Relativistic PBTE:Biological Proper Time Along the Worldline

Abstract

Biological aging is conventionally indexed by chronological time, yet every organism is a physical system tracing a worldline through spacetime, so the time available to its metabolism is not coordinate time $t$ but relativistic proper time $\tau$. Building on the established Principle of Biological Time Equivalence (PBTE), whose thermodynamic foundation and aging dynamics are taken here as prior results \citep{TayeBook2026,TayeAging2026,TayeCardiac2026}, we ask how internal physiological time relates to the proper time of physics. The central result is that biological age is an entropy-production functional evaluated along the proper-time worldline, \begin{equation*} A_{\rm PBTE}=\frac{1}{\Sigma_{\rm ref}}\int_{\tau_0}^{\tau_1}\dot\Sigma_p(\tau)\,d\tau, \qquad \frac{dA_{\rm PBTE}}{dt}=\frac{\dot\Sigma_p}{\gamma\,\Sigma_{\rm ref}}, \end{equation*} where $\dot\Sigma_p$ is entropy production per unit proper time in the local rest frame and $\gamma$ the Lorentz factor.