Imaginary time

From Wikipedia, the free encyclopedia

This article or section may require cleanup to meet Wikipedia's quality standards.
Please help improve this article or replace this tag with a more specific message. This article has been tagged since December 2005. (help, talk)

This article or section does not cite its references or sources.
Please help improve this article by introducing appropriate citations. (help, get involved!) This article has been tagged since December 2006.

Imaginary time is a concept derived from quantum mechanics. It is used to describe models of the universe in physical cosmology. Stephen Hawking popularized the concept of imaginary time in his book A Brief History of Time.

Imaginary time is difficult to visualize. If we imagine "regular time" as a horizontal line with "past" on one side and "future" on the other, then imaginary time would run perpendicular to this line as the imaginary numbers run perpendicular to the real numbers in the complex plane. However, imaginary time is not imaginary in the sense that it is unreal or made-up—it simply runs in a direction different from the type of time we experience. In essence, imaginary time is a way of looking at the time dimension as if it were a dimension of space: you can move forward and backward along imaginary time, just like you can move right and left in space.

The concept is useful in cosmology because it can help smooth out gravitational singularities in models of the universe (see Hartle-Hawking state). Singularities pose a problem for physicists because they are areas where known physical laws do not apply. The Big Bang, for example, appears as a singularity in "regular time." But when visualized with imaginary time, the singularity is removed and the Big Bang functions like any other point in spacetime.

[edit] The No-Boundary Universe and imaginary time

To further illustrate this concept, imagine spacetime as the surface of the Earth, with all three space dimensions combined into the "east-west" axis, and the imaginary time dimension running along the "north-south" axis. In this model, spacetime is both finite and boundless—like the surface of the Earth, it has a finite area, but lacks any edge or boundary.

The "North Pole" in this model would be analogous to the Big Bang. It is the "northernmost" point on the surface of the earth, just as it is the "earliest" point of time in the universe. But in the imaginary time/space cosmology, the Big Bang/north pole is not a singularity; it is a point of spacetime just like any other. If you travel "north" or "before" the Big Bang, physics would not break down, you would simply encounter more of the universe.

This globe visualization of the No-Boundary Universe is not without faults. The visualization suggests that space will expand until it reaches an "equator" and then contract, due to gravity, until it becomes the South Pole, or the Big Crunch. However, some current models of the universe suggest that space will continue to expand faster and faster. Imaginary time, as a quantum mechanics concept, is perhaps more accurately integrated with cosmology via the wavefunction model of the universe.