fando

Hey, let's visualize those extra string theory dimensions! It's not that hard, really. The extra dimensions are usually described as 'curled up' into very small circles. That's actually not a very good analogy because the space isn't really curled in the usual sense of the word, that would require an extra dimension to curl into! So let's just toss out that description and I'll present a new one to help interested readers visualize these beasts.

Goal: To visualize extra space dimensions which are 'curled up'. We will start with one curled up dimension and work our way to many.

Gedankenexperiment: The Funky Room

Imagine if you will a square room with two doors on opposite walls, say the N and S walls. You live in this room. It's the entire universe to you, you've never been outside. But you're bored and would like to explore, so you go and open the N door. As soon as you open it, you hear a strange echoing noise. Ignoring that for a second, you look through the doorway and you see a very strange sight. Immediately through the doorway is another room that looks exactly like the one you're in, and on the far end of it lies an open door with a person looking through it. That person looks exactly like you! Through the doorway that this simulacrums is looking into lies an exact copy of what was just described. And through that copy's doorway, you see yet another copy, and so on ad infinum. After a split second, you realize you're looking at an infinite number of rooms, with an infinite number of people that look exactly like you looking through an infinite number of open doorways which open up to more of the same. An image echo! The same visual effect is observed when you look at a mirror that is facing another mirror. However, unlike mirrors, this is real -- if you were to step through the doorway, you will end up entering your room from the S door while an infinite number of yous appear to do the same thing.

Let's take this one step further and make the connection to the small curled spaces of the superstring theories. Imagine that the room were so small that you could reach through the doorway and pat the you in front of you on the back. Weird, but it's easy to imagine. Now, imagine if the room were much smaller, small enough that you can rech through several rooms! Maybe the room is just large enough to contain you. Try picturing what happens to your arm as you try and reach through as many rooms as you can. Let's say you're jabbing your arm as if punching straight. What happens? Here's a hint: You will see your hand go past your body several times! Also, you might notice that your arm will get in its own way unless you angle your arm to avoid itself. How funky!

Well, once you can imagine this, you've basically passed the course for one curled dimension. In order to imagine more than one curled up dimension at once, it is just a matter of creating more doorways in The Funky Room. For two curled dimensions, you'll have two doorways: N/S as above and E/W. For three, you'll have three dorways: N/S, E/W, and floor/ceiling. Three is probably the most anyone can handle, unless they're capable of imagining a four dimensional room!

To be complete, I have just described space dimensions that 'curve' back on themselves after a very short distance. We can be like a mathematician and call the distance for one particular space dimension its perimeter. If you wanted to draw this dimension schematically, you'd draw a small circle and mark the doorway as the 0 point. That circle would have a radius of (perimeter/2*Pi). This is where the description of 'curled up into little circles' comes from. What the superstring theories postulate is that there are many such 'curled up' dimensions in addition to the standard three that we experience. Each one has a very, very small perimeter.

So where do strings enter the picture? Easy, just get in The Funky Room with a very long piece of string and see what happens! It helps if you know about harmonics and music.

I hope that was interesting to someone.

Secular Pinoy

<img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" /> <img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" /> <img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" /> for that great analogy fando. I hope you can continue your discussion on string theory. Who needs amazon.com when we got clear-headed science writing like that here in IIDB. Two thumbs up!

Answerer

Well, according to string theory, the 'extra' spacetime are compactified, but I guessed things could be other way round where our familiar dimensions are actually the ones being compactified by higher dimensions.

Skeptictank

Damn you people! You are all melting my braaaain!!
Nevertheless, very cool reading.
However it seems that there is some confusion here on the "4th" dimension if i am not mistaken. There is the Einsteinein 4th dimension of time and then there is the mathamatical "hypercube" 4th dimension of weird intersections. You have to be specific as to which 4th dimension you are referring to!

gregw

Does the word have a "t" or an "s?" I'm so confused...:-) My brain's pretty fried at this point, too. But here's the explanation in "Cosmos." Sorry if it's already been posted:

Take a line. That is one dimensional; it has only length, but no height or width whatsoever. (Yes, I know that even its constituent atoms/quarks/strings have these, but it is a mathematical construct. Work with me here.) Take another line at a right angle to the first. Now you have a two dimentional object, with length and width. Take a third line at right angles to the other two. Now you have a three dimentional object, with length, width and height. Take a fourth line at right angles to the other three. Now you have a four dimentional object, with length, width, height and...and...well, call it "N." Take a fifth line at right angles to the other four. Now you have a five dimentional object, with length, width, height, "N" and...and...well, call it "O." Take a sixth line...

Actually, Sagan spoke of sweeping a line (1 dimensional) at a right angle to itself (through the 2nd dimention) to make a square (2 dimensional), then sweeping the square at a right angle to itself (through the 3rd dimension) to make a cube (3 dimensional,) then sweeping the cube at a right angle to itself (through the 4th dimention) to make a tesseract (4 dimentttssional :-) then sweeping the tesseract...

