Quantum Superposition as Dynamical Equilibrium and Energy-Dependent Collapse in Relative Cosmic Equilibrium Theory RCE

The Relative Cosmic Equilibrium (RCE) framework is a unified physical model that redefines all fundamental phenomena—mass, time, charge, forces, and spacetime— as emergent consequences of a single scalar energy deviation field ∆E(x, t) seek- ing equilibrium. In this paper, we extend the RCE framework to the foundations of quantum mechanics. Using a slow-envelope approximation, we show that the Schrödinger equation emerges naturally from the linear dynamics of ∆E near equi- librium, with Planck’s constant ℏ appearing as the minimal topological action unit, not an ad hoc input. Quantum superposition is reinterpreted as a multimodal dy- namical equilibrium, in which the field oscillates coherently between degenerate energy minima. Measurement is identified as the introduction of an external energy gradient that breaks this degeneracy, leading to exponential relaxation toward a single outcome. This mechanism yields a characteristic, calculable collapse time: τ ≈ ℏ ∆Emeas where ∆Emeas is the energy exchanged during measurement. In conventional measurements (∆E ∼ eV), this time is ∼ 10−16 s, well below detection. However, in weak measurements with extremely low exchanged energy (∆E ∼ neV), RCE predicts an observable collapse time of ≈ 0.66 μs (for ∆Emeas = 1 neV). We present an explicit comparison with standard quantum mechanics, which offers no defined collapse timescale, and propose a feasible table-top optical experiment to test this prediction. This renders RCE a falsifiable framework and transforms the quantum measurement problem from a philosophical issue into a testable physical question.