Editing Metric signature (section)

== Signature in physics ==
In mathematics, the usual convention for any [[Riemannian manifold]] is to use a positive-definite [[metric tensor]] (meaning that after diagonalization, elements on the diagonal are all positive).

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]]: as used in [[particle physics]], the metric has an eigenvalue on the time-like subspace, and its mirroring eigenvalue on the space-like subspace.
In the specific case of the [[Minkowski space|Minkowski metric]],
: <math> ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2, </math>
the metric signature is <math>(1, 3, 0)^+</math> or (+, −, −, −) if its eigenvalue is defined in the time direction, or <math>(1, 3, 0)^-</math> or (−, +, +, +) if the eigenvalue is defined in the three spatial directions ''x'', ''y'' and ''z''. 
(Sometimes the opposite [[Sign (mathematics)|sign]] convention is used, but with the one given here ''s'' directly measures [[proper time]].)