The Problem of Not-Time: Structural Absence and Temporal Surrogacy in Canonical Physics

The canonical Problem of Time is usually understood as arising from incompatibilities between the roles attributed to time in quantum mechanics, general relativity, and canonical approaches to quantum gravity. This paper proposes a different diagnosis. It develops a framework-relative characterization of primitive magnitudes in physical theories, identifying two structural conditions observed in established practice: irreducibility to inequivalent quantities within a framework and non-replaceability by structurally distinct magnitudes without altering a theory’s dynamical or symmetry structure. The analysis then examines the quantities designated as temporal across the canonical formulations of the Problem of Time. In non-relativistic quantum mechanics, the temporal parameter functions as an external ordering variable; in general relativity, temporal intervals are derivable from the spacetime metric; and in canonical quantum gravity, temporal roles are reconstructed from non-temporal dynamical variables and are structurally replaceable among inequivalent candidates. These quantities therefore fail to satisfy the structural profile characteristic of primitive magnitudes. The instability grouped under the Problem of Time is accordingly reinterpreted as arising not from the incompatibility or disappearance of primitive temporal magnitudes, but from attempts to reconcile theoretical frameworks that employ temporal surrogates without instantiating time as a primitive magnitude.