Gravitation in the Fractal D = 2 Inertial Universe: New Phenomenology in Spiral Discs and a Theoretical Basis for MOND

Abstract

A particular interpretation of Mach's Principle led us to consider if it was possible to have a globally inertial universe that was irreducibly associated with a non-trivial global matter distribution, Roscoe [2002a]. This question received a positive answer, subject to the condition that the global matter distribution is necessarily fractal, D = 2. The purpose of the present paper is to show how general gravitational processes arise in this universe. We begin by showing how classical Newtonian gravitational processes arise from point-source perturbations of this D = 2 inertial background. We are then able to use the insights gained from this initial analysis to arrive at a general theory for arbitrary material distributions. We illustrate the process by using it to model an idealized spiral galaxy. One particular subclass of solutions, corresponding to logarithmic spirals, has already been extensively tested (Roscoe [1999a(Roscoe [ ], [2002b), and shown to resolve dynamical data over large samples of optical rotation curves (ORCs) with a very high degree of statistical precision.Whilst the primary purpose of the data analysis of Roscoe [1999a] was to test the predictions of the logarithmic spiral theory, it led directly to the discovery of a major new phenomenology in spiral discs -that of discrete dynamical classes -initially reported in Roscoe [1999b] and comprehensively confirmed in Roscoe [2002b] over four large independent samples of ORCs. In this paper, we analyse the theory more comprehensively, and show how the discrete dynamical classes phenomenology has a ready explanation in terms of an algebraic consistency condition which must necessarily be satisfied.Of equal significance, we apply the theory with complete success to the detailed modelling of a sample of eight Low Surface Brightness spirals (LSBs) which, hitherto, have been succesfully modelled only by the MOND algorithm (Modified Newtonian Dynamics, Milgrom [1983a], [1983b], [1983c). The CDM models have failed comprehensively when applied to LSBs. We are able to conclude that the essence of the MOND algorithm must be contained within the presented theory.