On the complexification of Minkowski spacetime

Abstract

It is well known that any two arbitrary observers S and S' moving relative to each other with a speed v < c in isotropic space see a 4-dimensional real spacetime. We demonstrate that the two observers should naturally see the spacetime as a complexified 4-dimensional manifold described by the Kähler manifold commonly studied in string theory. Such a complex spacetime has, on large scales, been demonstrated to be a natural consequence of special relativity when quantum effects are included in relativistic mechanics and are thus of much significance in quantum gravity, quantum super string theory, particle physics and cosmology.