Temporal Reparameterization via Differentiation Frequency

The divergence between quantum mechanics and general relativity is traditionally attributed to incompatible treatments of time. In this paper, we argue that this discrepancy arises from a deeper structural tension between the parameterization of temporal evolution and the geometric formulation of relativistic time. We introduce $\tau(x)$, a local differentiation frequency, defined as a local scalar derived from the metric, \tau(x) = \frac{E}{\hbar} \sqrt{g_{00}(x)}, it represents the rate at which quantum systems sustain coherent distinctions. Unlike coordinate time or external parameters, $\tau(x)$ reflects the internal rhythm by which a system transitions across distinguishable states. Reformulating quantum evolution in terms of $\tau(x)$ enables structural reconciliation with relativistic time dilation and yields testable physical effects, without invoking a full theory of quantum gravity. We discuss the philosophical implications of treating time as a derivative of differentiation, integrating perspectives from relational time and process ontology, and suggest that $\tau(x)$ offers a new perspective on temporality as an emergent structure grounded in epistemic contrast.