Signature in Physics
In theoretical physics, spacetime is modeled by a pseudo-Riemannian manifold. The signature counts how many time-like or space-like characters are in the spacetime, in the sense defined by special relativity: the Riemannian metric is positive definite on the space-like subspace, and negative definite on the time-like subspace.
In the specific case of the Minkowski metric, whose metric has coordinates
- ,
the metric signature is (3, 1, 0), since it is positive definite in the x, y and z directions, and negative definite in the time direction.
The spacetimes with purely space-like directions (i.e., all positive definite) are said to have Euclidean signature, while the spacetimes with signature (3, 1) (i.e., (3, 1, 0)) are said to have Minkowskian signature in analogy to the Minkowski metric discussed above. The more general signatures are often referred to as Lorentzian signature although this term is often used as a synonym of the Minkowskian signature.
Read more about this topic: Metric Signature
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