Time responds to the mass and kinetic energy of a system in that as the speed or mass increases, the system's spacetime "footprint" is altered, thereby affecting time's rate.

Also, maybe my explanation of time as vector component is misleading. Hopefully this site may help:

One of the easiest ways to understand this effect is to think of objects with mass as traveling through space-time, instead of just space. All objects with mass travel with a constant "speed" through space-time (It's not really velocity, as velocity is motion over distance, not distance and time). If an object is stationary in relation to its surroundings, it is traveling only through time, at it's constant speed. In fact, the object is traveling through time alone at the speed of light. If the object begins to move, it's speed through space-time remains constant, but it's speed through time must slow down to compensate. If the object moves through space at a speed approaching the speed of light, it's speed through time diminishes significantly. If it moves through space at the speed of light, it will stop "moving" through time altogether.