A Universal Limit on Time Discrimination from Quantum Dynamics and Gravitation

We derive a universal bound on operational time discrimination from quantum dynamics
and general relativity. For perfect single-shot discrimination of time intervals of size ∆τ with
real-time decision making, the required quantum dynamical resources necessarily induce sig-
nificant gravitational backreaction when ∆τ approaches the Planck time tP = pℏG/c5. The
bound identifies the precise scale at which quantum measurement theory and classical gravita-
tion become mutually inconsistent, providing an operational interpretation of the Planck time
without assuming temporal discreteness.