No Dynamical Time Implies Contradiction

We prove that a broad class of physical theories cannot simultaneously satisfy general covariance, local energy–momentum conservation, operational time measurement, quantum unitarity, and globally well-posed causal evolution if time is treated as a non-dynamical external parameter. The contradiction arises because unitary evolution and well-posed dynamics require a physically meaningful temporal ordering, while general covariance forbids elevating a coordinate parameter to physical status. We formalize this tension as a no-go theorem and show that the only consistent resolution is the introduction of a dynamical time degree of freedom, either as a fundamental field or an equivalent relational structure. This result provides a structural foundation for theories in which time is treated as a physical, dynamical entity.