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 Bangall dimensions were just 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 Green 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 a non-zero factor. A non-zero cosmological constant favors a flat universe,

The Cosmological Constant is a factor that was first introduced by Albert Einstein. It acts against the gravity and prevents the collapse of the universe. There is controversy about the origin and the nature of this constant. In fact, its effect surpasses the gravity and according to current believes it is creating an ever-expanding 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.

The notion of complex numbers indicates that 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.

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 has not been any 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 continues.

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 achievable.

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. It 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 10⁵⁰⁰ different worlds thus they indorsed multiverse concept.

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, 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. 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

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

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.

0-Dimension Singularity

Space-time settlers cannot imagine a point with no-dimension. The space-time way of thinking 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. The particles (or trace of them, whatever it may mean) do not have any dimension when they are out of space-time (particle-wave chapter). In this view we do not need to assume dimensions being tangible or hidden for explaining some of the physical findings.

In 1960s Stephen Hawking and Roger Penrose introduced the SingularityTheorem 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 scale of 10 ^-43s. Mindyou 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 the need to adherence to ovbservations. 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 pass the edge. 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).

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 videos in a layman terms presentation was produces by Brian Greene featuring Steven Weinberg and few other great physicists of our times. You can watch them at:

http://www.pbs.org/wgbh/nova/elegant/program.html