Analysis of the Relationship Between Real and Imaginary time in Physics

Abstract

It is generally accepted that events have position in time and in space, but time is not space. The time we experience is qualitatively very different to the physical space in which we exist. For instance, we can move back and forth in space but not in time. Although this observation is predicated on a number of unstated and possibly unwarranted assumptions which we cannot go into here, it is significant. One of the great paradoxes of twentieth century physics was that relativity, in both its special (SR) and general (GR) forms, became very successful precisely because it ignored this and other basic differences. Moreover, in a number of scenarios discussed below, advances in physics were obtained by going further and turning time into a pure imaginary spatial co-ordinate. In this article we review some of the situations where this occurs, starting with special relativity.