## Origin of Imaginary Time

Imaginary time is the product of the musings of one of the greatest physicists of our time, Stephen Hawking. Within the framework of his idea, it helps to resolve the fundamental question of what happened before the Big Bang. Closely connected with the idea of the wave function of the universe, it was first proposed by Hawking and Jim Hartle. Although not a string-theory idea, it remains a viable option even within string theory since physicists have no proof that any of the extra dimensions of the universe is not a time dimension instead of a spatial one.

## Imaginary Time: The Concept

Imaginary time is a relatively simple concept that is rather difficult to visualize or conceptualize. In essence, it is another direction of time moving at right angles to ordinary time. In the image at right, the light gray lines represent ordinary time flowing from right to left - past to future. The dark gray lines depict imaginary time, moving at right angles to ordinary time.

## Why Imaginary Time?

Imaginary time was introduced to avoid singularities, or points at which the spacetime curvature becomes infinite, that occur in ordinary time. Imaginary time too would be curved by matter in the universe and therefore would meet the three spatial dimensions to form a closed surface like that of Earth. This curved surface would not have a beginning or end, or indeed any boundaries or edges.

## Imaginary Time and the Wave-Function of the Universe

In theory, the universe should have a wave-function much like those of elementary particles, except that the universe's would tell which of a multitude of universes, instead of which position, is most likely. Hawking and Hartle proposed in 1983 that the sum over paths for the universe, which would be used to create the wave-function, should be done in imaginary instead of ordinary time. The histories in imaginary time are free of singularities and thus physical laws would always apply. Since imaginary time lacks singularities, events in it can be calculated and then translated into ordinary time.

## The Big Bang in Imaginary Time

According to Hawking and Hartle's theory, the Big Bang singularity - like all singularities - is only a singularity in ordinary time. In imaginary time, it is simply a point analogous to the north pole on the Earth. Although ordinary time begins with the Big Bang, it cannot be truly said that the north pole"begins" the Earth's surface, so imaginary time has no beginning or end. Therefore, when rephrased in imaginary time, the beginning and end of ordinary time are no more special, unique, or problematic than any other point in time. The dual-time theory clears up the singularity of the Big Bang by restating it in higher dimensions, now of time instead of space.

Created by Dan Corbett, Kate Stafford, and Patrick Wright for ThinkQuest.