In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? In the first part of my talk, I will introduce a general method to quantise reference frame transformations within a Galilean-relativistic setting, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”. We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws. In the second part of my talk, I will show how these ideas can be used to operationally define the localization of events with respect to quantum clocks, each of which identifies a “time reference frame". In particular, I will consider clocks that i) are quantum mechanical, and ii) interact, gravitationally or otherwise, with other quantum systems. We find that, when gravitational effects are important, the time localisability of events becomes a relative concept, depending on the time reference frame. We discuss the physical significance of "jumping" onto a time reference frame with respect to which specific events are localised, in the context of indefinite causal structures arising from the interplay between quantum mechanics and gravity.
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