Dimensions ?
 

I've read that our known universe is a break-off from a larger one. We ended up with four dimensions out of eleven? I know what the four we have are, 1-3 have to do with space and volume, 4 is time. So do we know what the missing ones are?

they don't have names. They are simply mathematical degrees of freedom.

That's the thing, living in a 4-dimensions world, being part of this world, we cannot really conceive what other dimensions would be.

I know a lot of mathematicians that are going to be real disappointed.

Well, first of whatever you read is far from firmly accepted fact. It's pretty safe to say that at the moment it is nothing more than wild speculation. I've never even heard of such a conjecture.

Perhaps you are confusing it with String Theory, which postulates the existence of extra dimensions which are twisted so tightly that they are too small to be noticed. This also is far from accepted as true. (Or maybe you are not reffering to this at all).

I read it in Steven Hawkings book "universe in a nutshell". It's just a overview type book so I was wondering if there were any more details out there.

A "dimension" isn't anything all that special. A "dimension" in math/physics-speak is not the same "dimension" that appears in scifi. It's not some alternate world where people wear goatees. A "dimension" is basically a free variable.
Consider phase space:
In classical mechanics, if you have some object, this object has certain properties. This object has a position, denoted by three numbers, and a moment, denoted by three more numbers. In total, the object can now be described by six numbers (three for position, three for momentum). These six numbers can be graphed in a six-"dimensional" graph, called phase-space. The object having a certain position and momentum will occupy one point in phase-space. As it moves in position-space, and as it's momentum changes, the object also moves in phase-space.
There. I've just created a six-dimensional space, and I did it without having to resort to using general relativity or string theory.
I believe that the other "dimensions" in string theory are also spatial dimensions, but I'm not really sure.
EDIT:oops, had to correct something

We do exist in 11 dimensions, we're just not capable of percieving the other 7 (maybe).

Superstring theory only works if the universe is 11 dimensional, fortunately existing in an such a universe is the only way to explain some of the behavior of quantum particles they've observed, lending some credence to superstring theory.

However, the idea that the other dimensions are somehow wrapped around each particle seems like a really far reach for an answer to me. I'm certainly no expert, but it seems to me that scientists are being shown evidence that we are living in a universe that has many, many aspects to it that they aren't capable of perceiving, so they try to come up with implausible explanations as to why this is. It's like they can't admit to themselves that there is a potential limit to their knowledge. But once again, I'm no expert and I might not know what the hell I'm talking about.

And here's another thing, how could we know if we existed in more than one temporal dimension? What if what we reffered to as 'time' was really the linear perception of the effects of the other 7 dimensions? There is no way to know for sure, since no experiment can be done outside of time. So the physicists assume that the other ones are spatial, because then it's easier to explain them away.

One last time, I could be wrong, but this is how it seems to me.

Here....this may help. A quick excerpt from the linked page:

One of the most remarkable predictions of String Theory is that space-time has ten dimensions! At first sight, this may be seen as a reason to dismiss the theory altogether, as we obviously have only three dimensions of space and one of time. However, if we assume that six of these dimensions are curled up very tightly, then we may never be aware of their existence. Furthermore, having these so-called compact dimensions is very beneficial if String Theory is to describe a Theory of Everything. The idea is that degrees of freedom like the electric charge of an electron will then arise simply as motion in the extra compact directions! The principle that compact dimensions may lead to unifying theories is not new, but dates from the 1920's, since the theory of Kaluza and Klein. In a sense, String Theory is the ultimate Kaluza-Klein theory.

For simplicity, it is usually assumed that the extra dimensions are wrapped up on six circles. For realistic results they are treated as being wrapped up on mathematical elaborations known as Calabi-Yau Manifolds and Orbifolds.

http://www.damtp.cam.ac.uk/user/gr/p...s.html#mtheory


The Ideas and theories surrounding M- theory/String theory are hypothetical constructs used to explain observations and mathemetical variances from relativity theory. As with all science, they are not fact, and never claim to be such. But as a work in progress there are intersting correlations between the observable, and the theoretical.

Allow me to rephrase ;)
We can know these dimensions exist, we can also define them mathematicaly, but how can we conceive and define them as dimensions?
In your head, "picture" the 1st, 2nd, 3rd dimension.. easy. Now the 4th, a little bit more abstract, but still easy. Now for the 5th.. whoops? What comes to your mind? A mathematical degree? Hardly conceiving the dimension in itself.
That's what I meant.

