On the Applicability Boundaries of Mass-Energy Conservation and the Concept of Locality in General Relativity—Toward a Thermodynamic Extension of General Relativity

The law of mass-energy conservation and General Relativity are fundamental laws of modern physics. However, their precise interpretation and domain of applicability, particularly within the dynamic spacetime of General Relativity, remain foundationally debated. This paper argues that the current understanding of this issue is hindered by a vague concept: the "locality" upon which the vanishing covariant divergence of the energy-momentum tensor relies. Through a critical analysis of this concept, we reveal a fundamental tension between the breaking of time-translation symmetry on cosmological scales and the idealized local inertial frames of Special Relativity. To resolve this tension, we propose a program for thermodynamically extending General Relativity, where the thermodynamic arrow of time is integrated at a foundational level. This framework explores a new paradigm in which local physical systems evolve via irreversible processes within finite spacetime regions. This not only provides a thermodynamic perspective beyond purely geometric explanations for phenomena like the Twin Paradox and Length Contraction but also naturally leads to a resolution of the Fermi Paradox based on the laws of physics themselves, rather than sociological factors. The appendices also propose a different viewpoint on the issue of the breakdown of General Relativity at singularities. By analyzing the tensions inherent in existing theories, rigorously examining their formulations of fundamental concepts, and identifying overlooked or conflated premise, this paper conceptually extends and integrates current theories to construct a conceptual framework enabling a smooth, continuous transition from macroscopic to microscopic scales—without proposing an entirely new theory.