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. I just briefly browse the fundamentals of them.
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
However, 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
To me there are fundamental issues with string theory and because of that I am going to play the devil’s advocate 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.
To respond to numerous calls from the boundaries of the 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 spatial 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's 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 known four dimensional space-time paradigm. However, one dimension added by Kalusa was not enough. Therefore, 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.

String theory is background dependant. It means that it is built and based on space-time fabric. Whereas Einstein proved that space and time are malleable and change constantly. How can you build a house on top of a stormy ocean and expect to reach to kind of stability such as laws of physics we have? For one, standard model of particles has to be described within a background independent theory. A background dependant theory is not the answer. It seems that we need to look for the answers where the space and time get fuzzy and melt down.

By assuming extra dimensions for space, string theory is actually an extension of classic mechanics. Surprisingly, in the supersymmetric string theory some forces have infinite range. Infinity is the amount that I attributed to the energy and information in the proposed singularity. In addition, Since the space and its dimensions and assumed extra-dimensions are unstable, collapse to singularity is an unavoidable consequence.

Quantum entanglement and Bose-Einstein condensate suggest non-locality in deeper level and take the totality of space as we now it under question. Theorists are faced with paradoxical state of space versus non-locality and are working hard to come up with a reasonable explanation.  
In Q2C Festival, Oct. 2009 Neil Turok from the Perimeter institute announced that mathematical tools emerged from String theory suggest that in some situations space may be an illusion.  He reasoned that one can describe a three dimensional object in a two dimensional quantum picture.  Is this an incidental mathematical finding or a construct guided by presupposed hypothesis, remains to be explored?   
In the Brain lateralization theory chapter a conjecture is proposed for the paradox. Based on the theory, it is suggested that space maybe just an approximation of a more fundamental element created by the left hemisphere.  

 

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.

the end-points of open strings terminate in membranes
www.damtp.cam.ac.uk

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. with the long string of assumptions in string theory, can we claim that it have been successful to describe physical reality? Not quite.  

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.

The dilution of the gravity force throughout the space.

www.ifa.hawaii.edu

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
The Hierarchy problem questions this immense difference of the strength between different fundamental forces of nature. Why does gravity so much weaker than the other forces?  This is against the Grand Unified theory assumptions.

In Brane-universe conjecture, there are other dimensions and branes. String theorists assume that although gravity is equal to other forces, but because it gets diluted in other dimensions, what we observe is the very feeble strength in comparison.
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 law dictates. 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. 

As it mentioned before, string theorists believe that gravity penetrates inside the extra dimensions as well. Claims that the extra dimensions are Planck distance small therefore the effect is negligible, cannot be sound for the reason that there are countless extensions of these extra dimensions along the way. So we should be able to measure the soaking effect in the gravity or magnetic force. This effect is not detected.
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-world scenario, extra dimensions could be as large as 1mm” ⁶⁹
So it was assumed that in scales less than 1mm, the inverse square law will break down. Currently, the gravity has been tested down to one tenth of the millimeter and inverse square law still holds.
Branes in string theory are assumed to be multidimensional and sometimes very large space-like entities. If they have existed the dilution of the forces should have certainly been detectable everywhere. None of these effects have been observed.

Flat Universe
In addition, string theorists have assumed that the main dimensions (four dimensions in Minkowski's space) are circular in big scale (spherical universe). So they speculated that at the time of Big Bang all dimensions evolved from a point. As the universe expanded, space opened up and created circular dimensions. So the observable dimensions are supposedly circular. They further assumed that if this is the case, so maybe there exist other dimensions, which did not open up. These guess work might offer some solutions so string theorists could avoid zeros. However, Brian Greene questions: “What if the spatial dimensions are not circular in shape? Do these remarkable conclusions about minimal spatial extent in string theory still hold? No one knows for sure.”¹
However, recently cosmological constant was announced as small but a non-zero factor. A non-zero cosmological constant favors an almost flat universe,
The Cosmological Constant is a factor that was first introduced by Albert Einstein. It wee supposed to act against the gravity and prevents the collapse of the universe. There is controversy about the origin and the nature of this constant. In fact, Recently it is shown that its effect surpasses the gravitational force of existing bodies in the universe and according to current believes it is creating the force for accelerating expansion of the universe. 
If the universe is flat, we may conclude that spatial dimensions are linear and not circular. Therefore, the base of the assumption of wrapped extra dimension is trembling.

