The Validity of an 11- or 26-Dimensional Universe

Great Debates
1

I have heard multiple theories about the universe having more spacial dimensions than humans can perceive or conceptualize (more than 3), but I’m still unclear as to the validity of these proposals. I’m assuming the ideas materialized as a result of physicists and astronomers dealing with multi-dimensional mathematical equations in real-life applications? Someone told me that “it’s been proven that the universe must have more than 3 spacial dimensions.” Is this true or is it just hogwash? And if it is true, what do the other dimensions actually represent? What is their purpose?

In addition, please excuse me for my deluge of initial posts. These are questions I have accumulated over the past year that I haven’t been able to find any decent answers to. Thanks in advance for everyone’s input. :slight_smile:

2

It is valid insomuch as to generate formulas which describe that which is observed.

Einstein’s General Theory of Relativity is based on a four dimensional field. When this field is distorted by mass (or perhaps a massive dollop of energy :wink: ) the result is a gravitational field. The validity is uphelddue to the theory being able to describe thing the previous gravitational theory (Newtonian) could not, such as the precession of equinoxes of Mercury’s orbit, or the distortion of starlight in the immediate vicinity of the coronal disc during a solar eclipse.

Furthermore, when you take the mathematical rules which govern General Relativity and apply them to a 5 dimensional field, you get gravity AND electromagnetism a set of physical phenomena of known observables.

Add enough dimensions and you get all the forces which govern the universe.

Of course, different competing theorys consist of 10, 11, or even 26 dimensions.

I’ll leave it to a real physisist to explain that one. :wink:

3

I’ll wait for a real physicist to happen by, but here’s some more tidbits. The “extra dimensions” idea is a theory, not proven. The idea is that the universe had all these dimensions (11/2, whatever) at the time of the big bang, and the extra dimensions “curled up” so small as to be indetectable. Think of standing on a rope – you can move in one long direction, but you can also move around the perimeter of the rope in a smaller dimension. Now shrink the rope’s diameter to smaller than an atom, and the “extra” dimension is now invisible, but still there.

4

I kind of understand what you are saying… but my original questions still remain. Hopefully someone out there can give some more insight? What do the other dimensions actually represent? What is their purpose?

5

I admit right off the bat to not knowing anything about string theory, and I can’t conceptualize extra dimensions. But can someone explain how time can really be the same SORT of dimension as length, width, and depth? I mean, I understand that a dimension in some sense is just a mathematical description of a variable on a plot… but then why do string theorists talk about how the extra dimensions have to be “rolled up” and that’s why we don’t “see” them? I mean, we don’t “see” time either (although we might experience it, but that’s not the same thing). If the fifth dimension could just be electromagnetism, then why couldn’t the sixth be Democrat/Republicanism and so on? Why would the other dimensions have to be “rolled up” if they could just be things that we know of and can measure just fine already?

And what’s all this about their coming a point when those dimension UNROLL and basically wipe out everything we know? Man, that would SUCK.

6

Each spatial dimension is perpendicular to the other one. Length is perpendicular to height which is perpendicular to width. The fourth dimension is perpendicular to all of those. The directions you can travel in the fourth dimension are usually called ana and kata. I don’t know why.
However, as for the other dimensions being “rolled up” or tiny, I don’t know how that’s supposed to work.

7

Well, I get the perpendicular thing, but I can’t see how time would be “perpendicular” to any of the other three since it’s not spatial in any way I understand.

8

It’s not spatial. It’s included as a dimension because dimension isn’t limited to physical things. Just about any type of measurement could be concidered a dimension. Time is included as another dimension to length, width and height because you can measure in time where something is, as well as where it is physically located. If we used a grid, I could be located at (3, 15, 42), and so could you. But how could be at the same exact location? Well, I could be there at 8:30AM and you could be there at 5:00PM
And I hope that helps, instead of sounding like I’m babbling (which I am :cool: )

9

But then how does electromagnetism fit in as a 6th dimension? And if any measured thing can be a dimension, what need to limit it to 11 or 20 or even 100? And why would they need to be rolled up? I’m back where I started. They should call it “all tangled the fuck up” theory.

