2011/11/06 by Edward Anderson, Anderson, Edward · 26 citations
Physics and Astronomy · #Quantum Mechanics and Applications #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1111.1472
This article contains a local solution to the notorious Problem of Time in\nQuantum Gravity at the conceptual level and which is actually realizable for\nthe relational triangle. The Problem of Time is that `time' in GR and `time' in\nordinary quantum theory are mutually incompatible notions, which is problematic\nin trying to put these two theories together to form a theory of Quantum\nGravity. Four frontiers to this resolution in full GR are identified, alongside\nthree further directions not yet conquered even for the relational triangle.\n This article is also the definitive review on relational particle models\noriginally due to Barbour (2003: dynamics of pure shape) and Barbour and\nBertotti (1982: dynamics of shape and scale). These are exhibited as useful toy\nmodels of background independence, which I argue to be the `other half' of GR\nto relativistic gravitation, as well as the originator of the Problem of Time\nitself. Barbour's work and my localized extension of it are shown to be the\nclassical precursor of the background independence that then manifests itself\nat the quantum level as the full-blown Problem of Time. In fact 7/8ths of the\nIsham--Kuchar Problem of Time facets are already present in classical GR; even\nclassical mechanics in relational particle mechanics formulation exhibits\n5/8ths of these! In addition to Isham, Kuchar and Barbour, the other principal\nauthors whose works are drawn upon in building this Problem of Time approach\nare Kendall (relational models only: pure-shape configuration spaces), Dirac,\nTeitelboim and Halliwell (Problem of Time resolving components). The\nrecommended scheme is a combination of the Machian semiclassical approach,\nhistories theory and records theory.\n