Strings as Particles
Particles in string theory are one-dimensional threads which we can see only the cross section of it (as a point). Point particles in quantum mechanics on the other hand, do not posses any dimension.
The strings in the String Theory are either loops or free end. These elements with their different vibration patterns can represent different energy level. Then the energy can be translated as mass of the particle. One expects that the liberty to choose any vibration should help us to find a particular vibration which matches at least one of the known particles. The problem is, after three decades of extensive research, there was no resemblance between particles in string theory and the actual sub-atomic particles.
Then the next assumption came to rescue. If extra-dimensions have different sizes, then the loop’s vibration in different dimensions with different sizes will open a new possibility to explore. Maybe if we find the right size for each dimension, we can come up with vibrations that resemble the common particles.    So the legend continued.
Branes as Particles
Even if particles arise as oscillation modes of strings, string oscillation don’t necessarily account for all particles found in nature. Therefore, Andy Strominger and colleagues at Santa Barbara came with another idea. They proposed that in certain space-time geometries the branes give rise to new types of particles. These are called p-branes. They speculated that since branes can come in different shapes, forms and sizes, we can assume a very tinny curled up brane acting as an independent object that interact with its environment. Therefore, assumed wrapped branes can be candidates for the particles that are not found in string form.
Then there were problems of complicated calculations so they assumed that there are symmetries in the whole elements of the universe. Calculations by using symmetry principles were easier and solvable.
The strings are so small that can not be detected so the whole idea could not be tested and therefore could not be proved. Then Super-symmetry came to picture and the assumption that there are much bigger particles which are symmetric to small and not observable strings. This assumption created the hope that sometime in the future we can observe the bigger partners and prove the conjectures.

Brian Greene himself questions the string particles:

“Just as string theory shows that the conventional notion of zero- dimensional point particles appear to be a mathematical idealization that is not realized in real world, might it be the case that an indefinitely thin one dimensional strand is similarly a mathematical idealization.”¹

String of Assumptions
The string of assumptions does not stop here. The complexities imposed by confining ourselves to space-time arena, led the string theorists to even believe in possibility of existence of as many as 10⁵⁰⁰ different worlds. Thus they indorsed the multiverse concept. The multiverse idea advocates the presence of many parallel worlds
With so many assumptions, one can find a solution for any kind of puzzle. Imagine you have the liberty to redesign a crossword puzzle by moving around the black squares to your will and select your own words to place in the squares. Moreover, you take the liberty to choose the shape and the size of the puzzle. Solving the puzzle will get very easy this way. As the problems aroused more postulations came to rescue. Now we have built a fascinating theory that is mind wrenching and a good challenge for the boys to entertain themselves. Is this waste of talents and knowledge of brilliant physicists and mathematicians?  We do not know. For solving the biggest question of century, any path has to be explored. Nevertheless, this is my question;
Can the fundamental structure of our universe be so complicated? Ray Salmonoff suggests:

“If a given set of facts about the world can be explained by more than one theory, how do we choose between them? …The short answer is to use Occam's razor: you pick the theory with least number of independent assumptions.”⁷  

Localized Gravity
In 1999 two leading string theorists Lisa Randal and Raman Sundrum introduced the Localized Gravity or so-called SR273.  They investigated a 5-dimensional scenario with the fifth dimension being an infinite, out of site and attached to a brane.  They concluded that such a universe is feasible and normal gravitation can exist in this model.

cosmicvariance.com

In SR2 model the infinite fifth dimension is a reflective membrane. Therefore, particles that hit the brane simply bounce back, so they regain their energy when they hit this membrane. Surprisingly, particles in this scenario are normal point particles of standard model not strings.

