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Scientists predict how to detect a new dimension

Cynric said:
It looks quite wrong.

But I know what you mean.


I have to say, I've always struggled with this concept myself. Mathematically, no sweat, just keep adding dimensions, but trying to envisage it... gah! Headache.
I saw a pop science programme a while ago (Horizon I think) about string theory, and the debate about how many dimensions were required. At one stage they had a nice graphic of a sort of multi-coloured ribbon thing flying through the sky distorting everything behind it. One of the scientists said something along the lines of "these extra dimensions may be as small as a few millimetres across". WTF? How can you describe a width for a dimension? It's not as if you can say that "height" is about four feet wide.

I expect it was the conflagration of my visually-literal mind and poor science journalism, but still. Can anyone help? Dr Kitten?
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There's some merit to the idea.

IN string theory (as I understand it[Editor's Warning: This yahoo is not a phycisist..accept his knowledge at your own risk]), the extra dimensions are thought to be "curled up". The analogy is viewing a garden hose from a distance. IT appears, for all intents and purposes, to be a one dimensional line. As you get closer, you can see the second, and finally the third dimensions. They're just too small to be seen from a distance.

Likewise, the extra dimensions in string theory are presumed to be curled up. If you think of the universe as finite but unbounded (i.e.-spherical) in four dimensions (guess that should be hyperspherical), then you can grasp the concept a bit better. The universe extends in these extra dimensions, but because they are curled up, you can only go (for example) a few micrometers before your are back where you started in that dimension.

Hopefully I haven't muffed up the explanation too bad, and that makes some sort of sense. "The Elegant Universe" by Brian Greene gives a very good layman's summary of a lot of this.
 
neil said:
OK Now give me the reverse vector to infinity.FRANK ASK.
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Neil, in a month or two, only I shall remember you. Other's purge their minds, and computer histories, of trolls weekly. Few enjoy a troll as much as me...being partially one myself.
 
Huntsman said:
There's some merit to the idea.

IN string theory (as I understand it[Editor's Warning: This yahoo is not a phycisist..accept his knowledge at your own risk]), the extra dimensions are thought to be "curled up". The analogy is viewing a garden hose from a distance. IT appears, for all intents and purposes, to be a one dimensional line. As you get closer, you can see the second, and finally the third dimensions. They're just too small to be seen from a distance.

Likewise, the extra dimensions in string theory are presumed to be curled up. If you think of the universe as finite but unbounded (i.e.-spherical) in four dimensions (guess that should be hyperspherical), then you can grasp the concept a bit better. The universe extends in these extra dimensions, but because they are curled up, you can only go (for example) a few micrometers before your are back where you started in that dimension.

Hopefully I haven't muffed up the explanation too bad, and that makes some sort of sense. "The Elegant Universe" by Brian Greene gives a very good layman's summary of a lot of this.
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Having just watched the DVD of The Elegant Universe, and being halfway through the book, I'd say that's a pretty good summary answer to Cynric's question.
 
New dimensions

Ahh, my daughter is writing and illustrating books (a Gifted and Talented class assignment) on her adventures in the 11th Dimension.

According to Wallis, you float around past strings of energy and matter on staircases that you control with your feet.

That works for me! :)
 
Kiwiwriter said:
Ahh, my daughter is writing and illustrating books (a Gifted and Talented class assignment) on her adventures in the 11th Dimension.

According to Wallis, you float around past strings of energy and matter on staircases that you control with your feet.

That works for me! :)
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Reading your Writing of it, I'll say that works for me too. Kind of an Alice in Wonderland theme, but with twists that are flat.
 
It's interesting that they assert that this is a testable theory (I'm ignoring the "Frank" stuff completely for now).

I am curious as to why their theory means that black holes don't evaporate, but we'll get to see more about that anon, I suppose.

Given that they don't, it seems a bit interesting that they density they predict should, I think, imply that we've met one already.

Thing is, we're still here. So I begin to wonder.

I also wonder about the intersection of their theory with QM, but that's a different issue.
 
