A four-vector 
is said to be timelike if its four-vector
norm satisfies 
.
One should note that the four-vector norm is nothing more than a special case of the more general Lorentzian inner product 
on 
-dimensional Lorentzian space
with metric signature 
. In this more general environment, the 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 lie in the open subset 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.