10

I am not a physicist either, and I know even less string theory, but I think I have a general idea. (I will also admit that I’m posting this partly in the hope that someone more knowledgable will come along and correct my errors and misunderstandings).

As far as I know the idea behind string theory is this: Every elementary particle is made up of a string. If that string vibrates one particular way, it is realized as one particular elementary particle; if it vibrates another way, it is realized as another.

Now imagine a loop of string in a two dimensional plane. Sure, it can vibrate, but the freedom of its vibrations is somewhat limited (it can’t vibrate outside of the plane). On the other hand, if that same loop of string lives in three dimensions, it’s vibrations can be considerably more complex.

Now, I know absolutely none of the details or history behind this, but as string theory progressed it became evident that three dimensions are not sufficient to provide for the freedom of movement needed by the strings to realize the assortment of elementary particles we have. Eleven dimensions are necessary, apparently.

We only perceive three of these eleven (spatial) dimensions because eight of them are “rolled up”, or “compacitified”. For example, say you are a two dimensional being, but the two dimensional universe in which you live is actually the surface of a very thin wire. It might be the case that you only perceive one of the dimensions–the length of that wire. The fact that the surface is two dimensions (rather than one) may not be perceived by you, because that second dimension is very small, being curled up around the (tiny) diameter of the wire.

I welcome any corrections here, because again, I’m not a physicist, and am curious to know if this is the basic idea of string theory.

11

This will be my last post on this for a while, and then I’ll those who know what they’re talking about give it a shot.

  1. Electromagnetism is’t the 6th dimension (or the 5th, which is what I’ve usually seen mentioned when talking about electromagnetism). There is a link between electricity and magnatism. I’ve read that we can’t actually observe the link in 3 dimensional space, we need more. If we could take a peek into 5 dimensional space, we could then see how they are related. Or so I’ve read.
  2. Although most or all measurements can be described as dimensions, in this context, the only ones that count are spatial dimensions and time.
  3. Why would they need to be rolled up? I have no clue.
12

You know, I just realized that “rolled up” and “compactified” have about as little meaning to me as if you’d said that they were “Dolemitized baby!”

But the idea that the strings would need more degrees of freedom does sort of sound on the right track to me understanding it, unless I am completely wrongly associating it with my much more extensive knowledge of statistics.

13

That’s understandable, it’s not necessarily an easy subject (in fact, I’m currently writing my (math) dissertation on certain compactifications).

In some cases, however, it’s fairly intuitive, like the example I gave regarding the two dimensional surface of a thin wire. This is a very basic “compactification”:

First, imagine the basic two dimensional (infinite) plane. Now compare that with the two dimensional surface of a thin wire. What’s the difference? A fundamental difference is that in the latter, one of the dimensions has been “rolled up” (compactified) into a circle (namely, the circumference of the wire). In the former, on the other hand, that same dimension extends infinitely in either direction–it is not “compact”, or not “rolled up”.

It’s much harder (if not impossible) to visualize this when you’re talking about higher dimensions (such as eleven), which is why I chose this particular (low dimension) example to illustrate it.

There are also compactifications which are much more complicated than simply “rolling up” a single dimension into a circle, though I don’t know whether or not they would have any applications in string theory.

14

I’m not so sure anyone will turn up here who is of the calibre to facilitate an “Ask the String Theorist”-type thread, and so we might largely have to make do with the understanding gleaned by those of us who’ve dabbled here and there.

Admittedly, I am limited only to popular books, articles and maybe the odd paper on the subject, but it seems to me that there is a blatantly obvious question which needs answering:

Why do we only have three spatial dimensions?

Three is a rather arbitrary number in physics (one lecturer told me that if the answer isn’t zero, infinity or one, and can;t be normalised to one, you’ve probably gone wrong somewhere).Why not two, or four? Granted, a two dimensional universe wouldn’t have strong enough gravity to allow for “interesting” structure like galaxies, stars and ultimately us, and a 4-D universe’s gravity would be too strong: Three dimensions appears to be the little bear’s bed and porridge which the Goldilocks of intelligent life finds just right. But that is taking the anthropic principle a bit far, surely?

