A Category Error in Relativistic Aging: On the Missing Constitutive Link between Proper Time and Biological Emergence

Title: A Category Error in Relativistic Aging: On the Missing Constitutive Link between Proper Time and Biological Emergence Abstract: The resolution of the twin paradox through the extremization of relativistic proper time is a rigorously established result for ideal clocks and elementary physical systems within special and general relativity. However, the widespread interpretation that relativistic time dilation entails proportional retardation of biological aging rests on an implicit extrapolation across descriptive levels that has never been formally justified. Relativity constrains the geometry of spacetime and the parameterization of local physical dynamics by proper time, but it does not define biological age as a physical observable. Biological aging is an emergent, non-equilibrium phenomenon arising from the irreversible evolution of high-dimensional, dissipative metabolic and regulatory networks that are history-dependent and non-ergodic. Such dynamics do not, in general, admit reduction to a unique scalar quantity integrable along spacetime worldlines. We formalize this distinction by defining biological aging as a path-dependent functional over trajectories in biological state space, rather than as a clock-like integral of the spacetime metric. Within this framework, proper time constrains local biochemical process rates but does not uniquely determine global biological state evolution. A minimal damage–repair toy model is introduced to demonstrate how generic non-linear network dynamics break scalar integrability even under uniform proper-time evolution. This analysis reveals a constitutive gap: no formal law currently exists that maps relativistic proper time to biological aging across scales. Consequently, statements asserting that relativistic motion necessarily entails reduced biological aging are not theorems of relativity, but modeling assumptions made in the absence of a constitutive mapping. By delineating the boundary between spacetime kinematics and biological organization, this work clarifies a long-standing interpretive ambiguity and establishes a principled framework for treating biological temporality as an emergent, system-dependent quantity constrained—but not defined—by spacetime structure.