Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?

Quantum reference frames are expected to differ from classical because they have implement typical quantum features such as fluctuations and correlations. Here, we show that correlations of variables, in particular time, restricted by their very nature being used for reference. Mathematically, this property is implemented imposing constraints on the system make sure variables not physical degrees freedom. These only relate freedom order describe behavior, also restrict with We introduce notion “almost-positive” states a suitable mathematical method. An explicit application properties examples recent interest reveals previously unrecognized restrictions possible frame–system interactions. While currently discussed clock models rely assumptions that, shown here, them consistent frames, relaxing these will expose new appear be rather strong. Almost-positive shed some light debate about consistency relational mechanics.