The localized gravity model is a big set back from bold exploitations of string theorists. String particles and many dimensions and branes are crossed out. This is a more sensible model. Although here again the fifth dimension is a space-like dimension. Being a physicists string theorist have to work inside a tangible arena. However, this is ignoring the intangible aspect of reality where we are so much acquainted with within our consciousness.
Please note that, the notion of particles bouncing back to 4-dimentional space-time is in line with our bouncing ball model introduced in wave-particle chapter.
Maybe we'd better accept point particles as the building blocks of the universe and take violent quantum jitters as the process of two-way transformation of matter and energy at Planck's Length level (or Planks pores).  
Helge Kragh questions String Theory:

“Even on the theoretical level, there were several problems, namely, that theories were plagued by infinities and what are technically known as anomalies. Anomalies are terms that violate the symmetries or conservation laws when the theory is quantized. And therefore make the theory inconsistent…The entire development of super string unification was mathematical.” ³  

Lisa Randall one of the string theory fort runners writes ⁷³;

“String Theory is a beautifully design suit that does not quite fit. In its current state, you can hang it on the rack and admire its fine stitching and intricately woven pattern_ it really is beautiful_ but you can’t wear it unless you make necessary adjustments…….Right now, we don’t even know whether we have the right tools to tailor string theory correctly.”

Just being beautiful and elegant is not enough for a construct to be a true feature of nature. When the first Calabi-Yau compactification (extra dimension's configuration) was found, it was beautiful and elegant. In addition, it could accommodate the three particle generations of standard model. 

Shape of space with extra-dimensions
web.mit.edu

Therefore, it was introduced as a unique candidate for the shape of space with extra-dimensions. However within a week, Gary Horowitz found several other candidates. Now there are tens of thousands of Calabi-Yau candidates. Any mathematical construct has to conform to physical evidences to be considered as a feature of nature, otherwise we fabricate abstract and non-physical math.

String theory and God

Space-time point of view of string theorists led them to the speculation that god actually is made of material substance that leaves in another world (brane). The Can String Theory detect God video that is made by Nova and features Brian Greene tries to convey the above assumption. If that’s the case, then we probably should find paradise and hell with sinners burning in it at that brane as well.   It is not clear if this video is a vehicle to attract religious people to science and draw their support for string theory or to solve the puzzle of spirituality. But this kind of assumptions turns god and heavens to an external entity made of matter that dwell in a space –time setup.   It also substantiates the old beliefs that are within the frameworks of existing faiths. These outdated beliefs are far from scientific principles and logical thinking.
It seems to me that spirituality is an internal realization. It evolves from deeper levels of consciousness. Consciousness does not contain matter, space or time. My conjecture about consciousness is fully detailed in related chapters.

Elegant mathematics of string theory

Roger Penrose believes that mathematics is a vast platonic domain and physical reality just uses a portion of this domain. Therefore in his opinion mathematics has an actual external existence⁵. In the contrary the lateralization theory of brain (explained in quantum brain chapter) suggests that mathematics is a fabrication of left brain hemisphere. According to the theory, in his analytical task to explain the physical reality, the left brain construct a logical mathematical framework to be used as reference.
It seems that the mathematical structures created in super string theory supports the brain lateralization theory version of the origin of mathematics. String theorists were successful to create all kind of math equations to support their imagined many-dimensional reality. Amongst them is the so called Grassmann variables which lead to strange relations like

AB = -BA or

A² = -A² = 0 and

B² = -B² = 0⁹¹.
Obviously the above equations cannot be related to known physics. Mathematical elegance is the back-bone of the string theory. However, the fact that mathematics followed every originally accepted and later on rejected branch of string theory puts this main supporting substantiation under question.

