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 $\mathbf{O}$.

The positions of atoms in the classroom frame are defined by counting the number of intervening atoms in the three-dimensional, NaCl crystal lattice.

Because the Earth is explicitly included as part of a Classroom Reference Frame, the total number of quarks in any description will be huge, like bigger than 10^{30}. So displacements and phase-angle increments can be made very small. Space-time is effectively continuous, and calculus is useful.

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.

This is different from if the central proton is unattached to the Earth. Then we keep quantization.