Classroom Reference Frames
consider a ground-state proton, in the nucleus of a Sodium atom, in a macroscopic crystal of NaCl, that is rigidly attached to the Earth in the corner of a ordinary classroom with vertical walls, and a rectangular floor. The Cartesian coordinate system centered on this specific proton is called the Classroom reference frame. The location of this proton is called the origin of the reference frame. We note it as $\mathbf{O}$.
For particles that are as large as atoms, in the particle-centered coordinate system, motion is always confined to the $z$-axis because displacements along the $x$ and $y$-axes add-up to zero over atomic cycles. But for atoms and molecules, in a classroom reference frame, the explicit description of visual sensation has been eliminated. So there is no reason to expect that sensory descriptions are consistent between particles. Instead we start by assuming the most general possibility that any atom under discussion might have a spatial orientation that is different compared to $\mathbf{O}$. So if atom $\mathbf{A}$ is described by its momentum $\bar{p}^{\mathbf{A} }$, then we assume that $\bar{p}^{\mathbf{A} }$ can take on any three numbers in the classroom-frame.