# Physics: String Theory The Wave Structure of Matter (WSM) explains why String Theory is a Mathematical Theory Only (Founded on Wave Theory & Resonance)

In String Theory, the myriad of particle types is replaced by a single fundamental building block, a `string'. These strings can be closed, like loops, or open, like a hair. As the string moves through time it traces out a tube or a sheet, according to whether it is closed or open. Furthermore, the string is free to vibrate, and different vibrational modes of the string represent the different particle types, since different modes are seen as different masses or spins. One mode of vibration, or `note', makes the string appear as an electron, another as a photon.

Just like an ordinary guitar string, a fundamental string can vibrate in different modes. And it is these different modes of vibration of the string that are understood in string theory as being the different elementary particles. (Smolin, 1997)

### Introduction to String Theory

Superstring Theory, M Theory and Brane Theory all evolved from the original String Theory back in the mid 1980s. As I see it, String Theory (and its derivatives) are an example of theorists being taught mathematical Physics while completely neglecting Philosophy and Metaphysics. Thus there is no awareness that a complete description of Reality must be founded on ONE thing (not on many discrete things / strings!). The reason for the partial success of String Theory is that it utilises Wave Theory and resonant frequencies. The strings can only vibrate at discrete frequencies which correspond to different 'particles' and their energy states.
I must admit that I look forward to the future when the Wave Structure of Matter is equally famous, for then they will see how truly absurd string theory is (founded on 9 dimensions of Space, but six dimensions 'magically' curl up so we don't see them!).

Below you will find several summaries of String Theory from the main web sites that promote this theory. I think that after reading on the Wave Structure of Matter you will understand why String Theory evolved as a mathematical theory (founded on waves / resonance), and also why its literal interpretation is nonsense.

Sincerely,
Geoff Haselhurst

PS - There is a very good essay on the many problems of string theory at;

http://www.newyorker.com/archive/2006/10/02/061002crat_atlarge

### The Standard Model

In the standard model of particle physics, particles are considered to be points moving through space, tracing out a line called the World Line. To take into account the different interactions observed in Nature one has to provide particles with more degrees of freedom than only their position and velocity, such as mass, electric charge, color (which is the "charge" associated with the strong interaction) or spin.

The standard model was designed within a framework known as Quantum Field Theory (QFT), which gives us the tools to build theories consistent both with quantum mechanics and the special theory of relativity. With these tools, theories were built which describe with great success three of the four known interactions in Nature: Electromagnetism, and the Strong and Weak nuclear forces. Furthermore, a very successful unification between Electromagnetism and the Weak force was achieved (Electroweak Theory), and promising ideas put forward to try to include the Strong force. But unfortunately the fourth interaction, gravity, beautifully described by Einstein's General Relativity (GR), does not seem to fit into this scheme. Whenever one tries to apply the rules of QFT to GR one gets results which make no sense. For instance, the force between two gravitons (the particles that mediate gravitational interactions), becomes infinite and we do not know how to get rid of these infinities to get physically sensible results.

### String Theory

In String Theory, the myriad of particle types is replaced by a single fundamental building block, a `string'. These strings can be closed, like loops, or open, like a hair. As the string moves through time it traces out a tube or a sheet, according to whether it is closed or open. Furthermore, the string is free to vibrate, and different vibrational modes of the string represent the different particle types, since different modes are seen as different masses or spins. One mode of vibration, or `note', makes the string appear as an electron, another as a photon. There is even a mode describing the graviton, the particle carrying the force of gravity, which is an important reason why String Theory has received so much attention. The point is that we can make sense of the interaction of two gravitons in String theory in a way we could not in QFT. There are no infinities! And gravity is not something we put in by hand. It has to be there in a theory of strings. So, the first great achievement of String Theory was to give a consistent theory of quantum gravity, which resembles GR at macroscopic distances. Moreover String Theory also possesses the necessary degrees of freedom to describe the other interactions! At this point a great hope was created that String Theory would be able to unify all the known forces and particles together into a single `Theory of Everything'.

### From Strings to Superstrings

The particles known in nature are classified according to their spin into bosons (integer spin) or fermions (odd half integer spin). The former are the ones that carry forces, for example, the photon, which carries electromagnetic force, the gluon, which carries the strong nuclear force, and the graviton, which carries gravitational force. The latter make up the matter we are made of, like the electron or the quark. The original String Theory only described particles that were bosons, hence Bosonic String Theory. It did not describe Fermions. So quarks and electrons, for instance, were not included in Bosonic String Theory.
By introducing Supersymmetry to Bosonic String Theory, we can obtain a new theory that describes both the forces and the matter which make up the Universe. This is the theory of superstrings. There are three different superstring theories which make sense, i.e. display no mathematical inconsistencies. In two of them the fundamental object is a closed string, while in the third, open strings are the building blocks. Furthermore, mixing the best features of the bosonic string and the superstring, we can create two other consistent theories of strings, Heterotic String Theories.
However, this abundance of theories of strings was a puzzle: If we are searching for the theory of everything, to have five of them is an embarrassment of riches! Fortunately, M-theory came to save us.

