Photo / NOVA

A Calabi-Yau shape: One of the many two dimensional visualization of the six additional spatial dimensions required by string theory. ⁴⁶

String Theories are proposed to resolve the inconsistencies between GTR and Quantum Mechanics. Currently string theory is the prime candidate for the theory of everything. In the Standard Model of particle physics the building blocks of matter are point like zero-dimensional particles. Whereas, in string theory the building blocks are one-dimensional extended objects (strings). Strings can be open threads or closed loops. Many texts are available which explain the detail of the theory. It is beyond the scope of this book to describe the elements and principles of string theories.

One of main objectives of the super string theory is to solve the problem of the so-called space-time singularities. It tries to define a kind of world that its boundaries stop at Planck distance.

Uphill struggle has been done in order not to pass to sub Planck distances and deny zeros and infinities. The string theorists by-pass zero and singularities, by assuming that the building block of space is a string which is the size of Planck distance (1.6* 10^-33 cm). Therefore, they suggest that there is no zero or singularity in the fabric of space.In addition, it assigns more dimensions to the space-time to be able to solve the other theoretical physics paradoxes. Steven Hawking believes:

“All one can say is whether mathematical models with extra dimensions provide a good description of the universe. We do not yet have any observation that requires extra dimension for their explanation.” ⁶

He does not completely reject it, he later mentions:

“String theory is good for calculating what happens when a few high energy particles collide and scatter off each other. However, they are not of much use for describing how the energy of a very large number of particles curve the universe or forms a bond state” ⁶

Denying Singularity

Underneath, I will address the occasions where String Theory faces the singularity (Sub-Planck arena in this model's terms.
Etienne Klein & Marc Lachieze-Rey show how string theorists tried to open the field by adding extra dimensions in order to bypass singularities to no veil. Even after adding numerous hypothetical elements to physical world, they are still facing with singularities but from a new angle.

“One of the motivations of those who are working on this theory is to get rid of troublesome singularities in field theory calculations…Quantum Theory gets around these difficulties with a method that is as artificial as it is effective. It is called renormalization…(String Theory) deals from outset with the structure of space and elementary objects...Sure enough, problems of singularities show up in a totally different way in that string theory.” ²

In a way one can claim that, Singularity is the central dilemma of contemporary physics. Brian Greene one of the main advocates of string theory in his famous book The Elegant Universe explains: “The whole conflict between general relativity and quantum mechanics arises from sub-Planck- Length properties of the spatial fabric” ¹

He continues: “There is a limit to how finely our conventional notion of distance can even be applied to the ultra microscopic structure of cosmos.” ¹

Brian Greene rightly mentions that our conventional notion of distance cannot be applied on ultra-microscopic structure of space. If Planck length is the smallest unit of distance, anything less than that cannot be considered space. One can conclude that no notion of distance could be applied, being conventional or non-conventional, to Sub-Planck Sea.

In his recent book “The Fabric of the cosmos”, Brian Greene confirms that;

“The theory intimates that the familiar notion of space and time do not extend into the sub-Planckian realm, which suggests that space and time as we currently understand them may be mere approximations to mere fundamental concepts that still await our discovery.” ⁶⁹

In my view trying to deny zero and infinity is avoiding the reality. So I have fundamental issues with string theory and because of that I am going to get very bold against it in the following paragraphs. Of course these are my personal opinions.

String Theory: A Theory of Everything

The assumed particle for curving the space-time and creating gravity is called “Graviton”. The graviton has not been found experimentally but it is further assumed that it should be mass-less and should have spin-2 (have two times faster spin than photon).

In 1974 John Schwartz and Joel Schrek claimed that a mass-less spin-2 particle that is predicted by string theory is the long sought and never found graviton. They further claimed that the equations of string theory embodied a quantum mechanical description of gravity. Therefore, they declared the string theory a candidate for the theory of everything.

Remember, the theory of everything is supposed to bring the the general theory of relativity and quantum mechanics under one umbrella.

Space in String Theory

Space in the String Theory is continuous but granular. The granules being Planck distance size strings. These strings are supposedly the building block of space.

Furthermore, to respond to numerous calls from the boundaries of universe received through mathematical calculations and physical experiments, string theorists chose to introduce extra dimensions. The original assumed dimensions were wrapped and compact and ultra small, therefore they were out of our sight. String theorists are claiming that the unexplained space-time phenomena are coming from elements present in other dimensions.

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 freedom. 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 space-time context. However, one dimension added by Kalusa was not enough. Therefore, string theorist had to add another 5 dimension 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 contradicting each other and at the same time each claimed to be the theory of everything, they introduced M-theory and took the liberty to add the 7^th 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. They introduced kind of membranes, which are called D-branes. D-branes are hypothetical spaces, which can have up to ten dimensions with any size.

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?

Did the string of assumptions solve the problems? Not quite.

String’s 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 lawreflects the three-dimensional space. The reason being, the gravity force spreads and gets diluted in three dimensionality of space. Electromagnetic 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

In Brane-universe conjecture, while other fundamental forces are confined to three-dimensional brane-world, gravity is getting diluted in extra-dimensions as well.

The gravity decline is directly related to number of extra-dimensions. For a ten dimension space is governed by;

G = M * m / d^(10-1) = M * m / d⁹

Of course, the force decline is related to the size of extra dimensions as well. Nevertheless, one would expect that the force of gravity gets diluted much greater than what inverse square lawdictates. At least, such a gravity decline should reveal itself in astronomical calculations. So far, cosmological observations confirm the Newton’s inverse square law. No further decline has been observed.

In 1988, the gravity law could be tested down to 1mm with the then current probes. This led Nima Arkani-Hamed, Savas Dimopolous, and Gia Devali to speculate that “in the brane-worldscenario, extra dimensions could be as large as 1mm” ⁶⁹

So it was assumed that in scales less than 1mm, the inverse square lawwill break down. Currently, the gravity has been tested down to one tenth of the millimeter and inverse square law still holds.