Imagining the Tenth Dimension

[Innit]

I was always really confused about the concept of the 10 (and now some believe 11) dimensions. I came across this video that explains it in a simplified form (it's a video for the first chapter of a book):

 

http://youtube.com/watch?v=qU1fixMAObI

 

Pretty interesting. I got lost a few times, but I get it now!

[insane_alien]

we've seen this one before. it doesn't really apply because it doesn't follow any known veiw of reality. the extra dimensions from string theory are all curled up(or somethin, its weird) BenTheMan seems to know string theory maybe he can explain further.

[Innit]

^ I see. Well, my knowledge isn't deep enough to have understood it so fully, but I guess I'll be awaiting BenTheMan's respones

[BenTheMan]

Innit---

 

Is this ``Inuit'' with an upside down `u'?

 

No matter.

 

Ask your questions and I will do my best to answer. You can also trust a guy named ajb (he knows MUCH more about the mathy side of things than I do). His avatar is a penguin (presumably because he likes Linux).

 

Anyway, perhaps we should start a general string thread? If this discussion goes long enough, perhaps we can get a moderator to do that (not Martin---I don't think he likes string theory very much).

 

Ok, extra dimensions.

 

The canonical example is a line strung between two poles. First some semantics---a dimension means that you can put a coordinate on it. The number of dimensions is the number of coordinates that you need to describe a surface. So, if you have a line strung between two poles, you only need one coordinate (i.e., distance from one end or the other). The top of your table needs two coordinates (`x' and `y' if you like), as does the surface of a sphere (think latitude and longitude).

 

Suppose that you're a tightrope walker, and you wish to walk across the tightrope. Well, you can describe your position with only one coordinate, right? You can use your distance from one of the end-points to describe your location. And as long as you tell me which endpoint you're starting from, and how far from that endpoint you are, I can find you.

 

Now suppose you're an ant living on that same string. If you're an ant, things look much bigger to you. If you are small enough, and the rope is sufficiently thick, you can see two dimensions now---you can see the distance along the rope, but you can also travel in circles laterally around the rope. In order for your ant friends to find you, you must give them two corrdinates---not only where along the rope you are, but also where around the rope you are.

 

The thing is, unless you are an ant, or unless you look sufficiently closely, you will NEVER notice that the rope has any more than one coordinate.

 

If this isn't clear, ask questions! Please!

 

Now extrapolate this out. Suppose we live in four dimensions. We know very well that we live in four dimensions, but we are big. Suppose we are very very small. Are four numbers enough to describe our position? The answer that strings gives is no.

 

Depending on HOW small you are, you either need 10 numbers or 11 numbers to describe your position. An easy way (and not completely inaccurate way) to think of this is to think of every point in space time as being described by four numbers (x,y,z,t), along with coordinates around 6 little circles. When I say little, I mean VERY little.

 

Again, because we are so big, we never notice the little circles---just like the tightrope walker may never notice the thickness of the rope, but the ant does.

 

I hope that this was a little clear. I haven't seen this video you have linked to, but hopefully my example was different from the video's example.

[Innit]

Innit---

 

Is this ``Inuit'' with an upside down `u'?

 

No matter.

 

Ask your questions and I will do my best to answer. You can also trust a guy named ajb (he knows MUCH more about the mathy side of things than I do). His avatar is a penguin (presumably because he likes Linux).

 

Anyway, perhaps we should start a general string thread? If this discussion goes long enough, perhaps we can get a moderator to do that (not Martin---I don't think he likes string theory very much).

 

Ok, extra dimensions.

 

The canonical example is a line strung between two poles. First some semantics---a dimension means that you can put a coordinate on it. The number of dimensions is the number of coordinates that you need to describe a surface. So, if you have a line strung between two poles, you only need one coordinate (i.e., distance from one end or the other). The top of your table needs two coordinates (`x' and `y' if you like), as does the surface of a sphere (think latitude and longitude).

 

Suppose that you're a tightrope walker, and you wish to walk across the tightrope. Well, you can describe your position with only one coordinate, right? You can use your distance from one of the end-points to describe your location. And as long as you tell me which endpoint you're starting from, and how far from that endpoint you are, I can find you.