### Extra Dimensions

One of the most remarkable predictions of String Theory is that space-time has ten dimensions! At first sight, this may be seen as a reason to dismiss the theory altogether, as we obviously have only three dimensions of space and one of time. However, if we assume that six of these dimensions are curled up very tightly, then we may never be aware of their existence. Furthermore, having these so-called compact dimensions is very beneficial if String Theory is to describe a Theory of Everything. The idea is that degrees of freedom like the electric charge of an electron will then arise simply as motion in the extra compact directions! The principle that compact dimensions may lead to unifying theories is not new, but dates from the 1920's, since the theory of Kaluza and Klein. In a sense, String Theory is the ultimate Kaluza-Klein theory.
For simplicity, it is usually assumed that the extra dimensions are wrapped up on six circles. For realistic results they are treated as being wrapped up on mathematical elaborations known as Calabi-Yau Manifolds and Orbifolds.

### M-Theory

Apart from the fact that instead of one there are five different, healthy theories of strings (three superstrings and two heterotic strings) there was another difficulty in studying these theories: we did not have tools to explore the theory over all possible values of the parameters in the theory. Each theory was like a large planet of which we only knew a small island somewhere on the planet. But over the last four years, techniques were developed to explore the theories more thoroughly, in other words, to travel around the seas in each of those planets and find new islands. And only then it was realized that those five string theories are actually islands on the same planet, not different ones! Thus there is an underlying theory of which all string theories are only different aspects. This was called M-theory. The M might stand for Mother of all theories or Mystery, because the planet we call M-theory is still largely unexplored.
There is still a third possibility for the M in M-theory. One of the islands that was found on the M-theory planet corresponds to a theory that lives not in 10 but in 11 dimensions. This seems to be telling us that M-theory should be viewed as an 11 dimensional theory that looks 10 dimensional at some points in its space of parameters. Such a theory could have as a fundamental object a Membrane, as opposed to a string. Like a drinking straw seen at a distance, the membranes would look like strings when we curl the 11th dimension into a small circle.

### Black Holes in M-Theory

Black Holes have been studied for many years as configurations of spacetime in General Relativity, corresponding to very strong gravitational fields. But since we cannot build a consistent quantum theory from GR, several puzzles were raised concerning the microscopic physics of black holes. One of the most intriguing was related to the entropy of Black Holes. In thermodynamics, entropy is the quantity that measures the number of states of a system that look the same. A very untidy room has a large entropy, since one can move something on the floor from one side of the room to the other and no one will notice because of the mess - they are equivalent states. In a very tidy room, if you change anything it will be noticeable, since everything has its own place. So we associate entropy to disorder. Black Holes have a huge disorder. However, no one knew what the states associated to the entropy of the black hole were. The last four years brought great excitement in this area. Similar techniques to the ones used to find the islands of M-theory, allowed us to explain exactly what states correspond to the disorder of some black holes, and to explain using fundamental theory the thermodynamic properties that had been deduced previously using less direct arguments.
Many other problems are still open, but the application of string theory to the study of Black Holes promises to be one of the most interesting topics for the next few years.

http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html

## Basic Ideas of Superstring Theory

In 1984-85 there was a series of discoveries that convinced many theorists that superstring theory is a very promising approach to unification. Almost overnight, the subject was transformed from an intellectual backwater to one of the most active areas of theoretical physics, which it has remained ever since.
By the time the dust settled in 1985, it seemed clear that there are five different superstring theories, each requiring ten dimensions (nine space and one time). To have a chance of being realistic, the six extra space dimensions must curl up into a tiny geometrical space, whose size should be comparable to the string length Lst..
A string's space-time history is described by functions Xm(s,t) which describe how the string's two-dimensional 'world sheet,' represented by coordinates (s,t), is mapped into space-time Xm. There are also functions defined on the two-dimensional world-sheet that describe other degrees of freedom, such as those associated with supersymmetry and gauge symmetries.
Surprisingly, classical string theory dynamics is described by a conformally invariant 2D quantum field theory. (Roughly, conformal invariance is symmetry under a change of length scale.) What distinguishes one-dimensional strings from higher dimensional analogs is the fact that this 2D theory is renormalizable (no bad short-distance infinities). By contrast, objects with p dimensions, called 'p-branes,' have a (p+1)-dimensional world volume theory. For p > 1, those theories are non-renormalizable. This is the feature that gives strings a special status, even though, as we will discuss later, higher-dimensional p-branes do occur in superstring theory.

