\(ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } }a_{\psi\,c}))=\cfrac{1}{4}\)
\(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } }a_{\psi\,c}=0.7369\)
the particles stick into lumps without end.
The particles in black and red surround a central piece. The green dotted particles is a second layer on top of the black and red.
The problem is, the particles continue to lump without end. Only if \(\psi\) merge into one and the particles "grows" to
\(ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } }a_{\psi\,\pi}))=ln(cosh(\pi))=2.450311\)
\(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } }a_{\psi\,\pi}=\pi\)
the size at which the force around the particle decreases with distance from the center of the particle as Coulomb's inverse square law applies, does this sticky issue resolve itself.
How many particles must merge?
\(\cfrac{a_{\psi\,c}}{a_{\psi\,\pi}}=\cfrac{0.7369}{\pi}\)
\(n\left(\cfrac{a_{\psi\,c}}{a_{\psi\,\pi}}\right)^3=n\left(\cfrac{0.7369}{\pi}\right)^3=1\)
\(n=77.486\)
\(\left\lfloor n \right\rfloor =78\)
which would make the resulting big particle slightly over the limit,
\(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } }a_{\psi\,\pi}=\pi\)
This implies, it is possible to split a big particle into a smaller fractions. The smallest of which is \(\cfrac{1}{78}\) of the original big particle.
The magic number to look for is \(78\).
