Physical Time: Geometry, Clocks, and the Limits of Temporal Reconstruction

Physics uses the word time for structures that are related but not identical: causal and chronological order, metric duration, coordinate parameters, clock readings, frequency ratios, dynamical parameters, relational quantum evolution, and temporal orientation. This paper asks which of these structures determine which others, and what additional information is required when they do not. The central method is target-by-target reconstruction. A temporal claim must specify the target being reconstructed, the physical substrate supplied as input, the auxiliary completion information, the residual equivalence class, and the empirical or mathematical validation status.

In Lorentzian spacetime, causal structure can determine substantial conformal information under appropriate distinguishing conditions, but positive conformal rescaling preserves causal cones while changing proper duration. Chronometric scale and temporal orientation are therefore separate residual problems. Orientation itself separates into global time-orientability, representation-covariant reversal structure, observable reversal information, and physical selection of one orientation.

Relational quantum clocks recover conditional evolution only relative to a specified clock/system decomposition, state, constraint or Hamiltonian structure, and conditioning rule; they do not derive every temporal observable from an empty temporal substrate. The resulting picture is neither a single universal clock nor unrestricted temporal pluralism. Physical temporal unity is architectural: order, duration, clocks, lawful evolution, and orientation are connected by explicit, domain-limited bridges whose assumptions and residual freedoms can be audited.