"At a right angle" does not mean "diagonally." All angles are right angles in each of these examples.

Make sense? I'm not sure how or if the "small" or "curled up" dimentions fit into this. (I read "The Elephant..." I mean "The Elegant Universe" as well. I'm still recovering...)

nyx

Aldehyde,

I've seen diagrams of the hypercube that may help you visualize.

Anyone out there with this?

Models are often helpful in visualizing. Heck, most people can't imagine a finished house from the floor plan.

Nyx

nixon

to DNAunion:

I understand where you're coming from, but I have 2 problems with this "theory" ?!?

1)If a(n) objects motion spacially affects it's "speed" timewise, wouldn't our world be extremely time fragmented due to everything moving at different speeds? Like if I drive somewhere @ 60MPH, wouldn't I be out of time with someone who hasn't?

2)And that leads me to problem 2: If I have to move near light speed spacially, (Which is what I think your answer to prob 1 will be) then why must I expend so much energy within the first 3 dimensions to equate a move that in the 4th requires little to no expenditure. It would seem illogical that altering movements along any dimensional pathway (1,2,3 or time) would require a different amount of energy from each other, assuming a state of rest exists on the object that will be moved.

Are you suggesting that the 4th dimension is different, maybe that it's not at rest?

Personally I find it easier to visualize dimensions 1-3 as a frame in a movie, and time as the movie strip. The present is where the light from the projector is shining through. However, what is controlling the speed of the projector. Or even more creepy is what determines the amount of light the bulb in that projector shines (100W or 500W?)

Abacus

I'll take a crack at these.

This is precisely what happens according to Einstein's Theory of Relativity. Though at 60 mph, the effect will not be noticeable. But if you had access to the starship Enterprise ...

I'm confused about what you are asking here. Could you try to clarify?

Yes, it is easier. But this is the old Newtonian view of mechanics. It has been replaced by Relativity Theory.

DNAunion

DNAunion: As Random Number Generator pointed out, that is what actually happens. But the discrepancies are too small to notice.

Time dilation due to relative motion has been verified experimentally. One method was to take two atomic clocks and synchronize them, then fly one around the world while the other remained at rest. When they were brought back together again and their times compared, the "moving" clock had less time elapsed on it (I believe about 9 billionths of a second: although far too small to be noticed by humans, scientific measurements of that magnitude are rather large).

Relativistic time dilation has also been confirmed by examining muons. The half-life of muons is found experimentally in a lab. Then scientists went to the top of a mountain and counted the number of muons that passed through a given area in a given amount of time. Based on this, it is easy to calculate how many should survive at sea level (i.e., how many per unit area should be found to have not decayed). The measurements at sea level were found to be far too high to explain, except if one took into account time dilation. The muons travel at about .99 c, so their internal "clocks" - which determine their rate of decay - were running more slowly than when they were in the lab. So the half-life of muons at .99c is longer than their half-life at rest, and this accounts for the excess muons surviving the trip from the top to the bottom of the mountain.

DNAunion: I didn't follow that either. You don't have to move near light speed spatially, unless you are trying to slow down the passage of time relative to someone at rest.

Probably the most common visualization of relativistic time dilation is that of a light clock. If I have time, I might come back and post something on that.

Oh yea, did I mention that gravitational time dilation also occurs!

davidm

Aldehyde, I think gregw gave the best explanation, if you're read his post. Time has been considered the fourth dimension since Einstein came along, but you are asking about a fourth spatial dimension. In principle, there could be any number of spatial dimensions, even an infinite number. To travel into the fourth dimension, all you have to do is find a direction in space that is simultaneously perpendicular to the other three directions that define a line, a plane, and a volume.

If you try to do this, you will fail, because we live in 3-space and our minds are adapted to 3-space. So no one can visualize what a fourth (or fifth or x-dimension) would look like, but the mathematical properties of extradimensional space have been understood since the 19th century. Have you ever read Flatland?

What interests me is that in recent years, scientists have scrutinized hypothetical multidimensional space to see what their physical properties would be like, even if no one can directly visualize those properties. Turns out, curiously, that almost all configurations of spacetime different from our own 3+1 would produce universes devoid of any imaginable life or even ordinary structures. For example, it has been shown that universes of four or more spatial dimensions (but otherwise incorporating all our physical laws) would have no stable gravitational orbits. They would also be highly chaotic in other ways. With spatial dimensions of fewer than 3, gravity would not propagate beyond its source, and the sort of information processing necessary to life and a lot of other things would fail. You could even imagine more exotic combinations, such as three dimensions of time and one of space -- in which case, the physicist Max Tegmark says, you would get a world consisting of nothing but tachyons. A lot of this dimensional analysis is due to Tegmark.