No, say some. Indeed, they ask, would it not make non-arbitrary sense if we merely lived in a three dimensional region of the universe? Might evidence of the 2-D or 4-D region be apparent at high enough energies in the Large Hadron Collider in Geneva next year, or its successor, or its great-great-grandchild in centuries or millennia?

Perhaps, perhaps not. String theory was, itself, far too arbitrary to be the Theory of Everything: it gave five different types of string with no reason to favour one over another except by inelegantly forcing our universe’s variables into it with a veritable tyre iron. Its successor, M theory, attempts to remove its arbitrariness by explaining the 3-Dness of the universe we inhabit. (As this excellent article implies, maybe those ‘extra’ dimensions are unnecessary, or so Witten suspects). However, it is not yet strictly a theory, but a model. Models only become theories if they predict things, and we are at too early a stage for that. (Sadly, it might never if the required engineering slips out of reach of the physics - what if it needed a collider bigger than Earth?)

As for the dimension called ‘time’, this is just a measure of the change in a spatial configuration of the universe: if the universe does not change in any way (eg. expanding or contracting), no time can be said to have “passed”: Time is just an axis on which configurational ‘events’ exist. The Big Bang, Big Crunch (or whatever) and 26th January 2005 are all different places in the 3-D region of the universe. There is no such thing as ‘now’.

15

My understanding is that time isn’t a dimension but simply the way that dimension is revealed to us. It is the way we experience a 4th dimension. Someone correct me if I’m wrong.

16

As I understand it, there are important differences between the dimension we call time and the ones we call length, breadth and depth: it is clearly does not have exactly the same relationship with breadth as breadth has with, say, depth (two need a ruler, one needs a stopwatch!). However, the idea that time as an axis on which different configurations are placed (just as those configurations are placed along axes of length, breadth and depth) is a common one.

17

IIRC all of the “extra” dimensions are space-like, rather than time-like.

18

The difference in how we measure space and time is a function of our limitations as 3-dimensional beings; the fourth would probably appear like a spatial dimension to a 4th dimensional creature. The 4th dimension is considered physical, not temporal. If you’re using time as a 4th coordinate, whose “time” are you using? I would probably liken measuring the 4th dimension with a clock to measuring mass with a scale. As long as your at 1g (keeping the extra variagble constant) your ok, but change that variable and a scale is no longer useful. For instance, the twin who takes the trip on the spaceship may appear to have been “lost in time” because it was traveling along the 4th dimension. Maybe as velocity increases, more of the movement occurs along the 4th axis relative to the other three. Just speculating.

Another thing: If Gravity warps the space around it, perhaps the attraction is a collapsing/expanding of the 4th dimension.

19

The universe is static from this perspective: configurations differ over shorter scales within it according to Special Relativity, and the position of a clock hand is a configuration of the universe.

In a static, time-as-an-axis universe, one does not “travel” in time, one simply exists as different configurations. The twin configuration merely differs on a shorter or longer scale.

20

Someday when I have time I’ll start the “Ask the (Former) String Theorist” thread, but for now…

The answer to the OP is: NO, extra dimensions have NOT been proven. They show up in many theories, but there is as yet not a single shred of experimental evidence for them. All of these theories are extremely speculative, and most physicists who write about them say that (tho maybe not clearly enough).

Check out Brian Greene’s books (The Elegant Universe, The Fabric of the Cosmos) for a good introduction to these ideas.

Cabbage did a good job of explaining why there needs to be extra dimensions, and the reason they need to be rolled up is that we only see three spatial dimensions. In fact, they DON’T need to be rolled up if you treat them as “internal”, non-spatial dimensions (like the Republican/Democrat dimension someone mentioned). I believe this type of theory is equivalent to a rolled-up theory if you pick the correct rolled-up space.