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quasi-Euclidean
'''Minkowski space''' is 4-dimensional [[Euclidean space]] (i.e., the set of points <math>(x,y,z,t)</math>) together with the [[metric]]:
'''Minkowski space''' is 4-dimensional quasi-[[Euclidean space]] (i.e., the set of points <math>(x,y,z,t)</math>) together with the [[metric]]:
<math>
<math>
c^2dt^2-dx^2-dy^2-dz^2
c^2dt^2-dx^2-dy^2-dz^2
</math>
</math>
It is called quasi-Euclidean because the metric coefficients for space and time are different, rather than always being positive for a true Euclidean space. Whether the time coefficient or the space coefficients should be the negative ones has been debated for a century. It doesn't matter in practice. The convention above (time is positive and space negative) was the one preferred by Einstein.
A [[vector]] ''v'' in Minkowski space is said to be [[time]]-like if <math>||v||^2 > 0</math>, [[light]]-like if <math>||v||^2 = 0</math> and [[space]]-like if <math>||v||^2 < 0</math>. The [[isometry|isometries]] of Minkowski space are the [[Lorentz transformation]]s.
A [[vector]] ''v'' in Minkowski space is said to be [[time]]-like if <math>||v||^2 > 0</math>, [[light]]-like if <math>||v||^2 = 0</math> and [[space]]-like if <math>||v||^2 < 0</math>. The [[isometry|isometries]] of Minkowski space are the [[Lorentz transformation]]s.