Thursday, September 8, 2016

More And Smaller

If,

\(a_{\psi\,74}=14.77\)

and from the post "Sticky Particles Too...Many" dated 24 Jun 2016,

\(\cfrac{n_1}{n_2}=\left(\cfrac{a_{\psi\,n_1}}{a_{\psi\,n_2}}\right)^3\)

\(a_{\psi\,c}=a_{\psi\,1}=3.52\,\,nm\)

This is the size of the smallest particle possible, breaking off from the tip of a sonic cone in a sonic boom or when big particles disintegrate in high speed collisions.

This particle has \(\small{\cfrac{1}{4}}\) the charge magnitude (gravity, electric or temperature) but \(\sqrt [ 3]{\cfrac{1}{74}}=0.2382 \) the radius of a big particle.

But the classical electron radius is quoted at,

\(r_e=2.817 940 3267[27] e-15\,\,m \)

What is this value \(a_{\psi\,1}\), a million times bigger?  Then again, the visible spectrum is \(390\le\lambda_{vis}\le 700\,\,nm\); can we expect particles that are photons to be that much smaller that their wavelengths?

\(\lambda_{\psi}\) or \(\lambda_{n}\) is not \(\lambda_{vis}\)!

Could it be that \(r_e\) measured under the formulation for point particles, is actually the size of the void where \(v=c\) along a radial line, at the perimeter of this void?


Which suggests that interactions between particles allow overlaps in \(\psi\) and that such interactions (mechanical/gravitational, electrical, ie field interactions) is limited down to \(r_e\), below which \(\psi\) does not exist.

\(r_e\) is the size of the hole in all particles that changes with exterior conditions acting on \(\psi\).  Pushing \(\psi\) at the start of the plateau in the \(\psi\) vs \(x\) graph, at resonance frequency, increases \(r_e\) and the over all size of the particle.

Maybe...