The deepest mystery of quantum mechanics is the smallest quantum of action introduced by Planck in his proof of Planck's law:
The smallest quantum of action $h\nu$ appears in Einstein's celebrated law of the photoelectic effect:
- $h\nu = W + P$,
Einstein's formula models generation of an electric current corresponding to $P >0$ from input of light of frequency $h\nu$, scaling with the intensity of the light.
Einstein interpreted $h\nu$ as the "smallest packet of energy" of a wave of frequency $\nu$ later named photon with $h\nu - W>0$ required for the generation of an electric current with $P > 0$. We can view
- $h\nu > W$
- $h\nu > kT$
Recall that Einstein was awarded the 1921 Nobel Prize in Pbysics for his above law of photoelectricity, but it was explicitly stated in the award motivation that he was not given the Prize because of his derivation of the formula based on photons, only for the "discovery" of the formula as if formulas are laying around waiting to be discovered.