Quadrupole Framework for Gravitational Wave Radiation from Binary Inspiral in Two-Dimensional Wave Field Theory and the Dimensional Projection Problem

Within the framework of the two-dimensional linear matrix wavefield theory, this paper systematically derives the physical mechanism and mathematical form of gravitational wave radiation generated during the inspiral of binary star systems. This paper first specifies three fundamental axioms of the two-dimensional wavefield theory: the origin of the universe is a two-dimensional wavefield; matter corresponds to standing waves, while light and gravitational waves are traveling waves; observer effects arise because observers themselves consist of standing waves. On this basis, gravitational waves are defined as concentration traveling waves of the two-dimensional wavefield medium, rather than metric perturbations of spacetime as described by general relativity. Two massive standing waves orbit each other within the wavefield, forming a periodically varying rotating quadrupole source over time, which radiates outward wavefield concentration perturbations in the form of traveling waves. Starting from the general structure of quadrupole radiation in classical wave theory, this paper progressively derives a universal expression for radiation power, demonstrating that it is isomorphic to the Peters–Matthews formula of general relativity in mathematical structure, differing only in numerical coefficients and propagation dimensionality. This paper further indicates that electromagnetic waves, as traveling waves in the wavefield, inevitably perturb the wavefield medium during propagation, and such perturbations constitute gravitational waves. Accordingly, gravitational wave detection can be regarded as direct evidence for the existence of the wavefield medium. This paper also introduces quantitative parameters within the new aether framework, incorporating frequency-dependent attenuation, quality factors and viscosity coefficients into the analysis of gravitational wave propagation. It is shown that the wavefield medium is highly transparent to gravitational waves, allowing gravitational waves to propagate over cosmological distances with nearly no loss. This paper clarifies that the precise projection mapping from physical quantities in the two-dimensional wavefield to the strain amplitude h in the three-dimensional observational space has not yet been completed in the current theory. Hence, theoretical coefficients cannot be uniquely determined from a single gravitational wave event before the dimensional projection relation is established. The contribution of this work lies in constructing a complete theoretical framework for wave-source radiation and explicitly identifying the key challenges to be addressed in follow-up theoretical research.