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 mechanical energy $E$ of a particle P is proportional to its frequency ν so that

$E = h \nu$

where $h$ is an unvarying number called Planck's constant. Here is a plausibility argument for the postulate based on understanding a particle as a repetitive chain of events. As discussed earlier, the action associated with a typical quark in any particle is given by

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

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

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

Plausible or not, it is an experimental fact that Planck's constant is well known to about one part in a billion, and apparently unchanged over the last century. So we freely make use of Planck's posulate for particles composed from 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 $\delta E / E$ can be understood as a signal to noise ratio in that stream of sensory consciousness.
Right.png Next step: the period.
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