The Real Physical Meaning of Planck's Constant

The mystery of discrete lumps or quanta and the strange energy relation $E=h\nu$ with strange dimension of energy x time. 

Planck's constant $h = 6.626 \times 10^{-34} Js$ is supposed to represent a fundamental property of the Universe we happen to live in.

Prandtl introduced $h$ as a fictional mysterious quantity in his proof of Planck's radiation law in 1900 based on statistics with $h$ representing a smallest "quantum of action". Today 114 years later the fiction and mystery remains, and it is time to pass on to reality.  In the recent series of posts we have seen that $h$ enters into Planck's law in a high-frequency cut-off condition of the form

• $\nu > \frac{kT}{h}=\frac{T}{\hat h}$ where $\hat h =\frac{h}{k}$,

$\nu$ is frequency, $T$ is temperature in Kelvin $K$ and $k = 1.3806488\times 10^{−23}\, J/K$. Here  

• $\hat h =4.8\times 10^{-11}\, Ks$,

shows up as the real effective Planck constant in Planck's law. 

We see that $\frac{T}{\hat h}$ acts as a threshold value for frequency $\nu$, or equivalently $\hat h\frac{c}{T}$ acts as a threshold value for wave length $\lambda =\frac{c}{\nu}\, m$ with $c\, m/s$ the speed of light. The real effective Planck constant $\hat h$ thus has the form of a material parameter for a blackbody as a web of oscillators with a characteristic high-frequency cut-off  $\frac{T}{\hat h}$ or wave-length cut-off $\hat h\frac{c}{T}$, which expresses Wien's displacement law.

The mystery of $h$ as a "smallest quantum of action" thus can be deconstructed and the real meaning as $\hat h$ can be readily understood, all following Einstein's device to make everything as simple as possible, but not simpler. 

For the full story, see Computational Blackbody Radiation.