Quantum Inertial Field Hypothesis (QIFH): A Scalar-Field Interpretation of Gravitational Attraction

This work presents the Quantum Inertial Field Hypothesis (QIFH), a field-based hypothesis proposing a scalar-field interpretation of gravitational attraction. The central formulation represents gravitational attraction through the chain ρₘ → P → −∇P, where ρₘ is the matter source density, P is a scalar potential field, and −∇P defines the corresponding gravitational acceleration. The scalar field is governed by a Poisson-type equation, −∇²P = 4πGρₘ. In the current executable formulation, the matter source is associated with an underlying nonlinear field u through ρₘ ∝ |u|², giving the coupled relation −∇²P = 4πG|u|². The underlying field evolves according to a nonlinear dissipative equation incorporating diffusion, nonlinear potential dynamics, a frozen reference spectral projection, nonlocal coupling to the scalar field, and external forcing. The formulation therefore provides an explicit mathematical connection between the underlying field configuration and an effective gravitational interaction. The work also develops the spherically symmetric realization of the scalar-field construction and shows how the corresponding field equation yields an inverse-square form for localized sources under the appropriate conditions. A numerical realization is described using finite-dimensional discretization and independent dynamical and stationary-residual diagnostics for assessing executable equilibrium. QIFH is presented as a theoretical hypothesis and executable mathematical framework rather than as a completed physical theory. The present work does not establish a complete quantum field theory, a replacement for general relativity, continuum existence or uniqueness, universal attraction, or observational and astrophysical validity. Dimensional calibration, numerical robustness, continuum analysis, derivation of measurable observables, and quantitative comparison with gravitational observations remain separate areas for further investigation. This repository contains the present formulation of QIFH and its mathematical and executable framework for further analysis, numerical investigation, and independent validation.