Euler Equations System: A Unified Energy–Phase Framework for Gravitation, Electromagnetism, and Quantum Theory

We propose a minimal unified description of gravitation, electromagnetism and quantum theory based on a single complex amplitude Φ characterized by an energy modulus R and a phase angle θ. Starting from Euler’s trigonometric identity as a purely mathematical mother structure, we interpret all relevant physical quantities as orthogonal projections of the same energy modulus in a complex phase plane. In this framework, the gravitational sector (GR), the electromagnetic sector (Maxwell theory), classical and relativistic dynamics (Newton and SR), and quantum states (wave functions in QM, Dirac and Schrödinger theory) are recovered as different choices of projection axes and different limits of the same underlying object Φ. Inertia and acceleration arise from the time response of the energy modulus and phase; electric and magnetic fields become complementary phase components of a single electromagnetic energy; quantum dynamics becomes phase dynamics in space and time. The apparent “fundamental” splits between GR and EM, classical and quantum, particle and field are thus reinterpreted as coordinate choices rather than ontological differences. At a special critical phase, where real and imaginary components of Φ are balanced, the symmetry of the construction is mathematically isomorphic to the critical line of the Riemann zeta function, hinting at a possible common structure behind physical interaction symmetries and deep number-theoretic properties.