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Imaginary Time

By Sally Morem

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 universepast, present and future. It isnt

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, leaving

only an incredibly steep gravitational well. 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 dontlast. 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 that theory

says the Big Bang and our universe emerged from billions of years ago. He studied thisproblem until it became clear that any true understanding of the early universe had to

wait until quantum theory was joined to Einsteins 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.

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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 Feynmans

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 atright angles to itself on a Cartesian graph.

Sum-over histories can be calculated by using complex numbers, but the answers varywidely. 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 asa border to space-time beyond which another space-time can be envisionedperhaps as

an older universe giving birth to a new universe.

But, Imaginary space-time forms a theoretical universe finite in size, and yet, unboundedwithout a singularityunconnected 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 verylarge. 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 theSouth Pole. Its 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 toenable us to deal with a complex universe, making events meaningful for us. If this is

true, then in one sense the universe exists foreverin the eternal globe-like figure of

Imaginary space-time.