  Our way of describing Nature is based on local relativistic quantum field
theories, and then CPT symmetry, a natural consequence of Lorentz invariance,
locality and hermiticity of the Hamiltonian, is one of the few if not the only
prediction that all of them share. Therefore, testing CPT invariance does not
test a particular model but the whole paradigm. Current and future long
baseline experiments will assess the status of CPT in the neutrino sector at an
unprecedented level and thus its distinction from similar experimental
signatures arising from non-standard interactions is imperative. Whether the
whole paradigm is at stake or just the standard model of neutrinos crucially
depends on that.
