Mass = Planck Frequency Towards Quantum Gravity and a Unified Field Theory with a New Scalar-Soliton Paradigm Bülent Kuşçu ORCID: 0009-0000-4160-1927 Independent Researcher, Ankara, Turkey E-mail: bulentkuscu@gmail.com September 2, 2025 Abstract This article presents a novel theoretical framework that defines the universe’s fundamental building blocks as a complex scalar field Ψ oscil- lating at the Planck scale. The “Mass = Planck Frequency” paradigm posits that mass and energy are directly derived from the nonlinear os- cillation modes of spacetime. The core framework relies on nonlinear Klein-Gordon-Maxwell equations with local U (1) gauge symmetry. The model holds the potential to simultaneously explain particle formation through scalar soliton solutions, charge and spin quantization via topo- logical winding numbers, and gravitation through Einstein field equations. Numerical simulations conducted on a 256³ grid using Planck units have confirmed the mass-frequency linearity with 0.2 1 Introduction The incompatibility between quantum mechanics and general relativity neces- sitates the search for a unified theory. String theory, loop quantum grav- ity, and network approaches are mathematically rich but challenging to test experimentally [1–3]. This study argues that fundamental particles are sta- ble soliton modes of spacetime at the Planck scale ( l p ≈ 1.616 × 10 −35 m, t p ≈ 5.391 × 10 −44 s ). Mass m is directly proportional to the angular fre- quency ω of these modes: m = ¯ hω c 2 . Thus, the concept of “mass” is reduced to a geometric frequency identity at the Planck scale. 1