The deepest mystery of quantum mechanics is the smallest quantum of action introduced by Planck in his proof of Planck's law:
- $h\nu$
where $h=6.626\times 10^{-34}\, Js$ is Planck's constant and $\nu$ is frequency.
The smallest quantum of action $h\nu$ appears in Einstein's celebrated law of the photoelectic effect:
- $h\nu = W + P$,
where $W$ is the energy required to liberate an electron and $P$ and the energy of a liberated electron.
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
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.
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
- $h\nu > W$
as a cut-off condition for photo-electricity similar to the cut-off condition in Planck's law with $T$ temperature and $k$ Boltzmann's constant:
- $h\nu > kT$
which according to Computational Blackbody Radiation expresses internal heating from exposure to radiation of frequency $\nu$.
We can thus view both photo-electricity and internal heating from exposure to radiation as being determined by a high-frequency cut-off condition expressing that no effect occurs for input frequencies below the cut-off, and that the effect scales with the intensity above the cut-off.
The idea of smallest packet of energy, which is strange as physical concept, can thus be replaced by the concept of threshold value on frequency or wave length, which is not strange from physics point of view. For details, see the book Computational Blackbody Radiation.
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.
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