2015/05/10 by Edward Anderson, Anderson, Edward
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1505.02448
openalex publication_date 2015/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers passing from the usual ℝd model of absolute space to \mathbbSd at the level of relational particle models. Both approaches' d = 1 cases are rather simpler than their d ≥ 2 cases, with N particles in \mathbbS1 admitting a straightforward reduction with shape space \mathbbTN - 1. The \mathbbS2 and \mathbbS3 cases - observed skies and the simplest closed GR cosmologies respectively -- are also considered, the latter in the contexts of both static and dynamical radius of the model universe. The space of relational triangles on \mathbbS2 is hyperbolic 3-space ℍ3. Overall, by passing to a closed underlying absolute space, and then to dynamical notion of space, we close some of the modelling gaps between relational particle models and geometrodynamics or its inhomogeneous perturbative regime of interest in cosmology. Quantum counterparts are also outlined, for use as model arenas of quantum cosmology. These models are useful in further considerations of both classical and quantum background independence.