Quantum mechanics and the covariance of physical laws in quantum reference frames

Flaminia Giacomini,Časlav Brukner,Esteban Castro-Ruiz

doi:10.1038/s41467-018-08155-0

Abstract

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? Here, we introduce a general method to quantise reference frame transformations, 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, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.

Highlights

In physics, every observation is made with respect to a frame of reference
Can we meaningfully define transformations between such quantum reference frames’ (QRFs)? Which transformations relate quantum states of systems defined with respect to one frame of reference to those defined with respect to a second frame of reference? What are the dynamical physical laws that are invariant under such ‘quantum transformations’?
When reference frames are considered as abstract entities, the reference frame transformation consists in a coordinate transformation, where the new coordinates x′ in which the system under consideration is expressed are functions of the old cordinates x and time t, i.e. x′ = x′(x, t)

Summary

Introduction

Every observation is made with respect to a frame of reference. reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. We find that a quantum state and its features—such as superposition and entanglement—are only defined relative to the chosen reference frame, in the spirit of the relational description of physics[16,17,18,19,23,24]. We propose an extension of the notion of covariance of the physical laws to include genuine quantum transformations, where one frame of reference is in a superposition of different relative positions, momenta or velocities with respect to another frame of reference. We find that the weak equivalence principle can be extended to QRFs: The effects as observed in a “superposition of uniform gravitational fields” are indistinguishable from those in a frame in a “superposition of accelerations” in flat space-time In all these transformations the quantum system considered as a reference frame acts as a control for the transformation on the observed system

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Conclusion