In our 3 space dimension world time flows freely, continuously. If we are able to rotate/transform a space dimension on to a time dimension then space along that dimension will flow freely. The time dimension that has been swapped with a space dimension will stand still unless kinetic energy is applied.
From the post "Eternal Embrace", time and space loop around each other. As we shorten time, space elongates. It might be possible that using the equation from the post "Time Travel Made Easy",
\(\cfrac{\partial\,t_{gf}}{\partial\,t}=\cfrac{1}{mc^2}(\cfrac{\partial\,t_{gi}}{\partial\,t}E_{\Delta h}+t_{gi}\cfrac{\partial\,E_{\Delta h}}{\partial\,t})+\cfrac{\partial\,t_{gi}}{\partial\,t}\)
and setting
\(\cfrac{\partial\,t_{gf}}{\partial\,t}=0\)
\(\cfrac{1}{mc^2}(\cfrac{\partial\,t_{gi}}{\partial\,t}E_{\Delta h}+t_{gi}\cfrac{\partial\,E_{\Delta h}}{\partial\,t})+\cfrac{\partial\,t_{gi}}{\partial\,t}=0\)
\(t_{ gi }\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } =-\left( E_{ \Delta h }+mc^{ 2 } \right) \cfrac { \partial \, t_{ gi } }{ \partial \, t } \)
but,
\( \cfrac { \partial \, t_{ gi } }{ \partial \, t } =c\)
So,
\(t_{ gi }\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } =-c\left( E_{ \Delta h }+mc^{ 2 } \right) \)
since,
\(t_{ gi }\gt0\), \(\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \lt0\)
Furthermore,
\( t_{ gi }=\cfrac { 2\pi a_{ \psi \, n } }{ c } =-c\left( E_{ \Delta h }+mc^{ 2 } \right) \left( \cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right) ^{ -1 }\)
\( a_{ \psi \, n }=-\cfrac { 1 }{ 2\pi } c^{ 2 }\left( E_{ \Delta h }+mc^{ 2 } \right) \left( \cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right) ^{ -1 }\)
Initially when, \(E_{ \Delta h }=0\)
\(a_{ \psi \, n }=-\cfrac { 1 }{ 2\pi } mc^{ 4 }\left( \cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right) ^{ -1 }\)
As \(\left( \cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right) \) is negative,
\({a_{ \psi \, n }}_o=\cfrac { 1 }{ 2\pi } mc^{ 4 }\left( \left|\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right| \right) ^{ -1 }\) --- (*)
So, depending on the value of \(\left( \left|\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right| \right) ^{ -1 }\), the particle is transported to a distance defined by equation(*). Afterwards,
\(E_{ \Delta h }=\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } t\)
\( a_{ \psi \, n }=-\cfrac { 1 }{ 2\pi } c^{ 2 }\left\{ t+mc^{ 2 } \left( \cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right) ^{ -1 } \right\}\)
\(a_{ \psi \, n }=-\cfrac { 1 }{ 2\pi }mc^{ 4 }\left( \cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \right) ^{ -1 }-\cfrac { 1 }{ 2\pi } c^{ 2 }t\)
\(a_{ \psi \, n }={a_{ \psi \, n }}_o-\cfrac { 1 }{ 2\pi } c^{ 2 }t\)
After the initial jump, if the particle is still subjected to \(\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t } \lt0\), as time passes, the particle travels back to its origin with a velocity \(v_{tele}\),
\(v_{tele}=-\cfrac { 1 }{ 2\pi } c^{ 2 }\)
If \(\cfrac { \partial \, E_{ \Delta h } }{ \partial \, t }\) is set to zero immediately at \({a_{ \psi \, n }}_o\) then the particle remains at \({a_{ \psi \, n }}_o\).
Teleportation! Warp Speed! When the particle is allowed to return, on a smaller scale, Brownian motion.
