Non-inertial quantum clock frames lead to non-Hermitian dynamics

Abstract The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion proper time. In standard quantum mechanics, however, an external parameter. Recently, many attempts have been made extend mechanics within relational framework. Here, we use similar ideas combined with mass-energy equivalence study accelerating massive particle internal clock system. We show that ensuing evolution from perspective particle’s non-Hermitian. This result does not rely on specific implementations clock. As particular consequence, prove effective Hamiltonian two gravitationally interacting particles non-Hermitian either particle.