Counting Quarks by the Bundle
//Asterias//, Jean Baptiste Lamarck. Tableau Encyclopédique et Méthodique des Trois Regnes de la Nature, Paris 1791-1798. Photograph by D Dunlop.
Asterias, Jean Baptiste Lamarck. Tableau Encyclopédique et Méthodique des Trois Regnes de la Nature, Paris 1791-1798. Photograph by D Dunlop.

To extend an earlier discussion about counting quarks, consider a particle P characterized by a repetitive chain of events

$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2}, \sf{\Omega}_{3} \ \ldots \ \right)$

where each cycle is some bundle of quarks

$\sf{\Omega}^{\sf{P}} = \left\{ \sf{q}_{1}, \sf{q}_{2}, \sf{q}_{3} \ \ldots \ \right\}$

Depending on the level of objectification each bundle $\sf{\Omega}$ may be thought of as; a set of sensations, or an orbital cycle, or an aggregation of seeds, or perhaps a compound quark. But for any interpretation we can make a mathematical description of P just by counting bundles.

sun.png
The chain Ψ is a sequence of an indefinite number of bundles, there may be two or two-billion of them. But we can specify a definite quantity $N_{\sf{\Omega}}$ by making the description relative to a reference sensation provided by seeing the Sun. Let $N_{\sf{\Omega}}^{\sf{P}}$ be the number of P's bundles observed during one solar day. This quantity has units of bundles-per-day or cycles-per-day. Solar clocks are historically important, but not much used anymore. So consider evaluating $N_{\sf{\Omega}}$ where the particle is an ordinary clock noted by $\mathbf{\Theta}$. If $\mathbf{\Theta}$ is calibrated so that its cycles are in seconds, then

$N_{\sf{\Omega}}^{ \mathbf{\Theta}} =$ 86,400 (seconds per day)

This number comes to us from the Sumerian and Babylonian peoples of ancient Mesopotamia.1 About four thousand years ago their astronomical observations and sexagesimal mathematics established what we mean by a second. Namely that one day is parsed as twenty-four hours of sixty minutes, each of sixty seconds. For WikiMechanics, we also associate $N_{\sf{\Omega}}^{ \mathbf{\Theta}}$ with the reference sensation of hearing a human heartbeat because the heart rateXlink.png of human adults usually pulsates between forty and one hundred beats-per-minute when resting. So $N_{\sf{\Omega}}^{ \mathbf{\Theta}}$ gives an order-of-magnitude account of the number of heartbeats-per-day for most people, thereby relating celestial and human-scale events. The foregoing tallies of bundles are used to define the angular frequency of P as

$\begin{align} \omega \equiv \frac{ 2 \pi N_{\sf{\Omega}} ^{\sf{ P}} }{ N_{\sf{ \Omega}}^{ \mathbf{\Theta}} } \end{align}$

This angular frequency has units like bundles-per-second or orbits-per-second. As descriptions are objectified, we speak more generally of radians-per-second.

Right.png Next step: a generic frequency.
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