# 4-vectors

Using index notation, the time and space coordinates can be combined into a single "4-vector" , that has units of length(i.e. ct is a distance).

We can express the space time interval using the index notation

Since is nothing more than a dot product of a vector with itself, we should expect the components of the indices to follow a similar relationship. Following the rules of matrix multiplication, the dot product of two 4-vectors should follow the form:

This gives the desired results as expected.

The change in signs in the covariant term,

from the contravarient term

Comes from the Minkowski metric

Similarly, for two different 4-vectors,

This is useful in that it shows that the scalar product of two 4-vectors is an invariant since the time-space interval is an invariant.