Quantum Reference Frames in Flat Space-Time and Gravity

It was argued recently that in Quantum Mechanics (QM) the correct definition of physical reference frame (RF) must differ principally from universally accepted one. [1]. The reason is that in exact theory the quantum properties of any massive object M₁ with which physical RF F¹ associated must be taken into account, despite their possible smallness in laboratory conditions. Consequently F¹ evolution must obey to Schrodinger equation, and its free state relative to external observer at rest F⁰ is the localizable wave packet Ψ(x₁,t), not the classical trajectory. As the example F¹ can be rocket in outer space and F⁰ earth, M₀ → ∞. If F¹ localized state Ψ(x,t₀) ~ δ(x) prepared by F⁰ it will smear in space unrestrictedly with the time σ_x ~ t^1/2. This smearing introduces additional uncertainty into the measurement of particles m_i space coordinates by F¹ x_i1 = x_i-x₁ in F¹, because x₁ is also operator, m_i states transformations between two such quantum RFs includes quantum corrections to Galilean transformations, which depends on RFs states vectors [1]. Consistent nonrelativistic quantization in such RFs of free particles m_i and other quantum systems in two alternative formalisms was proposed [2]...