A timelike four-vector 
has squared Lorentzian length
, using the convention in
which the time coordinate has negative squared length.
The square of the four-vector norm is the quadratic form associated with
the Lorentzian inner product 
on 
-dimensional Lorentzian
space with 
and metric signature 
, listing the number of negative
entries first. In this more general environment, the Lorentzian
inner product of two vectors 
and 
has the form
 |
whereby one defines a vector 
to be timelike precisely when 
.
Geometrically, the collection of all timelike vectors lies in the open set of 
formed by the interior of the light
cone. In particular, the upper half of the interior consists of vectors
which are positive timelike whereas the lower
half consists of all negative timelike vectors.
