I was recently reading the book called The Elegent Universe by Brian Green and I found it interesting(what I could understand of it), but gave it up before finishing it because towards the end I was pretty much unable to figure out what the hell he was talking about and exactly how it applied to anything else. I found it interesting though didn’t quite understand why all these caveats needed to be apply (It talked about Spin and then how all particles needed a companion with 1/2 the spin, but never quite explained why it was needed in the first place). I don’t know if that makes me stupid or if the book was obviously way over my head(the first half I understood pretty well). But I digress…
Anyway, At one point it talks about dimensions and how there are probably 9 dimensions, but we can only see 3 because the others are incredibly small and rolled up.
That led me to two questions:
1.Exactly how can something be a dimension if it’s all rolled up on a sub-microscopic level?
If there was a 4th spatial dimension, as opposed to the 3 we all know, how would the world be changed(or our perception of it)? I kept trying to imagine it but I couldn’t quite wrap my mind around it. I can see going from 1 to 2, or 2 to 3, but I’m not sure how to progress from 3 to 4.
Here is one example I can think of. You know what a 3-dimensional object is? Right? OK, when you think about a 3D object you generally think about it being a rest. Now, think about that object being in motion, that adds a 4th dimension to the object. I’m not saying that this is the 4th dimension, just a 4th dimension. Now to get from a 4th dimension to a 5th dimension, generally when you think about an object traveling, you think about it traveling in a straight line. Instead, lets think about this object traveling along the surface of a Mobius strip (you know a Mobius strip right? where you take a strip of paper, twist it 1/2 turn and attached the loose ends to each other). An object traveling in what appears to be a straight like on the surface of a Mobius strip will actually eventually come back to it’s point of origin. So, in this 5th dimension straight lines act more like circles. See how this progresses? Now, a 6th dimension, hmm… have to think about that one some more
The easy answer to going to four spatial dimensions is that the world would be changed a whole lot, because it wouldn’t exist.
Neither planetary orbits nor electron orbitals are stable in four spatial dimensions. You could have a universe with some individual particles flitting around, but nothing with more substance.
The fact that we exist is why scientists think those six other spatial dimensions have to be rolled up or in some other way not detectable under ordinary circumstances.
Gravity, however, can propagate through all the dimensions, which creates some interesting effects, including the possibility of reconciling general relativity and quantum theory.
I usually tell people to read The Elegant Universe for more about this, but since that’s failed, you’ll have to wait for others to come along and try their hand at a simplified explanation of this.
To be entirely honest, I don’t fully understand any of it either. I think that the idea of nine dimensions (no cite, this is just the best reasoning I can come up with) may be at least distantly related to the fact that if a two-dimensional object (i.e., a piece of paper. Even though technically it’s three dimensions it’s thin enough for this example) after being folded nine times it will have become a perfect cube, assuming it’s length and width are the same.
Anyhow, the whole idea that a fourth dimension is incomprehensible is because it’s beyond human comprehension. The only three dimensions that are comprehensible to humans are length, width, and height. The closest thing I can imagine to a fourth dimension is spherical geometry (again, no cite, I can’t remember where I heard that. I think it was Einstein who figured that spherical geometry was more efficient for calculating long distances like planets and all what-have-you in space, but not sure. Sorry!) but again a sphere is, to the human mind, comprised mainly of three dimensions.
The way i think of a 4th dimension of space is as follows:
A line is one dimensional. To a 1 dimensional being, the line is the universe. You only need one number to decribe your position. Now go to 2 dimensions - the line becomes a square. To a 2 dimensional being, that square if the universe, and you need 2 numbers to describe your position.
Imagine how that would look to a 1 dimensional being. It would look like lots and lots of 1 dimensional universes (lines). Some of these universes would be next to each other, some would be further apart. Even though this 1 d being couldn’t conceive of the 2nd dimension, it could conceive of lots of 1 dimensional universes. It would see the two numbers needed to describe your position as being the one “normal” number its used to, and the other one describing which line (universe) you’re in.
If you go from 2D to 3D its a similar story. A 2D being would see the 3D universe (a cube) as lots of squares somehow next to each other. It would think of 3D movement as being able to move up and across as it can, but also move from square to square.
So if i try to go from our universe to a 4 dimensional one, i see lots and lots of 3D universes which are next to each other in the 4th space dimension. I think of 4D movement as being able to move in 3 dimensions like i can, but also being able to move across all these universes.
Of course this isn’t a completely correct visualisation, but its as close as i’m going to get i think.
Unfortunately, the only analogy I can think of is to use linelanders (imaginary critters that inhabit a 1 dimensional universe). They would perceive only one dimension. Now imagine that instead of one dimension, their universe actually consisted of a long (infinitely, presumably) tiny tube, so small that the could not perceive it. That is what is meant by a dimension being rolled up.
One way they could detect this would be if they could measure this–at least in principle–would be by measuring gravity at very short distances, smaller than the circumference of the cylinder. Now in lineland, the force of gravity would not change with distance. Except that at distance scales small enough to feel the second dimension. At such scales it would obey a 1/d law. Similarly, if we could measure gravity at sufficiently small scales we might see something other than a 1/d^2 law. If we saw, say, 1/d^8, we could conclude that at that scale we were in a 9 dimensional universe.
As for trying to visualize it, forget it. Our brains are simply not made to perceive, or even imagine, any dimension higher than 3. We cannot not even imagine a universe in which the third dimension was curled into a circle. But the best way of thinking about that is to try to imagine that there was some direction in space such that if you went on a straight line in that direction you would eventually come back to where you started. Of course, it would also be possible that every direction was like that (that would be called a toroidal universe). Or you could imagine that you came back left-handed (assuming you were right-handed) with your heart on the right side. There are many possibilities.
Spherical geometry is two dimensional. You only need two coordinates to specify a point; think latitude and longitude. A sphere is a 3D object with a 2D surface.
