Stretching Out In Time

This post is wrong.

From the post "The Distribution Of $\psi$ Again",

 $\psi=D.ln(r)+C$ since $E=mc^2$,

we have equivalently,

 $m=A.ln(r)+B$

 where $m$ is now mass density,

 $A=\cfrac{D}{c^2}$ and $B=\cfrac{C}{c^2}$

 This mass is the neutral mass along a time dimension that serve to define energy via Einstein's $E=mc^2$ in that time dimension.

The problem is, $\psi$ is in space but $m$ is in the time dimension.  Could it be that,

 $m=A.ln(t)+B$

instead.  That $m$ stretches out in time in a corresponding way as $\psi$ stretches out in space?  That instead of a simple equivalence relationship we have a transform,

$E(r)=m(t)c^2$

from the space domain ($r$) to the time domain ($t$)?

What would be the significance of such a notion?