Quantum reference frames: towards a quantum description of space and time

In physics, observations are typically made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in 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 talk, I will introduce a general method to associate a reference frame to a quantum system, which generalises the usual reference frame transformation to a "superposition of coordinate transformations”. Such quantum reference frames transformations imply that the notion of entanglement and superposition are not given a priori, but depend on the choice of the quantum reference frame even in a non-relativistic setting. Quantum reference frames could be a useful tool at the intersection of gravity and quantum theory: for instance, they allow one to generalise the Einstein’s equivalence principle to superpositions of gravitational fields, and to describe the behaviour of quantum clocks ticking in a superposition of times relative to one another.