  Given a bipartite quantum system in an energy eigenstate, the dynamical
description for one component can be derived via entanglement using the other
component as a clock. This is the essence of the Page and Wootters mechanism.
Moreover, if the clock is subject to a gravitational-like interaction, relative
time evolution is then described by a Time-Dilated Schr\"odinger equation, in
which the so-called Redshift Operator describes a purely quantum effect,
analogue to gravitational time-dilation. Here we adopt a non-perturbative
approach and present a finite-dimensional generalisation of this mechanism,
expressing the quantum time-dilation effect as an effective interaction
involving previously non-interacting system components. We name this a
Time-Dilation induced Interaction Transfer (TiDIT) mechanism and discuss an
example using two coupled spins as a quantum clock model. Our approach is
suitable for implementations in current quantum technology and provides a new
tool for exploring gravity at the intersection with quantum physics.
