All Mathematical Interpretations Are Fiction

Consider the $\psi$ of a particle expanding from $x=x_a$ to $x=x_c$, $\psi$ is at velocity $c$ along $ix$, the gain in energy is,

$\Delta E=E_{x_c}-E_{x_a}=2\pi x_cmc-2\pi x_amc$

But,

$\Delta E=\bar F.\Delta x=2\pi mc(x_c-x_a)$

so,

$\bar F=2\pi mc$

We know that,

$F=-\psi$

where $F$ the Newtonian force due to $\psi$.  The average force on $\psi$ is,

 $\bar F =-(-\bar \psi)=\bar\psi=2\pi mc$

as the particle's $\psi$ expanded from $x_a$ to $x_c$.  Through out this process $KE=\cfrac{1}{2}mc^2$ remains unchanged.

The average acceleration,

 $\bar a_c=2\pi c$

Since the particle is in circular motion, and $\bar F$ is along a radial line,

$\bar F=2\pi c=\cfrac{c^2}{\bar x}$

and

$\bar x=\cfrac{c}{2\pi}$

What is $\bar x$?  $\bar F$ is a hypothetical average force, that extends up to $\bar x$ and is zero beyond.  But be warned, all mathematical interpretations are fiction next to bullshit.  Bullshit on the other hand, bulls will testify, is for real.

Have a nice day.