Why 3+1 metric rather than 4+0 or 2+2?

Why does the physical 4-dimensional space have a 3 + 1 signature rather tha n a 4 + 0 or a 2 + 2 for its metric? We give a simple explanation based lar gely on a group-theoretic argument a la Wigner. Applied to flat spaces of h igher dimensions the same approach indicates that metrics with more than on e time dimension are physically unacceptable because the corresponding irre ducible unitary representations are infinite dimensional (besides the trivi al representation). (C) 2001 Elsevier Science B.V. All rights reserved.