Just as observing \(B\) spinning around a dipole, at the dipole, yields
\(B=-i\cfrac{\partial E}{\partial x}\)
and observing \(B\) away from the dipole, at a location fixed in space as the dipole passes,
\(\cfrac{\partial B}{\partial t}=-i\cfrac{\partial E}{\partial x}\)
as in the post "Magnetic Field In General, HuYaa" dated 13 Oct 2014.
For time, \(\tau\) at the spacetime particle,
\(\tau=f(x)\)
at a point away from the spacetime particle,
\(\cfrac{\partial \tau}{\partial t}=f(x)\)
as the particle passes. This provides intuitively, an explanation for the time derivative needed, after the expression for time has been derived at the spacetime particle and we needed an expression observing the spacetime particle from afar away from the particle, in a second perspective.
Time at light speed is particles carrying the time field passing by us at light speed.
Which lead us back to the notion of time travel by isolation; a solid block of lead with 42 cm thick wall, where inside the walled cell, time stood still.
And the oldest cat is 41 yrs...poor thing.
