10 Dimensions In String Theory

The 10 Dimensions In String Theory

An animation attempting to depict a cube with 4 spacial dimensions.

Curled Dimensions

If we look at a hose from very very far away, it may look like a 1 dimensional line. If you consider an ant living on the hose however, it turns out that the ant can move in two dimensions. As you get closer and closer to the hose, you will realize that the hose is actually 2nd dimensional (ignoring the thickness and only looking at ways an ant on its surface could move), the extra dimension was just not visible from far because it was so small.

Let's extend this analogy to 3 dimensions.
Imagine a small ant living on a flat sheet of paper. From the ants perspective, it will be able to move in the 2 dimensions along the face of the paper. Additionally, the paper is made of many layers and is not just one sheet and so the ant may be able to move between the layers that make up the paper. Here the 3rd dimension is curled up and small and so to us looking at the paper from far, we may not see the paper's 3rd dimension.

String Theory's Extra Dimensions

All this seems pretty weird but string theory actually requires extra dimensions. Calculations in string theory gave negative probabilities which is never a good sign but when 9 spacial dimensions were used, then the negative probabilities cancel. This lead physicists to believe that the strings must vibrate in the 3 extended spacial dimensions that we see and in the 6 extra curled ones which we can't see.

This has some major implications because the strings are affected by the geometry of the dimensions that they vibrate in. The geometry of the curled dimensions determines the patterns of vibration which determines properties of particles and so ultimately, the fundamental properties of the universe are determines by the size and shape of the extra curled dimensions.

Unfortunately, the equations in string theory are usually so complicated that physicists can only use approximate versions of the equations and so it is not easy to know what the extra dimensions look like. We do know that Calabi-Yau shapes are the class of 6D shapes that meet the conditions in sting theory and so now physicist just need to decide which Calabi-Yau shape is the one in our universe. If string theory is correct, then every point in space has an extra 6 dimensions curled into Calabi-Yau shapes. This is impossible to visualize but you can use the earlier examples for 2D and 3D to get some sort of idea what curled dimensions are.

Implications Of 6 Extra Dimensions 

Calabi-Yau shapes have multidimensional holes in them and there is a group of lowest energy string vibrations for each hole. Fundamental particles should correspond with lowest energy string vibrations and so if the Calabi-Yau shape for our universe has 3 holes, then we will find 3 families of particles. This is called a post-diction as it will be explaining things we already know but it will be a pretty good one if we could say why there are 3 families of matter. The way the holes intersect and overlap also impacts the vibrations and so the masses of particles in families also depends on this,

The problem with this is that there are 10,000s of types of Calabi-Yau shapes and the number of holes vary massively between them. Currently we have no way of deciding a shape since we only have approximate equations where every shape has an equal chance of being suitable.

We could guess and check shapes staring with shapes with 3 holes but there are still an infinite number of shapes with 3 holes because they can all be smoothly deformed so that they are slightly different.

Determining the shape will be difficult but we have tested shapes and there are shapes that exist that could be our universe. If we were to find a way to eliminate all Calabi-Yau shapes apart from one, and that one gave physical characteristics identical to the laws of physics we see, then the case for string theory will be a strong one.



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