^{1}that the energy of a particle is directly proportional to its frequency in a fixed ratio called Planck's constant. Here is a plausibility argument for the postulate based on understanding some particle P as a repetitive chain of events

Baby Collar, Dong people. China, Yunnan province, 20th century, 39 x 17 cm. From the collection of Tan Tim Qing, Kunming. Photograph by D Dunlop. |

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

Let P be characterized by its angular frequency $\ \omega$ and mechanical energy $E$. Then we can specify a number called the **action** of P as

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

Also let each orbital bundle $\sf{\Omega}$ be composed from $N$ quarks as $\sf{\Omega} = \left\{ \sf{q}_{1}, \sf{q}_{2} \ \ldots \ \sf{q}_{\it{N}} \right\}$. Then the action associated with a typical quark is

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

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

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

$\widetilde{X} ^{\, \sf{P}} \cong \ \ \widetilde{X} ^{\, \sf{Earth}} \equiv \ \it{h}$

Then if $N$ is large enough, $\widetilde{X} = E / \nu$ implies that

$E = h \nu$

This is the conventional statement of Planck's postulate. It is an experimental fact that the 'constant' is well known to about one part in a billion, and apparently unchanged over the last century. So we make vigorous use of Planck's postulate for particles that contain many quarks.

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 randomly spread out between these bundles, then $X$ is like the energy in a typical bundle. And $\ \widetilde{X}$ is like the energy of a typical quark in a typical bundle. If we assume that Planck's postulate applies to some particle P, then the mechanical energy of P is proportional to the daily flux of Anaxagorean sensations associated with P. And $\delta E / E$ is related to the signal to noise ratio in that stream of sensory consciousness.Here is a link to the most recent version of this content, including the full text.

Planck's Postulate |