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Planck’s Postulate

Planck's postulate concerns the statistical distribution of sensations like the highly structured chromatic variations in this hand-woven textile from China.
Baby Collar, Dong people, 39 x 17 cm. China, Yunnan province, 20th century. Photograph by D Dunlop.

In 1900 the German physicist Max Planck asserted that the energy of any particle P, is directly proportional to its frequency, in a fixed ratio called Planck’s constant.1The Theory of Heat Radiation by Max Planck. Translated into English by Morton Masius and published by P. Blakiston’s Son & Co. in Philadelphia, 1914. Here is a plausibility argument for the postulate that is based on understanding P as a repetitive chain of events

\Psi^{\mathsf{P}} = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2}, \, \mathsf{\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

X \equiv \dfrac{2\pi E}{\omega}

Also let each repeated bundle  \mathsf{\Omega} be composed from  N quarks so that \mathsf{\Omega} = ( \mathsf{q}_{1}, \mathsf{q}_{2} \ldots \mathsf{q}_{N} ). Then the action associated with a typical quark is

\widetilde{X} \equiv \dfrac{X}{N} = \dfrac{2\pi E}{N \omega}

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

\widetilde{X} = \dfrac{E}{\nu}

Earthiness is illustrated by this planet icon for the sensation of touching the earth.

For terrestrial particles made from lots of quarks, the statistical law of large numbers 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}^{\, \mathsf{P}} \cong \widetilde{X}^{\, \mathsf{Earth}} \equiv h

Then if  N is large enough, the foregoing result that \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

Solar clocks are like this radiant icon.

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 the action  X represents 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 P, then the mechanical energy  E is proportional to the daily flux of Anaxagorean sensations associated with P. Any variation in this stream of sensory consciousness can be expressed using   \delta \! E and the signal to noise ratio.

References
1The Theory of Heat Radiation by Max Planck. Translated into English by Morton Masius and published by P. Blakiston’s Son & Co. in Philadelphia, 1914.