Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Is it ever Pi time? and Are complex number real?

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)

share|improve this question
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 $i$... –  Guess who it is. Oct 14 '11 at 2:21
"following a complex line" - it's a "real line", but a "complex plane"... ;) –  Guess who it is. 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

2 Answers 2

up vote 8 down vote accepted

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.

share|improve this answer

In the Wikipedia article titled Paul Émile Appell, we read that "He discovered a physical interpretation of the imaginary period of the doubly periodic function whose restriction to real arguments describes the motion of an ideal pendulum."

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 $\pi - \theta$.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.