Wikipedia: String theory/Talk

article says string theory permits space to have

: either 10, 11, or 26 dimensions

i thought it only allowed 10 or 26, not 11. comments from any real physicists here? -- SJK

Dug up my notes on M-Theory. If you want to help me finish please do. ~BF

BF: I honestly don't know that much about M-theory. I read a book on string theory a few years back, but it was the popular science sort of book that skips most of the technical details. M-theory it didn't even mention -- SJK

It so new ( 5 yrs or so) that I enjoy it ! Don't ask me to explain it though. It has been stated by the cutting edge Theoretic Physicists, that M-theory finally solves Einstein's problem with general relativity, the black holes' issue and a few other unsolvable physics questions. What I like about it, is Witten himself said at a lecture, " This is 21st century knowledge that somehow dropped into the 20th century." Very new age for physics !

OK, now as we all know, encyclopedias are supposed to explain difficult concepts. So, here in this article we are exposed, straight-facedly and without any explanation at all, the notion of 10, 11, or 26 (spatial?) dimensions. What on Earth does this mean? I'm just a stupid philosopher, see. I'm sure I've seen explanations before, but I'm also sure I didn't understand one bit of them and therefore promptly forgot whatever I read or was told. Now, based on touch and sight I think I have a pretty clear notion of what three spatial dimensions amounts to; it also seems to me that this pretty much exhausts my understanding of what "spatial dimension" means. I'm perfectly willing to believe that physicists know all sorts of stuff about dimensions that I don't know, and perhaps never will know. But at least the article should make some attempt to explain what the hail "dimension" means if it can, possibly, mean something that can be numbered more than four! So, go ahead--explain it, or try! --LMS, being deliberately provokative :-)

I think the article already handles this - it says the other dimensions are subatomic in size, and so can't be observed normally.

But what does it mean to call a dimension "subatomic in size"? That's kind of like calling length, width, breadth, or duration "subatomic in size." I am still not enlightened. I'm sorry, I don't mean to be raising objections. I'm just saying that you're going to have to say a lot more in order to make the very notion of fifth+ dimensions clear. (Why are they called "dimensions," whatever these theoretical entities are?) --LMS

LMS: Let me explain it for you. We have three normal spatial dimensions, x, y and z. Now the radius of the universe along the x, y and z dimensions is going to be big -- billions of light years -- e.g. it might be that the universe is twenty billion light years tall and thirty billion light years wide and forty billion light years deep. By contrast, the other spatial dimensions beyond the normal three, are very tiny -- nanometres, picometres across. Does that make any sense to you?

: No, none whatsoever.

As to the concept of a dimension, we all know what it is like to have one dimension (a line), two (a plane) and three (percievable space). Our minds really can't understand what more than three dimensions are like -- sure, we can manipulate the maths, we can do the reasoning -- but we can never intuitively understand what we are doing, in the same sense that we can for the normal spatial dimensions. -- SJK

: Have you added the above to an article, SJK, or do you think it's not clear enough for that? --LMS

I think that the concept of a dimension having any *size* at all is quite confusing - dimensions are supposed to be the infinite canvas on to which things with size are placed. I think that extra-dimensions can be handled intuitively, it is just that this intuition has to be learnt. Modern physicists will tell you that they can kind of see what extra dimensions are like, albeit without fully understanding them. The book 'Flatworld' deals with this - a 2D thing realising that their are other dimensions. --Na

: Precisely: "the concept of a dimension having any *size* at all is quite confusing."

It's not confusing at all so long as you realise it is a closed space (at least along the additional dimensions predicted by string theory) -- just like the surface of a sphere is two dimensional, and each of those dimensions can be said to have a size (the maximum distance you must travel along that dimension before you run into the same point again.) (Also, IIRC its called Flatland, not Flatworld.) -- SJK

If they have a definite size does that mean they have a definite position - are there millions of dimensions floating around inside the big 3D universe, or am I becoming more confused... --Na

No, there are only 10 (or 11, or 26, or whatever) dimensions; our three dimensions are a 3D slice out of the 10-or-whatever-D space. A dimension can't have a position: Height doesn't have a position, nor does length nor width. They are axes along which position is measured. So accurately, we really shouldn't say the dimension is subatomic -- we should say that the universe is subatomic measured along that dimension -- SJK

OK, OK, so let's start working on an article about this. :-) --LMS

I think there are two ways to think of dimensional size: 1. The baloon system described in the article. Since the size is how far you must go before bumping into yourself, think of a very very tall bug standing on a very very tiny baloon. It would not notice the balloon; it would think it is just standing on a point. 2. Point 1 raises a problem, as stated in a previous post: is there something outside the dimensions? My personal answer is "yes", but in a different way, and a way probably scientifically unfounded, so I'll say "no" and explain it this way: the dimension is, indeed, infinite. The thing is, if you stand at a point, you will see that one "dimensional size" away is an exact copy of everything at that point. In three dimensions, the "dimensional size" is so huge that we don't see the copy. But when the size is subatomic, everything is jammed up against exact copies. If you touch the copy in front of you, every copy touches every copy in front of it; the one behind you touches you. It is like the hall of mirrors. The reason we can't perceive these other dimensions is evolution; as explained in Michio Kaku's book Hyperspace (which I really recommend; it has great explanations) sabertoothed tigers do not jump out of the fifth dimension. Therefore, natural selection will not care about whether a species can see the fifth dimension. It might even be detrimental; it would use up valuable brain space.

Well, this isn't too bad -- we haven't even gotten into the math, after all, and that's the truly hard part. But staying on a conceptual level for now: a dimension is a degree of freedom in which an event may occur. Dimensions are orthogonal to one another, and may be visualized like the coordinate axes on a graph. In other words, a universe in which any event can be located with n numbers is called an n-dimensional spacetime. Our universe appears at a first glance to be 4-dimensional: three spacial dimensions and one time dimension. But this may not necessarily be the actual case.

To illustrate, I will paraphrase an example from The Elegant Universe: picture a simple universe with one space and one time dimension. It is named Lineland and is inhabited by one-dimensional Linepeople. As far as they can tell, their universe has only two dimensions in all. Later on, it is discovered that the supposed "line" universe is actually a thin tube, a two-dimensional surface with the 'new' dimension curled up into a circle so small that even the width of a Line-atom is many times greater than the circumference. Observing this extra dimension directly is therefore nearly impossible, but the rather subtle effects of its existance may be observed. Lineland, then, is basically a lower-dimensional picture of our own universe. There are all sorts of extra dimensions down there, but they're so damn small that we can't tell. -- Xaonon

Let me have a crack at what I got out of the "dimensions have a size" thing to see if a) I'm following it, and b) my explanation is then helpful to the layman.

The issue here is "how big is the universe in the given dimension". Obviously everything *in* the universe has to be smaller than the universe is in each of its spatial dimensions. So the universe is 13 billion light years across in the the x, y, and z spatial dimensions and microscopic in all others. All objects in the universe then have to be smaller than that. My desk, at about two feet by five feet by three feet fits within the universe in x, y, and z, and is mini-microsized in all the other dimensions, in order to fit as well.

So we don't see the other dimensions because the measurements of *everything* are too small to impact us in any way. This is why (getting back to the initial confusing statement) "the dimensions are subatomic in size" -- the entire universe is that small in those dimensions, so so is everything else.

Is that summation right? And if so, does it help? -- Paul Drye

Yep, great summation.

: Yeah, thats basically it.