If Planck's relation is not true this is still plausible because Planck is correct up to the first plateau of the stepped Energy vs Frequency curve. Energy is quantized because the electrons are arranged in shells and there is no interaction between the photons and the electrons when the radius of the photon helix path is between electron shells.
From the previous post "All Creatures Great and Small", we modeled the dipole as a spring of spring constant \(k=2h\). If we look at the expression for a dipole again,
\({\delta E_l}=\cfrac{1}{4\pi\varepsilon_o}\cfrac{q.a}{z^3}\)
where \({\delta E_l}\) is force per unit charge then obviously the load to the model spring is a charge \(q\).
We may also see that,
\(k=2h=\cfrac{1}{4\pi\varepsilon_o}q\), so
\(h=\cfrac{1}{8\pi\varepsilon_o}.q\)
We may have just derived Planck constant. Just kidding, the charge on the photon dipole is,
\(q= h.8\pi\varepsilon_o\)
\(q\) = 6.62606957*10^(-34)*8*pi*8.854187817620*10^(−12) = 1.4745*10^(-43) C
A very small partial charge indeed.
Furthermore, such a spring system has a resonance,
\({f}_{reso}=\cfrac{1}{2\pi}\sqrt{\cfrac{k}{q}}=\cfrac{1}{2\pi}\sqrt{\cfrac{2h}{q}}\)
\({f}_{reso}\) = (2*6.62606957*10^(-34)/ (1.4745*10^(-43)))^(0.5)/(2*pi) = 94.803/(2.pi)= 15.088 kHz
in which case the dipole distance \(a\) increases greatly or \(\sqrt{f}\) increases greatly and since energy is proportional to frequency (Planck relation), energy of the photon increases greatly. Death Rays!
Note: Do not confuse \({f}_{reso}\) with \(\sqrt{f}\), the dipole distance \(a\) is made to oscillate at \({f}_{reso}\), and begins to display wide swing, and the photon ray shows wide color variations as \(\sqrt{f}\) changes widely.
