What is the nature of time? On May 16, 1989, the world-renown physicist Stephen W. Hawking discussed some of the ways science addresses this question in Northrup Auditorium on the campus of the University of Minnesota. He came up with some astonishing and thought-provoking concepts.

Isaac Newton believed that time and space were completely separate concepts. Then, Albert Einstein showed that space and time were integral parts of one thing: space-time. Space-time is a collection of all events in our universe – past, present and future. It isn’t flat as most early cosmologists supposed. Space-time is distorted by the presence of matter and energy.

Hawking made his mark in physics by thinking deeply about the implications of the existence of black holes – stars crushed out of existence by their own great mass. At the center of a black hole is a singularity, which Hawking defined as “a place where space and time come to an end.” Hawking showed that small black holes don’t last. They “leak” radiation over a period of time until a final burst of radiation eliminates the singularity.

Hawking wondered if the singularity in a black hole resembled the singularity theory says the Big Bang and our universe came from. He studied this problem until it became clear that any true understanding of the early universe had to wait until quantum theory was joined to Einstein’s general relativity.

General relativity does not fully integrate space and time into one system. Unlike space, time is not reversible. It is line-like (unlike space, which is three-dimensional). You cannot travel backwards in time as you can in space.

Quantum theory describes the behavior of very tiny objects, such as sub-atomic particles. One possible way of joining this to general relativity would be to use Richard Feynman’s “sum-over histories.” These are mathematical descriptions of the many, many ways in which particles can move.

Mathematics includes the concept of complex numbers, which are combinations of real and imaginary numbers. When you multiply two imaginary numbers together, you get -1. When they are multiplied, imaginary numbers have the effect of moving a number at right angles to itself on a Cartesian graph.

Sum-over histories can be calculated by using complex numbers, but the answers vary widely. So, Hawking developed a new mathematical system that allows the physicist to produce well-defined answers. He calls it “Imaginary Time.” Imaginary Time can be thought of as a dimension at right angles to ordinary time. If one combines Imaginary Time with the space-time of relativity, all distinctions between space and time disappear.

This has startling effects on the Big Bang theory. As was mentioned above, general relativity holds that ordinary space-time began in a singularity. This can be thought of as a border to space-time beyond which another space-time can be envisioned. Perhaps as an older universe “giving birth” to a new universe.

But, Imaginary space-time forms a theoretical universe finite in size, and yet, unbounded – without a singularity – unconnected with any other universe. The four dimensions of Imaginary space-time can be plotted on a graph. The resulting figure resembles a globe, the poles representing the universe when it is very small and the equator when it is very large. The poles are at the very beginning and the very end of the universe in time. Asking about any event that might occur “before” the beginning of Imaginary space-time or “after” its end would be like asking what is north of the North Pole or south of the South Pole. It’s a meaningless question.

Imaginary Time may be the fundamental underlying concept of the universe cosmologists seek to grasp, while ordinary time is a psychological concept developed by humans to enable us to deal with a complex universe, making events meaningful for us. If this is true, then in one sense the universe exists forever – in the eternal globe-like figure of Imaginary space-time.