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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? The relational approach to physics suggests that all the features of a system —such as entanglement and superposition— are observer-dependent: what appears classical from our usual laboratory description might appear to be in a superposition, or entangled, from the point of view of such a quantum reference frame. In this work, we develop an operational framework for quantum theory to be applied within quantum reference frames. We find that, when reference frames are treated as quantum degrees of freedom, a more general transformation between reference frames has to be introduced. With this transformation we describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, which we explore in the case of ‘superposition of Galilean translations’ and ‘superposition of Galilean boosts’. In addition, we consider the situation when the reference frame moves in a ‘superposition of accelerations’, which leads us to extend the validity of the weak equivalence principle to quantum reference frames.

Abstract: There is a strong correlation between the sun rising and the rooster crowing, but to say that the one causes the other is to say more. In particular, it says that making the rooster crow early will not precipitate an early dawn, whereas making the sun rise early (for instance, by moving the rooster eastward) can lead to some early crowing. Intervening upon the natural course of events in this manner is a good way of discovering causal relations. Sometimes, however, we can't intervene, or we'd prefer not to. For instance, in trying to determine whether smoking causes lung cancer, we'd prefer not to force any would-be nonsmokers to smoke. Fortunately, there are some clever tricks that allow us to extract information about what causes what entirely from features of the observed correlations. One of these tricks was discovered by the physicist John Bell in 1964. In a groundbreaking paper, he used it to demonstrate the seeming impossibility of providing a causal explanation of certain quantum correlations. This revealed a fundamental tension between quantum theory and Einstein's theory of relativity --the two central pillars of modern physics. It is a tension that is still with us today.