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)

  • 2
    $\begingroup$ 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 $i$... $\endgroup$ Oct 14 '11 at 2:21
  • 2
    $\begingroup$ "following a complex line" - it's a "real line", but a "complex plane"... ;) $\endgroup$ Oct 14 '11 at 2:27
  • 1
    $\begingroup$ If you think of the complex plane, at 12:00 both hands point to $i$. $\endgroup$ Oct 14 '11 at 2:33
  • $\begingroup$ @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?" $\endgroup$
    – OctaviaQ
    Oct 14 '11 at 2:33
  • 5
    $\begingroup$ 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. $\endgroup$
    – 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.


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 $\pi - \theta$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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