The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena

This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle. The Problem of Time is that `time' in GR and `time' in ordinary quantum theory are mutually incompatible notions, which is problematic in trying to put these two theories together to form a theory of Quantum Gravity. Four frontiers to this resolution in full GR are identified, alongside three further directions not yet conquered even for the relational triangle. This article is also the definitive review on relational particle models originally due to Barbour (2003: dynamics of pure shape) and Barbour and Bertotti (1982: dynamics of shape and scale). These are exhibited as useful toy models of background independence, which I argue to be the `other half' of GR to relativistic gravitation, as well as the originator of the Problem of Time itself. Barbour's work and my localized extension of it are shown to be the classical precursor of the background independence that then manifests itself at the quantum level as the full-blown Problem of Time. In fact 7/8ths of the Isham--Kuchar Problem of Time facets are already present in classical GR; even classical mechanics in relational particle mechanics formulation exhibits 5/8ths of these! In addition to Isham, Kuchar and Barbour, the other principal authors whose works are drawn upon in building this Problem of Time approach are Kendall (relational models only: pure-shape configuration spaces), Dirac, Teitelboim and Halliwell (Problem of Time resolving components). The recommended scheme is a combination of the Machian semiclassical approach, histories theory and records theory.Comment: This v3 is a v substantial upgrade: previous v's did not yet announce a local solution, we're up by 77 pages (to 386) & by 35 figs (to 93). It is now a quartet of Theses, the Problem of Time one of v1 splitting into cl and qm parts. I Cl RPM's. II Cl Problem of Time. III QM RPM's. IV QM Problem of Time. Contains over 100 interesting & foundational suggestions for future project

Dynamical Regularization in Scalefree-trees of Coupled 2D Chaotic Maps

Abstract. The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the dynamics ’ time-evolution at the coupling strength of the stability threshold and examine the properties of the regularization process. The time-scales involved in the appearance of the regular state and the periodic state are determined. We find unexpected regularity in the the system’s final steady state: all the period values turn out to be integer multiples of one among given numbers. Moreover, the period value distribution follows a power-law with a slope of-2.24. Key words: complex networks, coupled maps systems, emergent behaviour, self-organization in complex systems