The Information-Theoretic Spacetime Manifold: Gravity and Inertia as Emergent Topological Phenomena

This paper presents a fundamental reformulation of physical spacetime. To resolve the methodological contradiction between the continuous metric of general relativity and the discrete, probabilistic nature of quantum mechanics, spacetime is not treated as an a priori background continuum. Instead, a discrete, information-theoretic state topology (the "Register Model") is postulated. In this paradigm, the absolute information content and its degree of topological correlation (entanglement) are the fundamental entities of physical reality. It is deductively shown that phenomena such as the gravitational constant, cosmological expansion, Bekenstein-Hawking entropy, and the decoherence limit are mandatory thermodynamic consequences of this information architecture. Furthermore, as a macroscopic consequence of this model, a formal violation of the weak equivalence principle for macroscopic quantum states is derived. The paper concludes by proposing a precise, differential matter-wave interferometry experiment on Bose-Einstein condensates to empirically verify the predicted inertia anomaly and falsify the classical nature of inertia.