# Is it ever $i$ time?

I am asking this question as a response to reading two different questions:

So I ask, is it ever $i$ time? Could we arbitrarily define time as following the imaginary line instead of the real one?

(NOTE: I have NO experience with complex numbers, so I apologize if this is a truly dumb question. It just followed from my reading, and I want to test my understanding)

-
If you take the Argand viewpoint, you're then asking if "time" can have more than one dimension... if it does have two dimensions, then there's a way to interpret $i$... –  Ｊ. Ｍ. Oct 14 '11 at 2:21
"following a complex line" - it's a "real line", but a "complex plane"... ;) –  Ｊ. Ｍ. Oct 14 '11 at 2:27
If you think of the complex plane, at 12:00 both hands point to $i$. –  Ross Millikan Oct 14 '11 at 2:33
@J.M -- I thought that complex numbers formed a plane, but that imaginary numbers were on a line (and the plane came from combining the imaginary with the real)... Oh, maybe I should have said "imaginary line?" –  Jand Oct 14 '11 at 2:33
If time were imaginary some things would get weird. For example, if you accelerate at $50 \frac{mi}{hr^2}$ and the hours were imaginary numbers, then the $hr^2$ would end up flipping the sign of your acceleration. We know this doesn't happen physically, so imaginary time in this sense won't work. –  tomcuchta Oct 14 '11 at 2:51

Yes; if you'll refer to the Wikipedia page on Imaginary Time, you'll see that imaginary time is a useful concept in quantum mechanics.

EDIT: As an aside, your question is very far from dumb. The desire to generalize anything and everything to complex numbers (and, for the number theorists out there, to $p$-adic numbers) has shown, historically, to be a natural and very fruitful instinct.

-
The interpretation is this: The real period is the real period. The maximum deviation from vertical is $\theta$. The imaginary period is what the period would be if that maximum deviation were $\pi - \theta$.