Quantum clocks and the measurability of spacetime distances

Standard quantum mechanics typically assumes the existence of an external, idealized reference frame to define states and observables. However, this "absolute" reference frame may be practically inaccessible or fundamentally unavailable becouse of symmetry principles, for instance general covariance in General Rel- ativity. In such situations, a consistent quantum mechanical description must rely on relational observables, where certain subsystems serve as (quantum) reference frames for the others. Within the framework of quantum reference frames (QRF), this thesis explores the limitations on mea- surements of spacetime distances, which are necessary to establish a physical reference frame. First, we investigate how the Heisenberg uncertainty principle imposes a fundamental limitation on Einstein’s syn- chronization of distant quantum clocks, preventing the attainment of perfect synchronization. Then, we investigate the interplay between the precision of a quantum clock and its spatial localization, revealing a fundamental trade-off: improving the precision of time measurements inevitably increases the uncertainty in the clock’s position, establishing a limitation in how precisely a quantum clock can serve as a reference for both space and time.