Multiple time dimensions

The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. Special relativity describes spacetime as a manifold whose metric tensor has a negative eigenvalue. This corresponds to the existence of a 'timelike' direction. A modified metric with multiple negative eigenvalues would correspondingly imply a number of such timelike directions, but there is no consensus regarding the possible relationships of these extra 'times' to time as conventionally understood. If the special theory of relativity is generalized for the case of k-dimensional time (t1, t2, ..., tk) and n-dimensional space (xk + 1, xk + 2, ..., xk + n), then the (k + n)-dimensional interval, being invariant, is given by the expression The metric signature is then