 

Now suppose you're an ant living on that same string. If you're an ant, things look much bigger to you. If you are small enough, and the rope is sufficiently thick, you can see two dimensions now---you can see the distance along the rope, but you can also travel in circles laterally around the rope. In order for your ant friends to find you, you must give them two corrdinates---not only where along the rope you are, but also where around the rope you are.

 

The thing is, unless you are an ant, or unless you look sufficiently closely, you will NEVER notice that the rope has any more than one coordinate.

 

If this isn't clear, ask questions! Please!

 

Now extrapolate this out. Suppose we live in four dimensions. We know very well that we live in four dimensions, but we are big. Suppose we are very very small. Are four numbers enough to describe our position? The answer that strings gives is no.

 

Depending on HOW small you are, you either need 10 numbers or 11 numbers to describe your position. An easy way (and not completely inaccurate way) to think of this is to think of every point in space time as being described by four numbers (x,y,z,t), along with coordinates around 6 little circles. When I say little, I mean VERY little.

 

Again, because we are so big, we never notice the little circles---just like the tightrope walker may never notice the thickness of the rope, but the ant does.

 

I hope that this was a little clear. I haven't seen this video you have linked to, but hopefully my example was different from the video's example.

 

That was an excellent explanation! Thankyou very much for that. There are only 2 small things. First thing is that I don't quite understand is why exactly we cannot describe our position with 4 numbers. I didn't quite understand the concept of the "6 little circles", and what exactly they are.

 

The second thing is that, if I am not mistaken, I believe that we actually live in the 5th dimension, not the 4th. I think it was proved by Kaluza in 1919 and later approved of by Einstein. You'll obviously know better than I, but it was just what I'd heard...

 

Thanks

[BenTheMan]

There are only 2 small things. First thing is that I don't quite understand is why exactly we cannot describe our position with 4 numbers. I didn't quite understand the concept of the "6 little circles", and what exactly they are.

 

The six little circles are the extra dimensions of string theory... We can describe OUR position with 4 numbers, but if we are small enough (like the ant on the rope), we need ten numbers.

 

The second thing is that, if I am not mistaken, I believe that we actually live in the 5th dimension, not the 4th. I think it was proved by Kaluza in 1919 and later approved of by Einstein. You'll obviously know better than I, but it was just what I'd heard...

 

No, this was the first attempt by Einstein to unify electromagnetism and gravity. If you have five dimensions, where one of them is a little circle, then you can naturally incorporate electromagnetism with gravity. BUT, the problem is that there is an extra particle predicted that isn't observed, and we now know electromagnesim isn't fundamental.

[Innit]

^ So that whole 5th dimension thing was just a theory that is now proved wrong?

 

And thanks for explaining the circles thing again. I get it now

 

And another thanks for replying so quickly. You're very efficient!

[BenTheMan]

^ So that whole 5th dimension thing was just a theory that is now proved wrong?

 

Well, the simple one that Kaluza and Klein were working on, anyway.

 

You're very efficient!

 

I do what I can.

[Innit]

^ Oh, and by the way, you were asking if my username was ``Inuit'' with an upside down `u'. Actually, my username is another form of the commonly known slang phrase "In it" that many people use in Britain. Inuit, on the other hand, would mean "a person from the arctic - an eskimo, in other words", if I'm not mistaken...

[Wormwood]

Hi Ben, I was hoping you could explain the circles a bit more

 

I get that we must be smaller to observe them. Like a mite walking around the ant that is walking around the rope right? But why 10? Why not 1000 or an infinite number?

[ajb]

Wormwood,

 

the answer is technical but I will outline it. If we are talking about superstrings then the theory must be formulated in 10 dimensions. Only in this dimension can the theory be quantised. Any other dimension leads to an "anomaly". An anomaly is the "quantum mechanical breaking of a symmetry" and these can be disastrous for the quantum theory.

[BenTheMan]

I'll start a string thread:)

 

Wormwood---

 

Look here: http://www.scienceforums.net/forum/showthread.php?t=28298.