John Page

Has Hawking finally concluded that the universe is contained within his head? See for yourselves in this month's Reason magazine.

<a href="http://www.reason.com/0204/fe.gb.leaping.shtml" target="_blank">Reason Magazine Article</a>

Friar Bellows

You do realise that "imaginary" in this article is not the "imaginary" that you find in your regular dictionary? "Real" numbers are the numbers with which we're all familiar e.g. 5, 7, -1.4532, 12/7. "Imaginary" numbers are constructed from the square root of negative 1, and are given the symbol i, e.g. 5i, -3.2i, 99i. Putting together "imaginary" numbers and "real" numbers gives us "complex" numbers e.g. 5 + 7i, -1.23 + 8.7i.

Electrical engineers find these numbers useful in analysing electrical circuits, for example (except, maddeningly, they used the symbol j instead of i). Sometimes you'll find textbooks on the special theory of relativity which use imaginary time, mainly because it makes 4-dimensional Lorentzian spacetime look like a 4-dimensional Euclidean space. So, if Hawking has gone off the deep end, then so have thousands of scientists and engineers (including the ones who designed your computer).

So, don't be misled (I'm not neccesarily saying you were) by the term "imaginary". That's just what we call those numbers. And re-read the following excerpts from that article:

Oh, and don't forget this one:

tronvillain

Uh, he's been talking about imaginary time since A Brief History of Time.

repoman

There is a good explanation of imaginary time in the book "An Imaginary Tale" by Paul J. Nahin, section 4.5 if you want to browse at your local bookstore.

He talks about Invariant Intervals, which I don't fully understand. But what I think he means is that Einstein took two ideas seriously: the first is taht the speed of light never changes and the second that physical laws remain the same no matter how you rotate or translate a frame of reference.
The law that remained the same was of course the Lorentz transformation.

Oolon Colluphid

On page 134 of ABHoT, Hawking says that, in order to include Feynman’s ‘sum over histories’ as part of uniting quantum and relativity theories,

As the book’s glossary says: "imaginary time: time measured using imaginary numbers", which as others have pointed out, are things like I (the square root of -1).

Hawking continues: “When we apply Feynman’s sum over histories to Einstein’s view of gravity . . .” [using imaginary numbers to allow the calculations, and taking the curved space-times to be Euclidean] “. . . time is imaginary and indistinguishable from directions in space”. From that, it leads to his ‘no boundary’ proposal.

But hey, it's said that hardly anyone makes it past page 34 in ABHoT anyway...

Oolon

Oolon Colluphid

And don't forget that at last count there were supposed to be ten (or is it now eleven? ) dimensions. All those vibrating strings have got to have somewhere to vibrate in, yeah? ( )

Oolon

Duck!

Did I read somewhere that in order for string theory to work, there needs to be either 10 or 29 dimensions to the universe?


Duck!

John Page

Thanks all for illuminating my darkness. I now gather that 'imaginary' time is something proposed as real and existing outside of our minds, and that its manifestation is modeled using negative roots (which I vaguely recollect from school).

Let's take the number "minus one" or -1. This is a mathematical concept. You cannot directly measure it, you only arrive at it by saying 3 minus four or n-(n+1) or some such. The negative number concept is a very useful tool, one can then calculate that you need to add one (thing) to have four things or n things respectively. At no time has a -1 thing existed, its a piece of mental math.

OK, so we can use math to reconcile between (mathematical?) models of reality as Friar Bellows explained. I can see that. But how can a something be directly measured as a negative number? We only have numbers in the first place because we can measure the "threeness" or "fourness" of a set of objects, they're just the abstraction of quantity.

I guess I need to read and understand more to determine whether Hawking's proposition is that 20 time root -1 seconds actually exists. Thanks repoman and others for the reading suggestions, now I'm really going to make a fool of myself!

Cheers!

Bill

The original version of String Theory required 26 space/time dimensions within which to operate. That was one dimension of time and 25 (or five squared) dimensions of space. However, using a concept known as "supersymmetry," the number of required spatial dimensions was reduced from 25 (five squared) to 9 (three squared), each plus the single dimension of time, yielding the numbers of 26 or 10 dimensions. This use of "supersymmetry" resulted in a new theory, which is called "Superstring Theory" (incorporating the "super" from "supersymmetry" along with the "String" from "String Theory" to indicate the mating of these two ideas).

Now, the 10-dimensional flavor of Superstring Theory has actually advanced quite a bit due to the discovery of a particular type of rolled up six-dimensional space called (I think) a "Cabau-Yau (sp?) space" which, allegedly, has a discrete existence at each and every point of 3-dimensional space within our normal perception of space. So, the required ten dimensions are now all accounted for in a reasonable way, where the bundle of six extra spatial dimensions actually affects the way the strings vibrate so as to produce certain very specific effects "in the real world."

Anyway, if you want to read about this sort of stuff, I highly recommend <a href="http://www.secweb.org/bookstore/bookdetail.asp?BookID=186" target="_blank">Brian Greene's book</a>.

== Bill

[ April 02, 2002: Message edited by: Bill ]</p>

tronvillain

I wasn't aware that we'd actually discovered those extra six dimensions.