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Atoms

In accordance with conventional chemistry, various atoms are defined from protons, electrons and neutrons. These subatomic components have all been specified from quarks and reference sensations. So for EthnoPhysics, atoms are ultimately defined from sensations too.

Atoms are generically represented using bold, serified upper-case letters like  \mathbf{A} or  \mathbf{B}. The smallest atom is hydrogen, noted by  \mathbf{H}. Hydrogen atoms are also the smallest stable particles defined from a fully three-dimensional octet of space-time events. And so, they are also the smallest particles to be precisely represented in three-dimensional space. The locations of larger atoms are easier to establish. So we assume that a position  \bar{r}, and a time of occurrence  t, can be associated with anything that happens to an atom. Assigning a position to an atom is discussed later in an article about molecular models. But we can readily assign a time-of-occurrence to atomic events by thinking of atoms as little clocks.

Atomic Clocks

Atoms oscillate and jostle about in complex ways. So many different modes of atomic vibration have been examined in the laboratory, compared with historical standards of timekeeping, and assessed for their practical use as clocks. Some are excellent. Atomic fountain clocks can make time measurements that are good to one part in 1014 and they are still being improved. High precision laboratory work often uses atoms of caesium. But here is a way to tell time using a generic atom,  \mathbf{A}. Let  \mathbf{A} be described by a repetitive chain of events

\Psi^{\mathbf{A}} = \left(\mathsf{\Omega}_{\mathsf{o}}, \, \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2} \, \ldots \, \mathsf{\Omega}_{k} \, \ldots \right)

where orbital cycles are composed of  N quarks as

\mathsf{\Omega}^{\mathbf{A}} = \left( \mathsf{q}_{1}, \, \mathsf{q}_{2}, \, \mathsf{q}_{3} \, \ldots \, \mathsf{q}_{N} \right)

Since  \mathbf{A} is being used as a clock, we assume it has been sufficiently stabilized and isolated so that its vibrations are steady and regular. We assume their period  \widehat{\tau} has been measured, so that  \mathbf{A} is calibrated. Then we can determine an elapsed time just by counting atomic cycles to determine k. We write

\Delta t \equiv t_{k} - t_{\mathsf{o}} = k \widehat{\tau}

Without loss of generality, let t_{\mathsf{o}} = 0 so that t_{k} = k \widehat{\tau}. And recall that the period is given by \hat{\tau}= 1/ \nu where  \nu is the frequency of  \mathbf{A}. Then t_{k} = k / \nu . Also, by definition the frequency is \nu \equiv N \omega / 2 \pi where  \omega is the angular frequency of  \mathbf{A}. And so event  k occurs at a time given by

t_{k} = \dfrac{2\pi k}{N \omega}

Recall that the phase angle  \theta of  \mathbf{A} is given by \theta_{k} = \theta_{\mathsf{o}} + 2\pi k/N. So we can write

t_{k} = \dfrac{\theta_{k} - \theta_{\mathsf{o}}}{\omega}

This relationship expresses the time-of-occurrence of the  kth event as a function of the phase-angle. Time is thus told. However, we often think of time as the independent parameter and write the phase-angle as a function of time; the  k-subscript is dropped, and   \theta ( t ) is substituted for   \theta_{ k}. Then rearranging gives

\theta (t) =    \theta_{\mathsf{o}} + \omega t

This form is good for describing the rotating motion of particles when they are framed in a Cartesian view.

Quantum Numbers for Atoms

Here are some quantum numbers for use in atomic descriptions that gloss over visual sensation. To discuss atoms objectively we adopt  \mathrm{n},  \ell,  s and  j instead of the four coefficients of rotating quarks  n^{\mathsf{u}},  n^{\mathsf{\overline{u}}},  n^{\mathsf{d}} and  n^{\mathsf{\overline{d}}} that previously accounted for achromatic sensation. The principal quantum number is given by

\mathrm{n} \equiv \dfrac{n^{\mathsf{d}}}{4}

This principal number is the same quantity that was developed earlier for the description of excited particles. The azimuthal quantum number is defined by

\ell \equiv   \dfrac{N^{\mathsf{U}} + N^{\mathsf{D}} + \left| N^{\mathsf{U}} - N^{\mathsf{D}} \rule{0px}{9px} \right| }{8}   -   \dfrac{n^{\mathsf{d}}}{2}

The spin angular momentum quantum number is defined as

s \equiv \dfrac{  n^{\mathsf{u}} + n^{\mathsf{\overline{u}}} - 3 n^{\mathsf{d}}+ n^{\mathsf{\overline{d}}}   }{8}

And finally, the total atomic angular momentum quantum number is

j \equiv \dfrac{\left|  N^{\mathsf{U}} - N^{\mathsf{D}} \rule{0px}{9px} \right|}{8}

These atomic quantum numbers also have historic mechanical interpretations. Taken together, they are said to specify an atomic state. Note that  \mathrm{n} and  s are defined from simple sums and differences of quark coefficients, so they are always conserved.

Atoms are objectified from eight-fold patterns of sensation, similar to the anthropomorphic motifs in this Indonesian textile
Two by Four Tampan, Paminggir people. Lampung region of Sumatra, 19th century, 55 x 59 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop.