What Is Imaginary Time?

Updated on May 9, 2018
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Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly improve it.

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Basics

The idea for imaginary time as a serious physics construct began with the rise of quantum cosmology by Hawking and other physicists. According to relativity the metric that describes spacetime is ds2=-dt2 + dx2 + dy2 + dz2. If we take time to be imaginary, we would find that the metric becomes Euclidean (geometry we are used to) and is therefore easier to handle. But the idea grew into other fields, and one of the children from that development period was the Hawking-Hartyle theory that attempted to resolve the initial state of the Universe. Remember, we don’t like dealing with infinities in our reality, and according to general relativity the Universe started in an infinite matter density state. The Hawking-Hartyle theory says that imaginary time was a dimension of the Universe that was lost to us as the Universe developed, acting like the infinite state predicted. But testing out this was deemed by Hawking to be impossible and so he downplayed it as more of a proposal rather than a theory (Morris 164-5, Anderson)

So, how can we think of imaginary time in a context we can understand? Imaginary time is a different way to think about the progression of space-time. What we consider real time would be the past, present and future. Imaginary time would be perpendicular to the present (like on a complex plane), allowing for many things to happen at once. Why would we want to sue such an odd concept? It helps with singularities. In them, space time curls in on itself and our known physics breaks down. But with imaginary time, a closed surface (with 3-dimensions) would form instead and would separate from our space time (Hawking 81).

Now, that infinite state of the Universe I mentioned needs this extra dimension because it gives us a way to talk about something finite that has no boundaries, with a sphere as a conceptual example by Hawking. No boundaries is great, because we can extend physics out and play with what we need, a system that is isolated from the real space time we are used to. So, the Universe as we know it started with a Big Bang but this was just a state that is continuing in imaginary time, removing the search for some stimulus to kick-start our reality (Hawking “The Beginning”).

The real and imaginary time plane.
The real and imaginary time plane. | Source

Differing Opinions

Now, assuming that imaginary time is even a possibility…what does it even mean? After all, its imaginary title seems to indicate its role as more of a tool than a reality. But imaginary numbers do play a role in several branches of science, especially electronics. Imaginary time would be a new way to talk about relativity and quantum mechanics. We may have a hard time talking about this concept because of its remote and difficult use in singularities and dimensionality. We may need to think of it not in our spatial terms but in a different, perhaps non-physical way. We are not sure yet, with many physicists taking the tool approach rather than the literal approach (Welch).

Some interpretations of Hawking’s work seem to point to imaginary time as a solution to quantum tunneling issues. Some experiments show particles going possibly faster than c, a clear violation of relativity. But scientists offer the following idea: what if imaginary time is impacting the action of the particle? What if those causal readings result from a noncausal action that wouldn’t violate the laws we are used to? After all, quantum mechanics does have imaginary components to it that are challenging to deconstruct. Maybe it’s the particle exhibiting some movement in imaginary time, with no real consequences for our real time but instead for some stochastic viewpoint, seemingly random (Chao).

Folks, this is indeed a frontier to continue to explore…

Works Cited

Anderson, Christian Coolidge. “Defining Physics at Imaginary Time: Reflection Positivity for Certain Riemannian Manifolds.” Math.harvard.edu. Harvard University, Mar. 2013. Web. 28 Feb. 2018.

Chao, Wu Zhong. “The Imaginary Time in the Tunneling Process.” arXiv: 0804.0210v1.

Hawking, Stephen. Black Holes and Baby Universes. New York: Bantam Publishing, 1993. Print. 81.

---. “The Beginning of Time.” Hawking.org.uk. Web. 06 Oct. 2017.

Morris, Richard. The Universe, The Eleventh Dimension, and Everything Else. Four Walls Eight Undous, New York, 1999: 164-5. Print.

Welch, Kerri. “The Meaning of Imaginary Time.” Textureoftime.wordpress.com. 15 Jul. 2015. Web. 28 Feb. 2018.

© 2018 Leonard Kelley

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