Two Explanatory Functions of Time in Physical Theories: A Functional Analysis from Classical Mechanics to Relativity and Quantum Theory

Physics uses temporal concepts to formulate evolution, order events, and compare processes, but “time” does not perform one function across theories. This article identifies two recurrent explanatory functions in classical mechanics, relativity, and quantum theory. The representational and ordering function parametrizes states, events, and histories; the process-based and timekeeping function ties temporal quantities to specified paths, changes, clocks, events, or protocols. These are context-dependent roles, not two substances or fixed classes of quantities: proper time, for instance, describes a worldline’s duration and can also parametrize its evolution. Four diagnostic indicators reconstruct a quantity’s predominant role. Case studies show how the functions overlap without making their mathematically distinct realizations equivalent. The distinction clarifies why clocks mediate between processes and representational scales, why the absence of a universal time operator does not exclude measurable temporal quantities, and why time–energy relations do not express a single uncertainty of “time.” It also constrains inference: a conclusion established for one temporal role cannot be transferred to the other without independent argument. Claims about the elimination, fundamentality, or emergence of time must therefore identify the function and theoretical level at issue. The framework reveals continuity in the architecture of temporal explanation while preserving the differences among physical theories.