Intrinsic Energy, Emergent Time, and a Covariant, Background-Independent Formulation for Quantum Mechanics

By positing energy as intrinsic and independent—with momentum, time, and spatial properties emerging as functions of boost energy (either directly or indirectly)—E-Theory achieves a fully covariant, background-independent formulation for quantum mechanics. This paper demonstrates that by anchoring special relativity in the invariant energy–momentum relationship and reinterpreting energy as an independent variable rather than a dependent property, we transform the traditional four-vector—typically expressed via complex differential relationships—into three simple algebraic functions for momentum, time, and space. We can then transform the standard Time-Dependent Schrödinger Equation (TDSE) into a covariant, background-independent version simply by scaling the time derivative by a universal factor derived from the boost energy.This shift from the time domain (time-dependent) to the energy domain (energy-dependent) has profound consequences: a covariant TDSE emerges; both relativistic and non-relativistic dispersion are recovered from the standard non-relativistic Hamiltonian; inverse relativistic effects appear at ultra-low energies; and a single wave equation governs quantum evolution across all energy scales and particle spins. Most importantly, we free quantum mechanics from its reliance on a fixed temporal background and place it on equal footing with general relativity, thus laying the foundation for their ultimate unification.