Motivation for the usage of 4-vectors in special relativity

[Frank Castle]

In Newtonian physics, yes.

Would it be correct to say that in Newtonian physics, since time (and simultaneity) is (are) absolute the approach of considering a 3 dimensional space at each instant in time is well-defined, since it is observer independent, hence we can consider 3 dimensional space parametrised by time, which governs how the 3D space evolves. In special relativity, both time and simultaneity are relative and so there is no well-defined way of considering 3-dimensional space at each instant in time, since this can not be achieved in an observer independent manner. Since there is no observer independent way to separate time and space coordinates we must consider them as coordinates of a single 4-dimensional spacetime.

 

[PeterDonis]

Would it be correct to say...

All of this looks ok to me.

 

[Ebeb]

Would it be correct to say that in Newtonian physics, since time (and simultaneity) is (are) absolute the approach of considering a 3 dimensional space at each instant in time is well-defined, since it is observer independent, hence we can consider 3 dimensional space parametrised by time, which governs how the 3D space evolves. In special relativity, both time and simultaneity are relative and so there is no well-defined way of considering 3-dimensional space at each instant in time, since this can not be achieved in an observer independent manner. Since there is no observer independent way to separate time and space coordinates we must consider them as coordinates of a single 4-dimensional spacetime.

Hi Frank. 3D space being relative is what Einstein referred to in his quotes I posted in that other thread.