• qubits clock
• quantum time dilation
• time-dilated Schrödinger equation
• quantum mechanics
• problem of time
• Page and Wootters (PaW) mechanism

Given a bipartite stationary Universe system, the dynamical laws for one component can be derived via entanglement using the other as a clock. This is the essence of the Page and Wootters mechanism. Applying this approach to address the problem of time reveals new aspects of dynamical evolution which cannot be derived from quantum mechanics alone: if the clock is subject to a gravitational-like interaction, the dynamics is described by a quantum time-dilated Schrödinger equation.
Its main feature is the emergence of a redshift operator, which describes a purely quantum effect analogue to gravitational time dilation. This result is discussed in the case of two spin-spin interacting qubits and the case of Newtonian gravity. Under some assumptions, the quantum time dilation effect can be translated into an effective interaction term affecting previously non-interacting subsystems of the Universe. We call this a Time-Dilation-induced Interaction Transfer (TiDIT) mechanism.