  Exact conservation of the angular momentum is worked out for an elastic
medium with spins. The intrinsic anharmonicity of the elastic theory is shown
to be crucial for conserving the total momentum. As a result, any spin-lattice
dynamics inevitably involves multiphonon processes and interaction between
phonons. This makes transitions between spin states in a solid fundamentally
different from transitions between atomic states in vacuum governed by linear
electrodynamics. Consequences for using solid-state spins as qubits are
discussed.
