# Quantum Cosmological Relational Model of Shape and Scale in 1-d - General Relativity and Quantum Cosmology

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Abstract: Relational particle models are useful toy models for quantum cosmology andthe problem of time in quantum general relativity. This paper shows how toextend existing work on concrete examples of relational particle models in 1-dto include a notion of scale. This is useful as regards forming a tight analogywith quantum cosmology and the emergent semiclassical time and hidden timeapproaches to the problem of time. This paper shows furthermore that thecorrespondence between relational particle models and classical and quantumcosmology can be strengthened using judicious choices of the mechanicalpotential. This gives relational particle mechanics models with analogues ofspatial curvature, cosmological constant, dust and radiation terms. A number ofthese models are then tractable at the quantum level. These models can be usedto study important issues 1 in canonical quantum gravity: the problem of time,the semiclassical approach to it and timeless approaches to it such as thenaive Schrodinger interpretation and records theory. 2 In quantum cosmology,such as in the investigation of uniform states, robustness, and the qualitativeunderstanding of the origin of structure formation.

Author: ** Edward Anderson**

Source: https://arxiv.org/