Mathematics majors. In this first article, we cover a first aspect: Temporal Relationalism. This generalizes the facet traditionally known as the Frozen Formalism Problem, that follows from the quantum form of GR's Hamiltonian constraint.