Action
//Tampan,// Paminggir people. Lampung region of Sumatra 19th century, 68 x 62 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop.
Tampan, Paminggir people. Lampung region of Sumatra 19th century, 68 x 62 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop.

Consider a particle P described by a repetitive chain of events

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

where P is characterized by its mechanical energy $E$ and its angular frequency $\ \omega$. We define a number called the action of P as

$\begin{align} X \equiv \frac{ 2 \pi E }{ \omega } \end{align}$

Now consider that each orbital bundle $\sf{\Omega}$ is composed from $N$ quarks $\sf{\Omega} = \left\{ \sf{q}_{1}, \sf{q}_{2} \ \ldots \ \sf{q}_{\it{N}} \right\}$. Then the action associated with a typical quark in P is

$\begin{align} \widetilde{X} \equiv \frac{ X }{ N } = \frac{ 2 \pi E }{ N \omega} \end{align}$

But recall that the generic frequency of any particle is given by $\begin{align} \nu \equiv N \omega \, / \, 2 \pi \end{align}$ so that the action for some average quark in P can be written in terms of the frequency $\nu$ as

$\begin{align} \widetilde{X} = \frac{E}{\nu} \end{align}$

sun.png
Sensory interpretation: The angular frequency $\omega$ is proportional to the number of sensory bundles observed per day. So if the mechanical energy of P is equally shared between these bundles, then $X$ is the energy-per-bundle and $\ \widetilde{X}$ is the mechanical energy associated with a typical quark in a typical bundle.
Right.png Next step: Planck's postulate.
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