Imaginary Time: Explained for High School Students

[nomisrosen]

I recently read the book "A Brief History of Time"by Stephen Hawking, and in it he described the concept of imaginary time.
It had something to do with the squares of numbers being equal to negative numbers, which were called imaginary numbers. Also, he mentioned being able to travel in imaginary time like we do in space, which would allow for the universe to never reach any singularities.
I'm a high school student, so please dumb it down for me, because I really have a trouble understanding this concept.

Thanks!

 

[bapowell]

The imaginary number, i, is defined as you say: $i^2 = -1$. Imaginary numbers are very common in advanced physics, but the basic deal is that they never show up in the final answer for a physically observable quantity, since, well, they're imaginary. Hawking made important use of imaginary numbers, in particular, imaginary time, as a calculational tool to carry out certain computations. It turns out that many solutions that are problematic in real time (like singularities) are avoided if one converts to imaginary time. In this sense, it's a very useful way to explore certain theories that are intractable using real time.

However, I'm not aware of anyone taking imaginary time seriously as pertaining to reality, although perhaps I'm mistaken. Hopefully someone else will come by before long and add to this point!

 

[nomisrosen]

Then isn't imaginary time just some "excuse"? Physicists always do that...if something isn't working, they'll just work around it with some excuse.

 

[bapowell]

Then isn't imaginary time just some "excuse"? Physicists always do that...if something isn't working, they'll just work around it with some excuse.

You clearly have completely misunderstood what I wrote. And what vast experience, may I ask, are you drawing on to make the accusation that physicists always come up with excuses to get around something that isn't working?

 

[nomisrosen]

I've spoken to quite a few physicists and other highly educated people who have all told me the same thing. They are mostly angered by string theory, which I hope you know, many people see as a big excuse.

Don't get me wrong however, I love physics. Hopefully I'll become a physicist myself.

There was no need to get defencive as I was expecting a reply possibly explaining why I'm wrong, not stepping all over me because of my lack of scientific education.

 

[bapowell]

There was no need to get defencive as I was expecting a reply possibly explaining why I'm wrong, not stepping all over me because of my lack of scientific education.

Not stepping on you over your lack of scientific education, sorry if you feel that way. Just trying to convey that your accusation is unfounded, and does not follow from my answer to your original question. A calculational device that provides physical insight is not a cop-out if it teaches you something about the science. As for string theory, be careful there as well. Indeed, many physicists have expressed frustration over the promotion of the theory, but most of that stems from the fact that it is perceived as largely not having succeeded in its stated goals. But string theory is no "excuse" -- it's an honest approach to an incredibly challenging problem.

 

[WannabeNewton]

I don't think its appropriate to call the use of the complex plane an excuse when it makes objects such as spinors construct-able which are extremely important in QFT and Classical GR as well. The problem with popular books is that they obscure the true power of the math by using terms, for example from complex analysis like imaginary numbers that the readers might interpret as some physical reality.

 

[nomisrosen]

I don't think its appropriate to call the use of the complex plane an excuse when it makes objects such as spinors construct-able which are extremely important in QFT and Classical GR as well. The problem with popular books is that they obscure the true power of the math by using terms, for example from complex analysis like imaginary numbers that the readers might interpret as some physical reality.

Exactly, and I really wish I understood the math behind all of it. Hopefully one day I'll achieve my long-term dream of becoming a physicist. I find it all so fascinating and all I can do is listen to others and adopt their opinion.
To get back to my original post, could someone explain why Hawking said imaginary time is something that you could travel through like space?

 

[yenchin]

Exactly, and I really wish I understood the math behind all of it. Hopefully one day I'll achieve my long-term dream of becoming a physicist. I find it all so fascinating and all I can do is listen to others and adopt their opinion.
To get back to my original post, could someone explain why Hawking said imaginary time is something that you could travel through like space?

I don't quite understand what he could have meant here as imaginary time is obtained by "Wick-rotating" real time (changing a real number to a complex number is a 90 degree rotation in the complex plane [http://plus.maths.org/content/os/issue32/features/baez/index] ), like many mathematical tools, it is not physical reality but only tool for calculations. What he could have meant is perhaps that originally spacetime has 3 space and 1 time dimension, once you perform Wick-rotation, you have 4 space dimension, i.e. imaginary time behaves like space. But it is at best misleading to say that you could travel through it like travel through space, after all, travel is a word with respect to the notion of real time. Analogy appears in popular books, but sometimes can be misleading.