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Time-evolution of an observer means how it changes over time; it's derivative over time. In quantum mechanics, it is described by the Hamiltonian. I.e.

$$H|\psi\rangle=i\hbar\frac{\partial|\psi\rangle}{\partial t}$$

This is also related to noether's theoremp, which proves that time-invariance is equivalent to energy-conservation.

DO NOT use this tag for evolving laws of physics.

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