English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this article, we consider a second Problem of Time Facet. This startedlife as Wheeler's Thin Sandwich Problem, within the narrow context of 1)GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangianvariables level treatment. Conceiving in terms of Barbour's Best Matching is afreeing from 1), now in the context of first-class linear constraints.Conceiving in terms of the underlying Background Independence aspect - thetitular Configurational Relationalism - serves moreover to remove 2) as well.This is implemented by the $G$-act, $G$-all method. I.e. given an object $O$that is not $G$-invariant, we act on it with $G$ and then apply an operationinvolving the whole group. This has the effect of double-cancelling theintroduction of our group action, thus yielding a $G$-independent version of$O$. A first example of whole-group operation is group averaging. This is avaluable prototype by its familiarity to a large proportion of Mathematics andPhysics majors through featuring in elementary Group Theory and RepresentationTheory courses (and which can be traced back to Cauchy). In particular, this ismuch more familiar than Thin Sandwiches or Best Matching! Secondly,extremization over the group, of which Best Matching, and taking infs or supsover the group, are examples. Some further significant examples of this methodin modern geometry and topology include those of Kendall, Younes, Hausdorff andGromov. In this way, we populate this approach with examples well beyond theusual GR literature's by DeWitt, Barbour and Fischer (which we also outline).

A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group Averaging