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 spatial 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. None of the speculations of string theorists have been experimentally observed. String theorists as physicists traditionally work and look within the objective and tangible arena. Therefore they assume presence of extra dimensions of space and unseen super-partner particles to find the answers and solve the paradoxes. Ironically, many of the forces in supersymmetric string theory have infinite range. Infinity is the amount that I have assumed for the energy in the singularity. In addition collapse of unstable extra-dimensions produces devil singularities! It seems that there is no running away from singularity.

Maybe we are looking in wrong places for wrong objectives. Maybe space, time and mass are not as solid. Maybe objective world is not the only aspect of our universe. It seems, the mainstream interpretation of quantum physics is pointing to an alternative direction.
One may assume that all of the speculations and inventions of string theorists such as, extra-dimensions, branes, super-partners and other conjectures that are supposedly solve the paradoxes exist within the perception and imagination of these physicists. In brain lateralization theory explained in the Quantum Brain chapter analytical approach to investigate reality is related to left brain hemisphere and is subject to error. The least that one may expect from this kind of approach is sticking close to physical experiments. Otherwise sky is the limit for our imagination. Building up abstract mathematical structures is also an artifact of left brain and by itself does not serve the purpose.

 Complex Numbers

The notion of complex numbers indicates that the real value of any computable (matter, space and time) are fundamentally discrete (assertion C5 in this text). Assuming any extended and continuous object is against the complex number mathematics which is the basis for quantum mechanics and modern science.

0-Dimension Singularity
We try to close our eyes on those mathematical answers that we dislike. We normalize (discard) the unfavorable results. We have been selective and biased. Denying zeros and infinities just adds to our uncertainty and confusion. Maybe the time has come to revisit the issue.
Space-time settlers cannot imagine a point with no-dimension. The classical mechanics view motivates the string theorists to assume wrapped and out of site dimensions to accommodate a sensible space-time thing. Above I suggested that we are exposed to singularity wherever there is no dimension (inside Planck Length and beyond the boundaries of universe). In twilight zone of boundaries the quantum leap is the constant communication between space-time universe and singularity. In this view we do not need to assume dimensions being tangible or hidden in order to explain some of the extraordinary physical findings.
In 1960s Stephen Hawking and Roger Penrose introduced the Singularity Theorem which showed that a Ricci flat extra space evolved in time has to be singular. This also includes the (9+1) dimensional space-time proposed by super string theory. Interestingly the time needed for compact extra dimension to turn to singularity is at Planck time of 10 ^-43s. Mind you that in my model space is four-dimensional (3-space + 1-time) and is discrete at the Planck distance and time level.
In his recent book, The Road to Reality, Roger Penrose writes
“If we wish to…obtain a non-singular perturbation of the full (1+9)-space… then we must consider disturbances that significantly spill over into…space-time as well. But in certain respects such disturbances are even more dangerous to our ordinary picture of space-time… (Which) is in gross conflict with observation” ⁵⁶

Please note that, no-dimension provides ultimate freedom and fulfills adherence to observations. We just need to free ourselves of the notion of space and time and imagine a no-space-time zone. To me the assumption of one dimensional string particle (extension of mass proper to unseen extra dimensions) and suggesting the existence of a super-space (which is still a space-like entity) beyond the familiar space-time is the frantic attempt of cliff settlers to keep their ground and not to cross the border to unknown. Maybe we have to assume that the entity beyond the boundaries of space-time is not space-like and has no dimension. Maybe we'd better off postulate that mass beyond space time can convert to something else (energy in this model).

Please note that by involving a non space-time element (singularity), this model is background independent.
 
Summary
Although String theory is the most popular model for theory of everything, it has its shortcomings. The theory is based on denying zero and infinities. It also employs frequent independent assumptions. At the same time it builds a complex and sophisticated model for space which is hard to prove. In my view, because it tries to deny zero and infinity, it overlooks a main portion of reality.
An excellent series of string theory videos in a layman term is produced by Brian Greene featuring Steven Weinberg and few other great physicists of our times. You can watch them at: Elegant Universe

The arguments presented are open for debate. The reader is encouraged to email his/her inputs to correct, modify or develop the contents. Please send your emails to; zpfields@yahoo.ca

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