Big Particle Exists

The following plot shows the change in $\psi$ along a radial line from the center of a particle,

A force $F_r$ on $\psi$ along a radial line, derived from the force density, $F_{\rho}$

$F_{\rho}=-\cfrac{\partial\,\psi}{\partial x}$

$F_r=\int{F_{\rho}}dx$

act opposite to the direction of increasing $\psi$.  If $\psi$ moves to higher value than a positive force is required in the positive radial direction to perform work on $\psi$, for $\psi$ to gain energy.  This force $F_{pinch}$ in the positive direction is countered by $F_r$ above in the negative direction, as $\cfrac{\partial\,\psi}{\partial x}$ is positive.

Work is done against $F_r$.  This work done increases the potential of $\psi$.

$F_r$ is subjected to the inverse square law.  When \cfrac{\partial\,\psi}{\partial x}\) at $a_{\psi}$ and beyond, is a constant or does not increase enough,

$\cfrac{\partial\,\psi}{\partial x}|_{x\gt a_{\psi}}\lt\cfrac{2}{r^3}$

where

$-\left(\cfrac{1}{r^2}\right)^{'}_r=\cfrac{2}{r^3}$

then $F_r$ decreases with distance from the center of the particle.  Any non zero force $F_{pinch}$ that displaces $\Delta \psi$ away from the center of the particle, pulls $\Delta\psi$ away to infinity with greater and greater acceleration.

$\Delta\psi$ is removed from the particle.

In this way, $a_{\psi}$ the probable size of a particle was arbitrarily set at,

$\theta_{\psi}=\pi=\cfrac{G}{\sqrt{2mc^2}}a_{\psi}$

where $tanh(\pi)\approx1$, for $F_r|_{a_{\psi}}$ to increase at greater distance from the particle center, that the particle remain intact with application of small $F_{pinch}$.  $\psi$ has minimum resistance from being pinched apart.

This does not mean that big particles of higher values of $a_{\psi}$ beyond the $\theta_{\psi}=\pi$ limit do not exist.

Such big particles will still interact at a constant (slightly higher) light speed limit.