A gauge-theoretic framework for the problem of time

We propose a novel canonical formulation of general relativity that promotes the local freedom in clock synchronization to a gauge symmetry, thereby establishing a consistent, physically meaningful definition of time. Unlike conventional coordinate time reparameterizations, which only relabel time without affecting physical clocks, the proposed gauge transformation alters the mapping from coordinate time to proper time, thereby affecting physical clock synchronization. To enforce local invariance, we introduce a compensating gauge field that renders the Arnowitt‐Deser‐Misner (ADM) lapse and shift gauge invariant. This yields a gauge-invariant time evolution vector and an intrinsic time variable in quantum gravity that provide a route toward deparameterizing the Hamiltonian constraint and restoring unitary evolution. In addition, the framework strongly constrains the cosmological constant sector, induces effective modifications of Maxwell-type dynamics, and produces concrete, testable predictions.