This is a chapter of a paper which is proposed as a model for theory of everything. For examining the principles, readers are either referred to look at the singularity as seperate entitiy in this library or to browse the whole paper at www.universaltheory.org.
Photo / NOVA
A Calabi-Yau shape: a two dimensional visualization of the six additional spatial dimensions required by string theory. (46)
String Theory
String theory is proposed to resolve the inconsistencies between GTR and Quantum Mechanics. One of its main objectives is to solve the problem of 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 theory tries to solve the singularity problem by assuming string shape for subatomic particles and assigning more dimensions to the space-time. 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 p54
Although 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-p57
Underneath, I will address the occasions where String Theory faces the singularity (sub Planck length and time).
Brian Greene on The Elegant Universe suggests that the presence of singularities will not create any catastrophe. "Strominger then showed, with a simple and standard physic calculation, that the wrapped three-brane provides a tailor made shield that exactly cancels all of the potentially cataclysmic effects that string theorists have previously feared would occur if a three-dimensional sphere where to collapse.. In Strominger's paper, he had studied what happens when a three dimensional sphere pinches down to a point, and had shown that, the newfound extended object in string theory insures that physics continue to be perfectly well behaved." 1- page 324-325
In the same page, he says; "There is no catastrophic jump, spike or any unusual feature.........as the tear (in space-time universe) occurs. From the point of view of physics, the moment of tearing has no distinguishing characteristics." 1- page 281
(The universe could currently be in the midst of a spatial rupture. If it were occurring slowly enough, we would not even know it was happening.)
“Our work showed that a new massless pattern of string vibration arising from the space-tearing conifold transition is the microscopic description of mass- less particle into which the black hole has transmuted” 1- page 331
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-Page 123 In a way one can claim that, Singularity is the central dilemma of contemporary physics.
"The whole conflict between general relativity and quantum mechanics arises from sub-Planck- Length properties of the spatial fabric" (1, page 156)
String theory tells us: "there is a limit to how finely our conventional notion of distance can even be applied to the ultra microscopic structure of cosmos." (1- page 157).
[BREAK]
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 have any distance. One can conclude that no notion of distance could be applied, being conventional or non-conventional, to Sub-Planck Sea. Particles in string theory are threads which we can see only one dimension of it (length). the other two other dimensions are out of our site. Point particles in quantum mechanics on the other hand, do not posses any dimension. Space-time settlers can not imagine a point with no-dimension. The materialistic way of thinking motivates the string theorists to assume wrapped and out of site dimensions to accommodate a realistic space-time thing. Above I suggested that we connect to singularity wherever there is no length (inside Planck Length and beyond the boundaries of universe). Quantum leap is constant communication between space-time universe and singularity. The particles (or trace of them, whatever it may mean) do not have any dimension when they are out of space-time In this view we do not need to assume dimensions being tangible or hidden for explaining some of the physical findings.
Why extra dimensions? because extra dimensions provide freedom. Imagine two dimension figures drawn on a piece of paper. They experience quite a lot of limitations. They do not enjoy the third dimension freedom. But one dimension added by Kalusa was not enough so string theorist had to add another 6 dimension to obtain the freedom to present their model. And in the year 1995 in order to explain why there are five different models of string theory which are contradicting each other and at the same time claiming to be the theory of everything, they introduced M-theory and took the liberty to add 7th extra dimension.
At one time even 26 dimensions were suggested. Please note that, no-dimension provides ultimate freedom and fulfil adherence with mathematical findings. We just need to free ourselves of notion of space dimensions and imagine no-dimension zone.
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 go very bold against it in the following paragraphs. Of course these are my personal opinions. Correct me if I am wrong. Please send an email or leave your input in message board.
String theorists question themselves; “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- page 165
To find a solution they had to introduce extra dimension. That means that the thickness can be find in another dimension, but that dimension is wrapped and it is out of our sight. Also in order to find a solution for particle wave phenomena, String theorist assumed that the principle thing is a string. This way it can wave and at the same time it is a particle. Unfortunately just one extra dimension would not offer a flawless solution. so the hard work of string theorists during the past decade, produced more ingredients with a variety of different dimensions. But then where are the dimensions? They had to assume again that these dimensions are circular and wrapped together. Originally, string theorists assumed that the main dimensions are circular in big scale (spherical universe). So if they are circular, It means at the time of big bang, they where wrapped and as the universe expanded they opened up and created the dimensions that we observe. If that is the case, so may be there exists other dimensions which did not open up. Luckily these guess work might offer some solutions so string theorists may be able to avoid zeros. but with introduction of non-zero cosmological constant and flat universe now we know the three dimensions are linear and not circular. So the base of the assumption of wrapped extra dimension is trembling . Now what?
Brian Green states "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." p 254 ref 1
The string of assumptions does not stop here. There came basic loop and its different vibrational patterns which can give different mass and create the known subatomic particles. Of course we can arbitrary choose any frequency to create the desired vibration. Then there were problems of complicated calculations so they assumed that there are symmetries. Calculations on those symmetries were easier and achievable. Plus the strings are not visible so the whole idea is not testable. because of the fact, it never can be claimed as a theory. Super symmetry came to picture and the assumption that there are much bigger particles which are symmetric to small strings and hopefully in the future we can observe them.
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 also select your own words to place in the squares. Moreover, you have the liberty to choose the shape and the size of it. 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 which 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. But this is my problem; The fundamental structure of our universe can not be this 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.” 7-135
Maybe we 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 (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-page 417
We try to close our eyes on those mathematical results, which we dislike. We have been selective and biased. It just added to our uncertainty and confusion. Maybe the time has come to revisit the issue.
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 singularities. It also employs frequent independent assumptions. At the same time it builds a complex and sophisticated fabric for space. In my view, because it tries to deny zero and infinity, it overlooks a main portion of reality.
An excellent series of videos in simple word presentation, was produces by Brian greene featuring Steven Weinberg and other great physicists. These videos explain String Theory in general public level. You can watch them at http://www.pbs.org/wgbh/nova/elegant/program.html
References
1 - The Elegant Universe, Brian R. Greene, March 2000, Vintage Books
2 - The Quest for unity, Etienne Klein & Marc Lachieze-Rey, Oxford University Press, 1999
3 - Quantum Generations, Helge Kragh, Princeton University Press, 1999
6 - The Universe in a Nutshell, Stephen Hawking, 2001, Bantam Books
This is a portion of a model for Theory of everything which is called universal theory. for studying the complete model, Please check
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