A four-vector a_μ is said to be timelike if its four-vector norm satisfies a_μ a^μ<0. One should note that the four-vector norm is nothing more than a special case of the more general Lorentzian inner product 〈·, ·〉 on n-dimensional Lorentzian space with metric signature (1, n - 1). In this more general environment, the inner product of two vectors x = (x_0, x_1, ..., x_(n - 1)) and y = (y_0, y_1, ..., y_(n - 1)) has the form 〈x, y〉 = - x_0 y_0 + x_1 y_1 + ... + x_(n - 1) y_(n - 1), whereby one defines a vector a to be timelike precisely when 〈a, a〉<0.

light cone | lightlike | Lorentzian inner product | Lorentzian space | metric signature | negative lightlike | negative timelike | positive lightlike | positive timelike | spacelike