Physics Illusion 13: Light as Stream of Photon Particles

                                      Light as a stream of photon particles or as electromagnetic wave?

Quantum mechanics is supposed to originate from Planck's proof in 1900 of Planck's Law of Black Body Radiation introducing a smallest quantum of action named Planck's constant denoted by $h$ with a value later determined to

• $h = 6.62606957\times 10^{-34}\, J\cdot s$ 

attributing the energy $E=h\nu$ to a wave of frequency $\nu$, as a smallest quantum of energy of the frequency $\nu$. Planck used the quantum of energy $h\nu$ to save the scientific world from the ultra-violet catastrophe of classical electromagnetics with radiation energy scaling with $\nu^2$ without limit for increasing frequency $\nu$,  using a statistical argument suggesting low probability of high frequency, thus effectively introducing a high-frequency cut-off in the radiation spectrum. Planck viewed his quantum as a mathematical trick without physical reality.

Then Einstein entered the game in 1905 with the article giving him the 1921 Nobel Prize in Physics presenting a formula expressing an energy balance for the photoelectric effect with electrons being ejected from a surface when exposed to light:

• $ h\nu = E + P$

where $E$ is the energy of an ejected electron and $P$ the energy required to release the electron from the surface. With this formula, where $h\nu$ would represent a smallest quantum of light of frequency $\nu$, Einstein seemed to explain the basic properties of the photoelectric effect: No electrons are ejected unless $h\nu > P$ independent of light intensity and the number of ejected electrons scale with intensity. The value of $h$ was determined in 1916 by Millikan using Einstein's formula with the objective to falsify Einstein's concept of quantum of light.

Neither did the Nobel Committee buy Einstein's derivation of his formula based on light quanta, but with the appearance of quantum mechanics in 1925 Einstein's idea received momentum and with the name photon by Lewis in 1927 became a trademark of modern physics, although it was basically the same old corpuscular theory of light once suggested by Hobbes but quickly replaced by the wave theory of Huygens. In the Standard Model ruling fundamental physics of today the photon has as a respectable position as the elementary particle carrying the electromagnetic force. Light as a flow $\nu$ photons per unit time then correponds to an energy flux of $h\nu^2$, which we now compare with Planck's Law. 

Let us in particular check out how Planck's constant enters into Planck's Law, which reads

• $R_\nu (T)=\gamma\nu^2T\times \theta(\nu ,T)$,

where $R_\nu (T)$ is radiated energy per unit frequency, surface area, viewing angle and second, $\gamma =\frac{2k}{c^2}$ where

• $k = 1.3806488\times  10^{-23} m^2 kg/s^2 K$

is Boltzmann's constant and $c$ the speed of light in $m/s$, $T$ is temperature in Kelvin $K$, and 

• $\theta (\nu ,T)=\frac{\alpha}{e^\alpha -1}$, 
• $\alpha=\frac{h\nu}{kT}$

is a high-frequency cut-off factor such that $\theta (\nu ,T)\approx 1$ for $\alpha < 1$ and  $\theta (\nu ,T)\approx 0$ for $\alpha > 10$. 

We see that Planck's constant $h$ enters into Planck's law as a high-frequency cut-off for $\frac{\nu}{T} > \frac{10k}{h}$, which reflects the original role of $h$ given by Planck, with the dependence on $T$ reflecting Wien's displacement law.

Computational Black Body Radiation presents an alternative derivation of Planck's law based on wave mechanics with finite precision computation serving as high-frequency cut-off. Maybe after all there is no compelling reason to speak about photons and light particles.