Why do strings have to exist in 10 dimensions?

[11thDimension]

so i came across string theory and i don't understand (if your going to go along with it) why it is tiny strings that make up the universe and why exactly do they have to exist in more then 4 dimensions?

 

[DaveC426913]

so i came across string theory and i don't understand (if your going to go along with it) why it is tiny strings that make up the universe...

In a very simplified nutshell:

The theory of relativity and quantum mechanics - two of the most carefully tested and confirmed models ever developed in scientific history - turn out to be incompatible.

If you try to resolve relativity over the subatomic distances where quantum theory applies, you get infinities. To oversimplify further, QM says that the smaller you look, the larger the uncertainty. Relativity, on the other hand requires zero-dimensional, infinitely small point particles. Put those two together and you get particle interactions (i.e. energy transfers) that are arbitrarily large and occur over zero time, i.e. infinite energy transfer. This makes no sense.

String theory proposes that particles are not zero-dimensional, but instead are one-dimensional (strings). This neatly resolves the whole issue, since it spreads any and all interactions over a non-zero distance and non-zero time.

As for the extra dimensions, well, the properties of matter (such as mass, spin, etc) are manifestations of the vibrations of the strings. These vibrations need these extra dimensions in order to vibrate (read about Kaluza -Klein theory).

 

[11thDimension]

so why do these strings also have to be able to exist in 11 dimensions

 

[nnnm4]

so why do these strings also have to be able to exist in 11 dimensions

I'm not an expert, but it's my understanding that there is no a priori reason that the strings must exist in 11 dimensions, it's a requirement for the theory to fit with predictions. I could be mistaken of course.

 

[Demystifier]

so why do these strings also have to be able to exist in 11 dimensions

They don't. They exist in 10 dimensions. 11 is the number of dimensions in M-theory, which is believed to be more fundamental than string theory.

Of course, now you will ask why 10? Well, classical string theory is well defined in any number of dimensions. However, some symmetries (like Lorentz invariance) may achieve anomalies when a classical theory is quantized. Anomalies destroy the symmetries, so you don't want them. It turns out that anomalies cancel in 10 dimensions only. That's why you need 10.