Searching for a physical description relative to a quantum system (2509.04186v1)

Abstract: Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The situation is no different when the model in use is quantum mechanics: states and observables are relative entities, and reference frames are not exempt from exhibiting quantum behavior. In recent years, the scientific community has shown renewed interest in quantum reference frames, particularly in connection with the covariance of physical laws and quantum resources. However, current approaches fall short of providing a complete prescription for predicting observables associated solely with degrees of freedom accessible from the quantum reference frame. In pursuit of such a description, we show that while this is fully feasible for two-particle systems, there are irreducible difficulties that arise in many-body systems. In particular, within the framework of Galilean relativity, with absolute time, we demonstrate that a canonical and relational description with respect to a particle in the system cannot be achieved through any unitary transformation. Our findings call for new strategies to address the problem of quantum reference frames.