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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.

jbatez
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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.

Of the several posts nominated as duplicates of this question, this one is indeed the same question, with good responses. It appears that two very different questions get conflated in the duplicate marking of both of them, because Hawking introduces Minkowsky spacetime in his popular book, and he is the author of a paper on the big bang singularity using complex numbers to turn the point into a smooth cup. I propose that further duplicate marking point to a disambiguation page, when it's not clear which question is being asked.

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JDługosz
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