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We study gravitational back-reaction within relational time formulations ofquantum mechanics by considering two versions of time: a time coordinate,modelled as a global quantum degree of freedom, and the proper time of a givenphysical system, modelled via an internal degree of freedom serving as a localquantum "clock". We show that interactions between coordinate time andmass-energy in a global Wheeler-DeWitt-like constraint lead to gravitationaltime dilation. In the presence of a massive object this agrees with timedilation in a Schwarzchild metric at leading order in $G$. Furthermore, if twoparticles couple independently to the time coordinate we show that Newtoniangravitational interaction between those particles emerges in the low energylimit. We also observe features of renormalization of high energy divergences.

Emergence of Gravitational Potential and Time Dilation from Non-interacting Systems Coupled to a Global Quantum Clock