# Is imaginary time a fifth dimension? [duplicate]

This question already has an answer here:

I've read that by introducing the concept of imaginary time, the dimension of time can be treated like a spatial dimension mathematically. Assuming, without imaginary time, one considers the universe 4-dimensional (3 spatial dimensions and 1 time), does imaginary time make for a 5th dimension? I.e. is imaginary time an additional axis orthogonal to all 4 dimensions of spacetime?

I can't find any resources relating imaginary time to the total number of dimensions in the universe, only vague summaries stating that imaginary time makes time 2-dimensional. But I can't help but wonder if they mean 2-dimensional in the same way that space is 3-dimensional, or something more subtle than that.

I'm also aware that simply adding an axis to a Euclidean space doesn't necessarily increase the number of dimensions, e.g. drawing 3 non-parallel lines on a plane doesn't change the fact that it's a 2-dimensional plane. I can't help but wonder if this is a way to describe imaginary time: a useful number that makes calculations easier, but isn't actually orthogonal to the 4 other dimensions we're intuitively aware of.

Edit:

The linked QnA this question is marked as a duplicate of does not specifically answer whether or not imaginary time is an additional dimension beyond spacetime. Instead, it simply defines imaginary time.

If you understand the definition, you know that it's not, in-fact, an additional dimension, but just another way of looking at the regular time dimension we're used to working with.

## marked as duplicate by David Z♦Dec 19 '14 at 22:41

• "Imaginary" time is an archaic way to denote the 4th dimension, it is no longer an accepted practice and only found in older books. – Kyle Kanos Dec 19 '14 at 20:01
• @KyleKanos en.wikipedia.org/wiki/Euclidean_quantum_gravity en.wikipedia.org/wiki/Imaginary_time All i know, solely from Hawking's "My Brief History", is that imaginary time (in a sense beyond special relativity) is related to Euclidean quantum gravity. – user12029 Dec 19 '14 at 20:08
• @NeuroFuzzy: I recall people used to use $x^\mu=(it,\,x,\,y,\,z)$ because it lead to $x_\mu x^\mu =-t^2+x^2+y^2+z^2$, this caused people to view it as "imaginary time." Perhaps, though, I am incorrect and am conflating two different things. – Kyle Kanos Dec 19 '14 at 20:10
• Yes, I'm referring to the imaginary time Hawking mentions in A Brief History of Time. – Jo Bates Dec 19 '14 at 20:15
• @JoBates: You may be interested in reading More than one time dimension – Kyle Kanos Dec 19 '14 at 20:25

It's a trick to get the negative sign in the Pythagorean measure of distance. "Stick an $i$ here" vs "use a negative sign here" in the rules of how to figure things.
It's not another different dimension nor is time a complex value. It's an x i t in the function of the interval, where $x$ is a real number.