Hey, can I ask a really stupid question? I should wiki it, I guess, but can somebody here give me an idiot's guide answer to 'What is a dimension?'

Athon asks. :)
 
These small black holes would initially only be the size of a proton. But in the early solar system there was a lot of dust. The black holes would have absorbed this dust and grown. They would have also combined with each other (That would be something spectacular to see!). One would have been thrown into the sun and the black hole would have absorbed the mass of the sun. In the end there be nothing but black holes orbiting a black hole. The same for every other star. This is proof that there are no stars. Can someone check to see if there are any stars around? If there are what is wrong with what I have written? Anything other than there are black holes in the solar system.

Edit to add: This appears to be an expansion of the third paragraph of JJ's last post.
 
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My pet theory is that there's no point listening for radio waves from space to detect other civilisations. The speed of light is way to slow for advanced communications. This 'other dimension' will be where the future of communications will be happening.
 
athon said:
Hey, can I ask a really stupid question? I should wiki it, I guess, but can somebody here give me an idiot's guide answer to 'What is a dimension?'

Athon asks. :)
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Part of figuring out if I've understood this stuff is trying to explain it to others in layman's terms, so I hope those of you who are more experienced will indulge me. :o

So here goes Jimbo's first layman's lesson in linear algebra... aherm...

...

i) A dimension is simply a direction.

The rest:

Stick your arm out in any direction and look down it and you've just defined a dimension by defining the direction. Now, let's define 2 dimensions (or directions):

y
|
|
|
|
|
-------------------- x

These two dimensions are directions that will define any point in a 2 dimensional space. It goes like this, the point (x,y) = (3,4) is 3 units along in the x direction and 4 units along in the y direction.

Now you can ask, why these directions and not, say, something between y and x? It is because once you have defined these two lines, any other line can be expressed as some combination of them. So a point 1 unit along a line 45 degrees between them is actually (0.707 x, 0.707 y). You can check this using Pythagoras (or 1 sin(45)). The mucky linear algebra term is to say that this line is linearly dependent on x and y. Now... you could take any two arbitrary lines (so long as they are not right on top of each other), but x and y as shown here have the nice property of orthogonality (that means they're 90 degrees apart). The reason math uses orthogonal, rather than 90 degrees is that when your vectors are equations or something else, it doesn't make sense to express their separation in spatial degrees.

ii) A dimension is often taken as a value and a direction

If you say "1 unit in the direction of x" you have defined a unit vector. It can be expressed (x,y) = (1,0). The y unit vector is (0,1). These two unit vectors span the space in that every other vector can be expressed by multiplying and adding these guys, so (3,4) = (3x(1,0), 4x(0,1))

iii) A dimension is merely a number

It is the number of these unit vectors that will define a point in a space. So a 1D space has the unit vector (1) and is 1 dimensional. A 2D space has the unit vectors (1,0),(0,1). A 3D space has the unit vectors (1,0,0),(0,1,0), and (0,0,1) or (x,y,z). Now we're in the "space" of everyday experience! How about a 4D space?

(x,y,z,ct) or (1,0,0,0), (0,1,0,0), (0,0,1,0) and (0,0,0,1)

You see that I have easily described 4 orthogonal vectors mathematically in a 4D space. However, just try to draw an everyday picture of 4 lines, each crossing all the others at 90 degrees! :D

Try writing out the unit vectors for a 5D space yourself. Since we are largely 3D creatures, try to visualize a 5D object in 2D. I can't, although I saw some neato attempts at 4D objects in Wikipedia (see tesseract).

iv) Physics!

