Echo Field Theory: A Dynamic Solution to the Galaxy Rotation Problem

The "missing mass" problem, inferred from anomalous galactic rotation curves, represents a significant challenge to modern astrophysics. The prevailing solution posits the existence of non-baryonic dark matter, a new form of matter yet to be directly detected. This paper introduces Echo Field Theory (EFT), an alternative framework that resolves the issue without invoking new particles. EFT proposes that the gravitational constant is not fundamental but is instead a manifestation of a dynamic scalar field that permeates spacetime. This "Echo Field" is disturbed by the presence of baryonic matter, altering the local strength of gravity. In high-density environments, EFT reproduces the well-tested results of General Relativity. However, on galactic scales, the theory predicts an amplification of the gravitational force that precisely accounts for the observed flat rotation curves. This paper details the EFT model, presents numerical results that validate its predictions against a range of galaxy types, and discusses its broader implications for cosmology.