  Dynamics, the physical change in time and a pillar of natural sciences, can
be regarded as an emergent phenomenon when the system of interest is part of a
larger, static one. This "relational approach to time", in which the system's
environment provides a temporal reference, does not only provide insight into
foundational issues of physics, but holds the potential for a deeper
theoretical understanding as it intimately links statics and dynamics.
Reinforcing the significance of this connection, we demonstrate, based on
recent progress [Phys. Rev. Lett. 131, 140202 (2023)], the role of emergent
time as a vital link between time-independent and time-dependent perturbation
theory in quantum mechanics. We calculate first order contributions, which are
often the most significant, and discuss the issue of degenerate spectra. Based
on our results, we envision future applications for the calculation of
dynamical phenomena based on a single pure energy eigenstate.