Is it me or did all of you watch the NOVA special on string theory?...It was on like 2 or 3 weeks ago. I watched some of it...but I can't say I can believe it. Just because some complex algorithm with mass-less particles and all kinds of symbols comes to a solution, doesn't mean it is fact.
But as always, it fun to watch physicists sweat.

A mathematician can define as many dimensions as s/he needs for a given problem. That doesn't make the dimensions meaningful to anyone who isn't directly concerned with the math. Some 2d problems can be made much simpler by treating them as 3d problems. That doesn't change the fact that the problem as an abstraction only exists in 2d. Don't know if this is relevant to this discussion-physics is not a strong suit at the moment.

I don't know about physicists sweating - I can see there being credence in further dimensions - we are only aware of the 4 we have access to, and one of which only in a limited way. Yet this didn't stop Einstein coming up with the idea of 'curved' spacetime. If you think about this for a moment, it suggests a 5th dimension right there, for something to curve, it needs a place to curve 'into'. Perhaps mass is simply an expression or movement in this 5th dimension that drags the fabric of the other 4 with it. So mass could be thought of as a kind of dimension (it effects the other 4 so intimately, it isn't too much of a conceptual leap to consider it as a dimension) - if mass and energy are equivalent, maybe it's just a matter of translating the mass (or some movement of things in the 5th dimension) into the remaining ones, E=MC2 If mass(and as such matter) is our perception of a 5th dimension, then what other properties might be purely dimensional effects?

I don't know, I'm making this up - but am happy to reinterpret my sensual perceptions in terms of some abstract space - for those who are interested, try reading Flatland, a really thought-provoking (and easy to read) book about a certain Mr. Square who lives in Flatland, and his ventures into various other geometric dimensions - it makes you think. Similarly, Plato's Allegory of the Cave might offer a way to look at these sort of conceptual problems and make some sense of them.

It's all theories so far, don't take it as a fact.

But accordingly the M-theory, there are 11 dimensions. 3 visible, 1 timedimension and 7 dimension tightly rolled with a diameter minor to the Plancklength of 10^-35m or something.

IT seriously disturbs me that people consider the fourth dimension to be time. That is going to make the hypercube a very sorry object since for having the same difference as all the others we all the sudden have to jump to a fifth diemnsional object.

Yes time is a dimension, it is not necessarily The Fourth Dimension. It was the fourht to be discovered however. This is said because time, as all the other dimensions, is linear.

The extra dimensions being wound up is still very much a theory and is being beaten down a bit. The original problem which caused string theory is now the wave-particle theorem which is working with the theory of probability. The extra dimension are seen as teh flux and spin of sub-atomic particles, and perhaps a couple other things. They are simply dimensions on a sub-atomic level. So just like you can't see the movements of a particle of water, you also can't see how it spins and so forth.

There are also many dimensional theories, if anyone were to pick-up a discovery they had an article on it sometime ago which was actually mentioned on their cover. There are many multi-dimensional theories, some so big we can't see them and some so small we can't see them. However there is still another, perhaps we can't percieve them.

Hypercube definition- a hypercube has been played with for many years. We are still trying to unlock all the mysteries behind and hyperacceleration perhaps beyond. A hypercube is probably the simplest model of a 4-dimensional object. For those who bear with me I can give two ways of understanding this hypercube, of which the first I wil give here:

begin by imaging or drawing a point. This is a zeroth dimesional object as it supposedly has no width, height, length etc.. Now draw another point an easily replicatable distance away. Now connect the twin points (being of course the one duplicated from the original and the original itself). What you should have now is a line. an object which has 1-dimension, which is often called length. Next you should draw another line of equal length parallel to it (for those in higher mathematics, I am speaking in a simple cartesian co-ordinate system) connecting the twin point you will notice you have made a square. Now this is where artistic skill comes in, or perhaps a visual mind. Take the square and make a duplicate and connect the twin points. You will notice you have a cube. Now I suppose those who have caught on to the patter will realize the next step, duplicate the cube and connect it's twin points and you have what can be drawn and percieved by us as a 3-d shadow of a hypercube.

I would suggest reading flatland, if you have this may seem tedious: Some may consider this still simply 3-d, as would I. However this is not due to the concept but due to our own kinesthetic relationship with the things around us. This should be dificult to imagine and at best difficult to extend into life. However for lesser dimensions to can see why this would work. Say for example you were to draw a person or look at a picture, that could be said to be a two dimensional shadow of what we percieve as a three dimensional object. If you would like a better explanation or to explore the topic message or e-mail me and I would be glad to go through it with you or give you places where you might be able to explore on your own.

