Notice: this page is under construction
Notice: this page is under construction

To summarize, we have defined particle-centered Cartesian coordinate systems and used them to start making space-time descriptions. By extending this to particles that are at least as big as atoms, we can invoke the hypotheses of spatial &/ temporal, homogeneity &/ isotropy to make the definition free from direct reference to chromatic visual sensations.

Now we will make models of molecules, as composite atoms, that are held together by chemical bonds. These bonds are defined from pairs of electrons. We intend to treat electrons, bonds and molecules as logically countable entities as for example in Lewis dot diagramsXlink.png or VSEPR theoryXlink.png. But by Pauli's exclusion principle we cannot have two identical electrons in the same mathematical set. So we need to distinguish the electrons from each other. And, in molecules with more than one bond, we need to distinguish bonds from each other too. We need at least three logically distinct bonds to extend Cartesian coordinates to outlying atoms in the classroom-centered description.
The Orange Free Quirk says, 'Don't forget about other sensations.'
The Orange Free Quirk says, 'Don't forget about other sensations.'

We traditionally meet this requirement by saying that different bonds are distinctly different from each other because they are in different places. But, by the premise of WikiMechanics, we cannot resort to satisfying Pauli's exclusion principle by resorting to a spatial explanation for their differences. Rather, we differentiate them by association with different chemical seeds. We cannot use any thermodyamic seed to make the distinction between electrons because they're already constrained by earlier hypotheses.

Later, after a discussion of classroom reference frames, we relax the requirement for an explicit display of bond-types. Then, we freely choose among the different symbols wedgebond.png linebond.png hashbond.png to make molecular structure diagrams that still convey three-dimensional information, but as simply as possible, and without regard to Pauli's principle.

Note that these assignments differ slightly from the conventional notationXlink.png used to describe molecular structures. Later, we relax the requirement for an explicit display of bond-types. And after that, we freely choose among the different symbols wedgebond.png linebond.png hashbond.png to make molecular structure diagrams as clear and simple as possible. So for example, to represent water we need two logically distinct bonds that could be shown as


But after properly defining extended three-dimensional space, we can assume that the two bonds are distinct because they are in different places. (This semantically liberates the bond-symbols defined above in much the same way as the hypothesis of spatial isotropy frees the use of color terms.) Then we drop the wedge-shaped symbol to represent water with the simpler diagram


This simplification is important for complicated chemical structures.

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 $\mathbf{O}$.

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 1030. 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.

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