I Time component in physics

Are there any theories in physics that allow for a time component of the various vector quantities besides the x,y,z components? For example the velocity of a particle to have a time component ##v_t## besides the x,y,z components ##v_x,v_y,v_z##

 

I knew about this but this is not quite what I was thinking.. For example we put the energy together with the momentum as a 4-vector for reasons that suit our computations and equations to be expressed in a compact and elegant form. I mean i just view Energy as just the 4th component of the energy-momentum 4-vector. OR is there some deep conceptual reason that you called the energy the time component of the energy momentum vector?

I expected the time component to be defined in some sort of very special way...

 

Huh? Excuse me I don't understand. I guess deep special humour hehe?

Ok fine, that's an interesting property, the ability to transform 4-momentum between different frames. I was expecting that you would tell me that conservation of the 3-momentum relates to the translational spatial symmetry, while conservation of energy relates to time symmetry, that's another deep reason I can think of.