From the previous posts on inertia densities, the constant
\(\cfrac{1}{c^2G^2}\)
appears in all expressions for particle mass density and has unit \(kg\). So,
\(\cfrac{1}{c^2G^2}=m_{dp}\)
\(G^2=\cfrac{1}{m_{dp}c^2}\)
where \(m_{dp}\) is mass in \(kg\). Since,
\(m_\rho=\cfrac{1}{2Dc^2G^2}=\cfrac{1}{2}\cfrac{m_{dp}}{D}\) --- (*)
where \(D=\pi a^2\) or \(D=a\).
For a consistent unit dimensions of \(m_\rho\). \(m_{dp}\) is the mass of the particle irrespective of its dimensions, 2D or 1D.
This derivation suggests that all particles has a common mass denominator \(m_{dp}\). All particles are derived from this value.
This was an assumption made previously when the expression,
\(m_{ \rho \, p }c^{ 2 }=m_{ \rho }c^{ 2 }-\int _{ 0 }^{ x_{ a} }{ \psi } dx\)
was written down. \(G\) was derived from a different path. \(G\) was a constant of integration from solving for \(F_\rho\) from the wave equation (posts, "My Own Wave Equation" and "Not Exponential, But Hyperbolic And Positive Gravity!").
Are all particles from a common mass? If so, what is this small mass? And why?
The posts "If The Universe Is A Mochi..." and "If The Universe Is A Banana...", it was proposed that the universe split into smaller and smaller particles. If all particles have a common small particle origin then there was no light, no gravity, no temperature, no charge, no time, no space at the beginning of the universe until the universe has split into small enough particles.
The half factor retained in (*) is important, it may be use to account for the kinetic energy of the particle.
