Temporal Curvature and Its Dependence
Temporal Curvature and Its Dependence In the Temporal Physics model, the curvature of time, denoted as \( K(\tau) \), is a function of the derivatives of the temporal flow. The curvature describes how the shape of the temporal dimension changes and is influenced by the rate of change of time itself. Simple Relationship: \[ K(\tau) \approx \frac{\partial^2 \tau}{\partial t^2} \] Here, \( K(\tau) \) approximates the second derivative of the temporal flow, indicating how the acceleration of time impacts its curvature. Advanced Relation: \[ K(\tau) = f\left(\frac{\partial \tau}{\partial t}, \frac{\partial^2 \tau}{\partial t^2}\right) \] This function \( f \) captures the relationship between the first and second derivatives of temporal flow and its curvature, similar to how the Ricci scalar \( R \) measures curvature in General Relativity: \[ R(\tau) \sim \nabla^2 S(\tau) = \frac{\partial^2 S}{\partial t^2} \] Connecting Mass-Energy with Temporal Flows The stress-energy tensor \( T_{\mu \n...