why do we need compactified dimensions?

[wendten]

I know that the compactified additional dimensions is the standart explanation, but the way I have thought of this is: The reason we can't see these dimensions, is that light fotons are bound to the 3rd D, and can't escape. Just like waves at the ocean can't escape its 2D surface. and neither can mass.
why is this much simpler theory not a valid explanation?

[javierR]

When it's said that "we can't see" the extra dimensions, it's not just that we can't visually see them, but that *no* particles have probed extra dimensions in experiments, and furthermore that gravitation does not carry direct evidence of extra dimensions. You can have non-compact extra dimensions in special circumstances, similar to what you're talking about, in which the particles we know in experiments only live on a slice of spacetime that makes up the 3+1 dimensions we are familiar with, though gravitational interactions extend to the extra dimensions due to the fact that general relativity applies to the total spacetime.
Extra dimensions aren't even necessary in quantum field theoretic models, though there are some phenomenological reasons why they have been considered in that framework. On the other hand, compactified dimensions were often considered in string theory because (1) extra dimensions ARE required and (2) the scenarios in the previous paragraph were only later realized in specific models (such as with intersecting branes or singular non-compact Calabi-Yau spaces). Until you can make these scenarios in the framework of string theory, the extra dimensions have to be tiny compact dimensions.

[DaveC426913]

The extra dimensions posited by these theories are far, far too small to interact with photons. They are many orders of magnitude smaller than atoms.

[Gear300]

The extra dimensions posited by these theories are far, far too small to interact with photons. They are many orders of magnitude smaller than atoms.

Planck length small?

[confusio]

The major benefit of compact dimensions in both string and field theories is that they produce the gauge group of the nonabelian gauge (Yang-Mills) symmetry. This is analogous to the Kaluza-Klein idea of a compactified 5th dimension generating the U(1) gauge group of electrodynamics. Additional curled up dimensions result in higher-dimensional gauge groups as required to describe the strong and weak nuclear forces.

Like other controversial aspects of some of the theories out there, there are a lot of predictions that cannot be tested, but the idea that something simple and geometric like curled up dimensions could result in this abstract gauge group is appealing to many.

Also, there have been a lot of papers written about large extra dimensions, which have had some theoretical success also.

[DaveC426913]

Planck length small?
Yes. On that order of magnitude.

[SW VandeCarr]

Extra dimensions aren't even necessary in quantum field theoretic models, though there are some phenomenological reasons why they have been considered in that framework. On the other hand, compactified dimensions were often considered in string theory because (1) extra dimensions ARE required and (2) the scenarios in the previous paragraph were only later realized in specific models (such as with intersecting branes or singular non-compact Calabi-Yau spaces). Until you can make these scenarios in the framework of string theory, the extra dimensions have to be tiny compact dimensions.

Do they all have to be compact? My understanding is that the preferred Type II string theory is the 10+1 version where the 10th dimension is not compact (ie 6 small compact, 3 large compact, 1 noncompact + time). Has this idea been abandoned? If so, has it been replaced by AdS/CFT? If understand it correctly, AdS/CFT is dual relation AdS_{5}S^{5}. Would this dual space rule out any noncompact dimensions?

EDIT: Another way to ask this question is: Can we have a model with only compact dimensions if the cosmological constant is zero (as it seems to be)?