Spacetime Spectral Dynamics: Reformulation of Gravity as a Scalar Frequency Field Gradient

We propose Derivative Frequency Theory (DFT) as a unification framework modeling physical reality as a manifestation of a fundamental scalar frequency field ω(x,t). In this paper, we derive classical gravitational dynamics from first principles using a Lorentz-invariant Spectral Lagrangian. We introduce an explicit matter-frequency coupling mechanism, where inertial mass acts as a source for frequency field perturbations. We prove analytically that in the static weak-field limit, the gradient of this frequency field recovers Newton’s Law of Universal Gravitation, with the constant G emerging as a combination of vacuum spectral inertia parameters. Furthermore, the theory naturally predicts a Yukawa-type modification at galactic scales that naturally yields flat rotation curve tendencies without the dark matter hypothesis. This paper presents a rigorous mathematical formulation and an experimental falsification protocol using LC oscillators.

Keywords: Frequency Monism, Spectral Lagrangian, Emergent Gravity, Galaxy Rotation Curves, LC Oscillator.