The dimensions (x,y,z,ct) might be thought of as (length, width, depth, time) and now you're working in the realm of mechanics! “ct” is a representation of the speed of light times time. This is what they call 4D spacetime. It makes sense, actually, if you represent x, y and z in units of metres, then ct gives (m/s times s), the seconds cancel out and you're measuring all of your 'dimensions' in units of metres! When they say that the 5th dimension (or whatever) is only a few millimetres long, I'm assuming (without any reference to the article) that they've done this sort of correction. (For those in the know... is this true?) so, if you haven't already guessed, the units in 5D are:

(m, m, m, (m/s)s, something something equalling metres ;) ) and the unit vectors are:

(1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0), (0,0,0,1,0) and (0,0,0,0,1). Your first point in 5D space might be (1,1,1,1,1) which means 1 unit along in every direction. Note that this still accounts for everyday experience! (1,1,1,0,0) would mean that you are at 1 unit of length, width and depth, now is time zero and zero in the fifth dimension!

v) Advanced physical theory

I'm not qualified to say anything about this, but I have to ask the question... why aren't there (physically) some number n arbitrary dimensions? Math allows for (1,0,0,0,0,0,0,0,0,... etc.) I assume that something particular in the individual theories constrains or dictates the number of dimensions they are working with.

… whew…

Easy enough? :D
 
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Dimension:

A direction of motion that is independent. In other words, it cannot be described as the vector sum of movement in other dimensions. Current dimensions knwon to exist are length, widht, and breadth (the three spatial dimensions) and time. Most modern examples of string theory and M-theory posit 7 additional dimensions, that are too small (do not extend far enough, think of the "X" line on a graph being a very small circle instead of a straight line) to be detectable.
 
Jimbo07 said:
I'm not qualified to say anything about this, but I have to ask the question... why aren't there (physically) some number n arbitrary dimensions? Math allows for (1,0,0,0,0,0,0,0,0,... etc.) I assume that something particular in the individual theories constrains or dictates the number of dimensions they are working with.
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I don't know the answer to this.

However, I have a guess that the number of dimensions in the universe, including wrapped-up ones, will turn out to map onto one of the hypercomplex numbers, and there are only a limited number of those. I'm betting on the post-Hamiltonion hypercomplex numbers, partially because quaternions already map so well onto GR and quantum behavior in ways that make me say "gosh!"

A lot of the things that you just sort-of have to remember in physics, like the right-hand rule, the Minkowski metric, and the fact that a 360 degree rotation in some sense is different from a 720 degree rotation but the same sense the same as a 1080 degree rotation just fall naturally out of quaternions. Yet Hamilton wasn't trying to do that; he was just looking for a successor to complex numbers that had some of the same algebraic properties.

That makes me say "gosh!" and guess that mathematics does constrain the universe in some way.

So, I'm guessing that if and when string theory matures, it will turn out to have a sedenion representation.
 
Jimbo, this is why I still come back to this board. I understood all of what you wrote (I taught high school maths, but have never been all that advanced in it myself), and gained further insight from it.

Thanks heaps!

Athon
 
One thought I have had with respect to some of this is that this might be more understandable if we could break out of our euclidean geometry biases.

We tend to think of a straight line as an absolute concept. But straightness that we sense is controlled by the space we are in. If the space we are in is curved we won't know it. Throw a ball and it goes in what we think of as a straight line (when not acted on by other forces), but that straight line wouldn't parallel to another straight line if something warps our space.

So if dimensions are curling maybe the idea is that the local space where the dimension are curling is warped.

But maybe these musings are all crap. I stand ready to not defend and to not explain any of them.
 
Cynric said:
It looks quite wrong.

But I know what you mean.


I have to say, I've always struggled with this concept myself. Mathematically, no sweat, just keep adding dimensions, but trying to envisage it... gah! Headache.
I saw a pop science programme a while ago (Horizon I think) about string theory, and the debate about how many dimensions were required. At one stage they had a nice graphic of a sort of multi-coloured ribbon thing flying through the sky distorting everything behind it. One of the scientists said something along the lines of "these extra dimensions may be as small as a few millimetres across". WTF? How can you describe a width for a dimension? It's not as if you can say that "height" is about four feet wide.

I expect it was the conflagration of my visually-literal mind and poor science journalism, but still. Can anyone help? Dr Kitten?
Click to expand...
I saw it. It was cool. I can't help you. But I can attest that the show aired. Damn, I so wish I could get a brain upgrade.

Oh, wait... it's comming to me, The Elegant Universe, PBS, Brian Greene.

http://www.pbs.org/wgbh/nova/elegant/
 
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