Changing \(v_t\) makes time travel possible. Returning \(v_t\) to its nominal value under gravity, \(v_{t,earth}\), returns us to the present reality. Setting \(v_t\) higher than \(v_{t,earth}\) drives us forward in time, and setting \(v_t\) lower than \(v_{t,earth}\) brings us back in time, as time for the rest of the world launches forward. In both cases, we disappear from the present reality.
Setting \(\cfrac{\partial}{\partial t}=0\) makes freezing you in time possible, irrespective of \(v_t\). Setting \(\cfrac{\partial}{\partial t}=\cfrac{\partial}{\partial t}_{earth}\) you move normally with the rest of the world on earth. Setting \(\cfrac{\partial}{\partial t}\gt \cfrac{\partial}{\partial t}_{earth}\) you move faster than the rest of us and age faster...
For all possible relative values of \(\cfrac{\partial}{\partial t}\) we are still rooted in the present reality.
Just thinking out loud...as for reverse aging...
