Gravitational Chronometry: Thermodynamic Emergence of Gravity via Information-Mass Equivalence in Incomplete Systems

Abstract: The unification of Quantum Mechanics and General Relativity remains one of the most persistent challenges in modern physics. This paper proposes a novel framework in which gravity is not a fundamental interaction, but an emergent, macroscopic phenomenon resulting from the thermodynamics of information processing. We postulate that biological observers, defined as thermodynamically open and formally incomplete systems, are compelled to actively reduce quantum entropy to maintain structural integrity. This process of "invariance formation" constitutes a symmetry breaking of the local wave function. By applying Landauer’s Principle and the recently proposed Mass-Energy-Information Equivalence principle, we demonstrate that this irreversible erasure of information generates an effective mass-energy term. Consequently, the spacetime curvature described by General Relativity is interpreted as the thermodynamic "friction" of cognitive processing against the quantum vacuum. The model predicts a specific, observer-dependent deviation in local time dilation—designated as the "Müller-Shift"—which exceeds the predictions of the standard metric. We propose an experimental verification using high-precision optical lattice clocks to detect this information-metric coupling. If confirmed, this framework suggests that gravity is the physical manifestation of the observer's struggle against entropy, fundamentally linking the arrow of time to biological imperative.