From the previous posts on inertia densities, the constant
1c2G2
appears in all expressions for particle mass density and has unit kg. So,
1c2G2=mdp
G2=1mdpc2
where mdp is mass in kg. Since,
mρ=12Dc2G2=12mdpD --- (*)
where D=πa2 or D=a.
For a consistent unit dimensions of mρ. mdp is the mass of the particle irrespective of its dimensions, 2D or 1D.
This derivation suggests that all particles has a common mass denominator mdp. All particles are derived from this value.
This was an assumption made previously when the expression,
mρpc2=mρc2−∫xa0ψdx
was written down. G was derived from a different path. G was a constant of integration from solving for Fρ 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.