  The Page-Wootters mechanism questioned the fundamental nature of time in
quantum physics. The mechanism explored the notion that a given physical
quantity is always defined and measured relative to a reference frame, in
general, not explained in the theoretical description of quantum physical
experiments. Recently, the resource theory of asymmetry deals explicitly with
what are the physical conditions for a quantum system to serve as a good
reference frame. Nonetheless, to quantify a quantum reference frame in relation
to another one it is a important task to establish an internal description of
quantum theory, i.e., without the need of a classical reference frame. In this
work we address this issue by the concept of mutual asymmetry and use this
machinery in the Page-Wootters mechanism by identifying the concept of mutual
asymmetry as mutual or internal coherence. To do so, the notion of quantum
coherence in relation of a quantum reference frame is revisited and a
quantifier is proposed in this scenario. Also, this open space to investigate
the link of internal coherence and correlations, as proposed by Page and
Wootters, under a resource theory approach.
