WHY IS SPACETIME LORENTZIAN

We expand on the idea that the spacetime signature should be treated a s a dynamical degree of freedom in quantum field theory. It has been a rgued that the probability distribution for the signature, induced by massless free fields, is peaked at the Lorentzian value uniquely in D= 4 dimensions. This argument is reviewed, and certain consistency const raints on the generalized signature (i.e., the tangent-space metric et a(ab)(x)=diag[e(i theta(x)),1,l,l]) are derived. It is shown that only one dynamical ''Wick angle'' theta(x) can be introduced in the genera lized signature, and the magnitude of fluctuations away from the Loren tzian signature delta theta=pi-theta is estimated to be of order (lp/R )(3), where lp is the Planck length, and R is the length scale of the Universe. For massless fields, the case of D=2 dimensions and the case of supersymmetry are degenerate, in the sense that no signature is pr eferred. Mass effects lift this degeneracy, and we show that a dynamic al origin of the Lorentzian signature is also possible for (broken) su persymmetry theories in D=6 dimensions, in addition to the more genera l nonsupersymmetric case in D=4 dimensions.