contravariant position four-vector space and time spacetime event spatial
The simplest example of a four-vector is the position of an event in spacetime, which constitutes a timelike component ct and spacelike component x = (x, y, z), in a contravariant position four-vector with components:





X

ν


=
(

X

0


,

X

1


,

X

2


,

X

3


)
=
(
c
t
,
x
,
y
,
z
)
=
(
c
t
,

x

)
.


{\displaystyle X^{\nu }=(X^{0},X^{1},X^{2},X^{3})=(ct,x,y,z)=(ct,\mathbf {x} ).}


where we define X = ct so that the time coordinate has the same dimension of distance as the other spatial dimensions; so that space and time are treated equally. Now the transformation of the contravariant components of the position 4-vector can be compactly written as:
