An Approach to Unification Using a Linear Systems Model for the Propagation of Broad-Band Signals

Abstract

We review the inhomogeneous scalar Helmholtz equation in three-dimensions and the scattering of scalar wavefields from a scatterer of compact support. An asymptotic solution is then considered representing the effect of the frequency approaching zero when a ‘wavefield’ reduces to a ‘field’. The characteristics of ultra-low frequency Helmholtz scattering are then considered and the physical significance discussed of a model that is based on the scattering of Helmholtz wavefields over a broad frequency spectrum. This is equivalent to using a linear systems approach for modelling the propagation, interaction and detection of broad-band signals and provides an approach to the classification of a field from a wavefield that is intrinsically causal and thus, consistent with the basic principle of information theory. The approach leads to the proposal that all fields are derived from wavefields interacting over a broad frequency spectrum and that there are two principal field types: (i) fields generated by low frequency scattering a ‘gravitational field’; (ii) fields generated by high frequency eigenfield tendency an ‘electric field’.