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 subjects of foundational debate. 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. Within this framework, we explore a new paradigm: the evolution of local physical systems is governed by irreversible processes within finite spacetime regions, consistent with the cosmic thermodynamic future. 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 appendixes also propose a different viewpoint on the issue of the breakdown of General Relativity at singularities. The goal of this paper is the deeper integration of thermodynamics, relativity, and cosmology, coupled with a clarification of the logical relationships between mass-energy equivalence, conservation, and the vanishing covariant divergence—thereby reconciling some classic unresolved puzzles within the existing framework, without proposing a complete new theory.