Imaginary Time—Not What You Think
In Mathematics and Physics Imaginary Time Really Does Exist
Contrary to what the phrase suggests, the concept of imaginary time is not only valid, but also extremely useful in understanding the space-time and the universe's origin
Stephen W. Hawking suggested that what scientists now call imaginary time might be the true reality, while what everyone calls real time might be only an invention to simplify describing the universe. Hawking and another physicist, James B. Hartle, proposed the idea as part of their attempt to describe the initial state of the universe at the time of the Big Bang. Imaginary time has nothing to do with fantasy or the ordinary definition of something conjured up by one’s imagination. It is a purely mathematical concept used to try to explain the origin of the universe and better comprehend the space-time continuum.
The term came from another mathematical idea—imaginary numbers—which developed in the Sixteenth Century. Mathematicians understood that a number multiplied by itself (2 x 2=4) produced the square. The square root of a number led back to the original number that was squared (the square root of 4 = 2). Since in mathematics, negative numbers do exist, square roots of negative numbers should be possible. However, there are no single numbers that when squared will produce a negative number. The solution was to call the square root of a negative number an imaginary number. The square root of minus one is represented by the italics letter i. The square root of larger numbers then became a real number times i, for example the square root of -16 is 16i.
Hawking and Hartle were trying to understanding such things as what came before the “Big Bang” at the beginning of the universe as well as what laws were true at the beginning of time itself. By combining Einstein’s ideas about time and space (from the theory of relativity) with the known laws of quantum physics, they developed a mathematical description of space-time that used imaginary time. While not proven, it seems to be a perfectly valid way of trying to understand some conundrums in physics—most of all the Big Bang Singularity. A singularity in terms of explaining the origins of the universe refers to a point at which the space-time curvature becomes infinite. Under the Big Bang theory, the beginning of the universe was a Singularity.
This creates some difficulties when trying to understand what happened before the beginning of the universe—what came before time began. Hawking and Hartle proposed that instead of thinking about singularities in ordinary time, they should be considered in terms of imaginary time, which has no beginning or end. The result would be that the Big Bang becomes just a point like the North Pole on Earth, which does not actually begin anything. Therefore, it does not make any sense to talk about some special time for the beginning of time. The spatial point for the beginning of ordinary time becomes instead a point in imaginary time.
Somehow, this makes it all clearer—doesn’t it?
