... Space in Sting Theory continues 

 

Why string theorists are introducing extra dimensions? Because extra dimensions provide freedom. Imagine two-dimension figures drawn on a piece of paper. They are subject to many limitations. They cannot enjoy the third dimension's freedom that we experience. That is how string theorists find relief from the limitations imposed on us by 4-dimensional space-time while trying to explain the paradoxes within known four dimensional space-time paradigm. The hypothetical one extra dimension added by Kalusa-klein theory in 1921 was not enough. String theorist had to add another 5 dimensions, to obtain the needed freedom to present their interpretations. In additions, in 1995 in order to explain why there are five different models of string theory, which are different from each other and at the same time each claimed to be the theory of everything, Edward Witten introduced M-theory and took the liberty to add the 7th extra-dimension. At one time even 26 dimensions were suggested.

 

D-Brane and Brane-World

 

The complexities and difficulties of fabricating a theory of everything which is limited to familiar space-time, led the string theorist to further assumptions. Joseph Polchinsky introduced kind of membranes, which are called D-branes. D-branes are hypothetical spaces, which can have up to ten dimensions with any size. A few dimensional extra space (D-brane) provides more freedom for new ventures. Some of these ventures were actually fruitful. Some of the versions of brane systems share some properties with a kind of black hole.

 

One of the most recent speculations of string theorists is the brane-world. Brane-world is a three-dimensional-brane, which embraces our universe.  Here is the question. Is the brane-space continuous or discrete? If continuous then what is going to happen to lengths smaller than Planck distance and zero in such a space? Are we going through the circle of introducing new elements to eliminate zero again? 

 

In general, some models can be derived from string theory which approximate some features of actual physical world, but a vast landscape of models are obtained from the theory as well that are nonphysical or not observed.

 

Gravity denies Extra-Dimensions

 

In 1987, Newton introduced the inverse square law. It simply declares that the force of gravity diminishes by the square of distance between two objects. G = M * m / d2  where M and m are masses of each object and d is the distance between them. The law simply indicates that if the distance is increased by factor of two the gravity force decreases by a factor of 4. Make the distance 3 times and gravity is decreased by a factor of 9. The inverse square law reflects the three-dimensional space. The reason being, the gravity force spreads and gets diluted in three dimensionality of space. Electromagnetism follows the same rule as well.

 

If we have n dimensions in space, then the gravity equation has to be written as;

G = M * m / d n-1.  The gravity decline is directly related to number of extra-dimensions. For a ten dimension string theory model, space the dilution is governed by; 

G = M * m / d (10-1) = M * m / d 9
The above law clearly supports the presence of just three dimensions that is in line with observations. However, because in Grand Unified theory, the fundamental forces of nature (Electromagnetic, weak, strong and gravity force) are assumed to be equal at origin, string theorists are busy finding models to explain the so called Hierarchy problem.
If you remember in Boundaries chapter we mentioned that the proportional magnitudes of different forces of nature are,
Strong nuclear force              10 ⁴⁰
Electromagnetic force            10 ³⁸
Weak nuclear force                10 ¹⁵
Gravity                                 10 ⁰