Planck's Postulate
//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.
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.
In 1900 Max PlanckXlink.png asserted1 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

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

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

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

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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 like the energy in a typical bundle. And $\ \widetilde{X}$ is like the energy of a typical quark in a typical bundle.

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

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

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For terrestrial particles made of lots of quarks, the statistical law of large numbersXlink.png guarantees that $\ \widetilde{X}$ has a definite value determined by the distribution of quarks on Earth. Moreover, this value is presumably constant because the quark distribution is at least as stable as rock formations that change on geological time scales. This constant is called Planck's constant, and noted by $h$. We can write

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

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.

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Sensory interpretation: 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.
Right.png Next step: time.
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