we can approximate,
\(E=hf=h*\cfrac{2\pi a_{\psi\,l}}{v}=\cfrac{1}{2}mv^2_{boom}\)
that all energy due to \(v_{boom}\) is stored in \(a_{\psi\,l}\) and the initial energy before impact and also the energy of the photon upon collapse remains unchanged in \(a_{\psi\,s}\).
We are not going to get \(m\), because,
\(h=2\pi a_{\psi\,l}mc\)
So,
\(2\pi a_{\psi\,l}mc*\cfrac{2\pi a_{\psi\,l}}{v}=\cfrac{1}{2}mv^2_{boom}\)
\(v^2_{boom}=2(2\pi a_{\psi\,l})^2\cfrac{c}{v}\)
\(v_{boom}=\sqrt{\cfrac{2c}{v}}*2\pi a_{\psi\,l}\)
or
\(a_{\psi,l}=\cfrac{v_{boom}}{2\pi\sqrt{2}}*\sqrt{\cfrac{v}{c}}\)
We may also define a \(k_{\psi}\) such that,
\(\cfrac{1}{2}ka^2_{\psi\,l}=\cfrac{1}{2}mv^2_{boom}=h*\cfrac{2\pi a_{\psi\,l}}{v}=(2\pi a_{\psi\,l})^2m*\cfrac{c}{v}\)
\(k=8\pi^2\cfrac{c}{v}m\)
as if the photon is a spring extended to accommodate and store the energy in \(v_{boom}\). Naturally,
\(f_{res}=\cfrac{1}{2\pi}\sqrt{\cfrac{k}{m}}=\cfrac{1}{2\pi}\sqrt{8\pi^2\cfrac{c}{v}}=\sqrt{\cfrac{2c}{v}}\)
This means a collision frequency at \(f_{res}\) will stretch a torus photon along its larger radius. Given \(E_p\) as the energy per photon, a power setting of,
\(P_{res}=f_{res}E_{p}\, Js^{-1}\)
will create a halo around the ray impacting a blocking medium. Since \(E_p\) is very small, \(P_{res}\) is low, the effect of which is small.
\(f_{res}\) is the frequency to resonate a torus photon and may also be the frequency to grow a basic particle, because if the torus collapses,
\(a_{\psi\,l}\rightarrow a_{\psi\,s}=a_{\psi\,c}\)
\(v\rightarrow c\)
\(f_{res}\rightarrow \sqrt{2}\)
Given a simple string-ball pendulum,
\(f=\cfrac{1}{2\pi}\sqrt{\cfrac{g}{l}}=\sqrt{2}\)
\(l=\cfrac{g}{8\pi^{2}}\)
\(g=9.806\,ms^{-1}\)
\(l=0.1242\,m\)
Do the balls heat up, start to glow, become positively charged and explode?
