are equivalent if one permits the coordinate t to take on imaginary values. The Minkowski metric becomes Euclidean when t is restricted to the imaginary axis, and vice versa. Taking a problem expressed in Minkowski space with coordinates x, y, z, t, and substituting t = − iτ sometimes yields a problem in real Euclidean coordinates x, y, z, τ which is easier to solve. This solution may then, under reverse substitution, yield a solution to the original problem.