A good site to see the hypercube is http://dogfeathers.com/java/hyprcube.html. I am actually still playing with it {;^)

I believe string-theory, for various technical reasons, is now called M-theory.

I also believe the M-theory extra dimensions are space-like. Just extremely small. By extremely, we are talking on a scale where protons and electrons are simply huge.

Not quite true, as I understand it. The simplest solution to the superstring equations is an 11 dimensional universe -- you could also get a much larger one.

Sadly, also not quite true. It isn't the only way to explain it. It is just a particularly elegant way. As far as I am aware, M-theory hasn't provided testable hypotheses yet.

Not wrapped around each particle.

An analogy helps. Imagine an ant living on a sheet of paper.

That ant has 2 space dimensions.

Now take that sheet of paper, and roll it into a relatively large tube.

The ant still has 2 space dimensions, however one of them is 'closed' and forms a loop.

Shrink the loop.

As the loop gets smaller, the dimension that goes around the loop becomes harder for the ant to see. Eventually, the tube of paper looks like a 1-dimensional line.

The extra dimensions are 'curled up' like the loop is, so small that to us, they are very hard to detect.

(thanks to Nova for that beautiful analogy)

You can take a 1 dimensional line, and 'add a line at every point' and make a 2 dimensional space. You can do the same thing to our small tube, and it looks like 2-dimensional space.

And that is their job. They don't admit there is a potential limit to their knowledge, until they are shown proof.

Time-like dimensions behave differently than space-like dimensions, in a few ways. I believe that M-theory requires extra space-like dimensions.

On the other hand, I have heard of one physicist who attempted to explain Einstien's Theory of General Relativity using extra time-like dimensions. Forgot his or her name.

The dimensions are, as far as I can tell, unordered. The "Fourth Dimension" is just a name. Humanity placed them in an order for convienience.

The order we give them also isn't important. A 4-dimensional object need not extend over 4 adjacent dimensions, because 'adjacent' doesn't mean anything.

Um, hypercubes are rather simple geometric objects. I am not aware of any mysteries surrounding them -- hell, I can't even think of anything interesting enough about them to be mysterious.

I am searching like mad to find the article either in Discover or Popular Science, but it was testing supergravity, a fun effect in M-Theory where particles brought close enough for the extra curled up dimensions to touch and gravity's force is greater than G m1 m2 / r^2, and showed that the dimensions were smaller than some extremely minute distance.

I havent read anywhere that the dimensions are smaller than Plank's length. If it were than this experiment is fairly useless since we cannot measure distance that small. If anyone remembers the issue with the article (and preferably what the cover was of) post it here.

Aren't the "dimensions" just 'folds' in the structure of the energies of strings, in which
their movements can't necessarily be described by conceptual dimensions, such as
length, width, and height?

Also, replying to topics about the dimension of time, it has always been a fourth
dimension in placements of any mass in a certain 'location.' No one dimension is
said to correlate with any specific property. I highly doubt people say that "Length"
is The First Dimension, but it is generally accepted as the first dimension is problems
dealing with volume, just as time is generally the 4th dim. used in space-time location
problems.

But can you make Legos with them? Or a 4-D puzzle? Wouldn't that be fun, sort the edges out of that bulk. I can't stand 2-D puzzles because I can't leave them till they are done.

Actually, my buddy found this interesting site. You don't have to break out your 3-D goggles though, sorry folks. http://www.geocities.com/CapeCanaver.../expansion.swf

Its a visual of what Zenir said.

2 questions
1) What exactly is the 1st dimension?
2) How do we know there are 7 other dimensions if we cant percieve them? Couldnt there be more or less than that?

Shit i guess thats 3 questions....

You mean to tell me that you guys can't PERCIEVE them!?!? No wonder I've been thinking you're all joking the whole time!!! Now from one who is gifted enough to be able to percieve them, they're all really cool and stuff, but there's TWELVE dimensions, not 11. Although you can only get to the 12th once you've existed in the other 11. The 12th is the "pimp status" dimension.

. . . . . :thumbsup:

The existance of the M-theory dimensions is demanded by the mathematics. M-theory is .. a bit immature still. I haven't heard of any observeable hard predictions coming out of M-theory yet.

The 3 large space dimensions seem to be interchangeable, and time seems to be different. What order we place them in is arbitrary. So, the 1st dimension is any dimension.

Augi, I believe there are N-dimensional tic-tac-toe and rubic-cube games on the internet.