In the IIA case the 11th dimension is a circle, whereas in the HE case it is a line interval (so that the eleven-dimensional space-time has two ten-dimensional boundaries). The strong coupling limit of either of these theories gives an 11-dimensional space-time. The eleven-dimensional description of the underlying theory is called "M theory." As yet, it is less well understood than the five 10-dimensional string theories.

Another source of insight into non-perturbative properties of superstring theory has arisen from the study of a special class of p-branes called Dirichlet p-branes (or D-branes for short). The name derives from the boundary conditions assigned to the ends of open strings. The usual open strings of the type I theory satisfy a condition (Neumann boundary condition) that ensures that no momentum flows on or of the end of a string. However, T duality implies the existence of dual open strings with specified positions (Dirichlet boundary conditions) in the dimensions that are T-transformed. More generally, in type II theories, one can consider open strings with specified positions for the end-points in some of the dimensions, which implies that they are forced to end on a preferred surface. At first sight this appears to break the relativistic invariance of the theory, which is paradoxical. The resolution of the paradox is that strings end on a p-dimensional dynamical object -- a D-brane. D-branes had been studied for a number of years, but their significance was explained by Polchinski only recently.
The importance of D-branes stems from the fact that they make it possible to study the excitations of the brane using the renormalizable 2D quantum field theory of the open string instead of the non-renormalizable world-volume theory of the D-brane itself. In this way it becomes possible to compute non-perturbative phenomena using perturbative methods. Many (but not all) of the previously identified p-branes are D-branes. Others are related to D-branes by duality symmetries, so that they can also be brought under mathematical control.
D-branes have found many interesting applications, but the most remarkable of these concerns the study of black holes. Strominger and Vafa[8] (and subsequently many others) have shown that D-brane techniques can be used to count the quantum microstates associated to classical black hole configurations. The simplest case, which was studied first, is static extremal charged black holes in five dimensions. Strominger and Vafa showed that for large values of the charges the entropy (defined by S = log N, where N is the number of quantum states that system can be in) agrees with the Bekenstein-Hawking prediction (1/4 the area of the event horizon).
This result has been generalized to black holes in 4D as well as to ones that are near extremal (and radiate correctly) or rotating. In my opinion, this is a truly dramatic advance. It has not yet been proved that there is no breakdown of quantum mechanics due to black holes, but I expect that result to follow in due course.

In the euphoria following the first superstring revolution in 1985, some of the less experienced participants in the enterprise thought that we were on the verge of constructing a complete fundamental theory of the physical world. To put it mildly, I found this naive. In this setting, the phrase "Theory of Everything" was introduced and propagated by the public media. This was very unfortunate for several reasons.
The TOE phrase is very misleading on several counts. First of all, the theory is not yet fully formulated, and when it is (which might still take decades) it is not entirely clear that it will be the last word in fundamental physics.
Furthermore, even if the theory is a complete description of quantum dynamics, it seems unlikely that it will also provide a theory of initial conditions, which is another key ingredient required to explain why we observe the particular universe that we do.
But even if a theory of initial conditions is also obtained, there will still be much about this universe that cannot be explained. Many things, such as our very existence, are a consequence of the inherent quantum indeterminacy of nature. I believe that cannot be overcome. Maybe that is just as well, because if we had old-fashioned classical determinism, the future would be fully determined, which would undermine our humanity.
There is also a more mundane sort of unpredictability that is also to be expected. Many of the things that the theory predicts unambiguously in principle could require intractable calculations. Part of the art of physics is to identify those things that can be calculated.
The other reason the TOE phrase upset me is that it alienated many of our physics colleagues, some of whom had serious doubts about the subject anyway.
Quite understandably, it gave them the impression that people who work in this field are a very arrogant bunch. Actually, we are all very charming and delightful.

http://www.theory.caltech.edu/people/jhs/strings/

### Related String Theory Websites

http://www.sukidog.com/jpierre/strings/links.htm - Comprehensive Links to Websites on Superstring Theory. From their Home Page: String theory is one of the most exciting and profound developments in modern theoretical physics. Unfortunately it is a highly technical subject that can only be well understood using the tools of Quantum Field Theory and General Relativity. It also doesn't hurt to know some mathematics like Group Theory, Differential Geometry, and Algebraic Geometry. Needless to say this is prohibitive for most people who are far too busy doing other things.

http://superstringtheory.com/ - General information on Superstring Theory from the 'Official' String Theory Site.

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