BASIC TERMS IN STRING THEORY


SUPERSYMMETRY

Supersymmetry is a theoretically attractive possibility for several reasons. Beyond that is the remarkable fact that it is the unique possibility for a non-trivial extension of the known symmetries of space and time (which are described in special relativity by the Poincare group).
Mathematically, it can be described in terms of extra dimensions that are rather peculiar. Whereas ordinary space and time dimensions are described by ordinary numbers, which have the property that they commute: , the supersymmetry directions are described by numbers that anti-commute:


PERTURBUTION THEORY

A useful way of studying theories that cannot be solved exactly is by computing power series expansions in a small parameter. Thus, if T(a) denotes some physical quantity of interest
and the first few terms can give a very good approximation. This approach, which is called perturbation theory, is the way superstring theories were studied until recently. The problem is that in superstring theory there is no reason that the expansion parameter a should be small.
More significantly, there are important qualitative phenomena that are missed in perturbation theory. The reason is that there are non-perturbative contributions to many physically interesting quantities that have the structure. Such a contribution is completely invisible in perturbation theory.
Perturbative quantum string theory can be formulated by the Feynman sum-over-histories method. This amounts to associating a genus h Riemann surface, which can be visualized as a sphere with h handles attached to it, to the hth term in the string theory perturbation expansion. The genus h surface is identified as the corresponding string theory Feynman diagram. The attractive features of this approach are that there is just one diagram at each order of the perturbation expansion and that each diagram represents an elegant (though complicated) mathematical expression that is ultraviolet finite (no short-distance infinities).
The main drawback of this approach is that it gives no insight into how to go beyond perturbation theory.

D-Branes

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"http://theory.caltech.edu/people/jhs/strings/ref.html" l "seven"
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"http://theory.caltech.edu/people/jhs/strings/ref.html" l "eight" (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.

M-Theory

The understanding of how the IIA and HE theories behave at strong coupling, which is by now well-established, came as quite a surprise. In each of these cases there is an 11th dimension that becomes large at strong coupling. 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.

S Duality

Suppose now that a pair of theories A and B are S-dual. This means that if f denotes any physical observable and l denotes the coupling constant. The expansion parameter a introduced earlier corresponds to l). This duality, whose recognition was the first step in the current revolution, "http://theory.caltech.edu/people/jhs/strings/ref.html" l "six" generalizes the electric-magnetic symmetry of Maxwell theory. Since the Dirac quantization condition implies that the basic unit of magnetic charge is inversely proportional to the unit of electric charge, their interchange amounts to an inversion of the charge (which is the coupling constant). S duality relates the type I theory to the HO theory and the IIB theory to itself. This explains the strong coupling behavior of those three theories.

T Duality

The basic idea of T duality(for a recent discussion see"http://theory.caltech.edu/people/jhs/strings/ref.html" l "five") can be illustrated by considering a compact dimension consisting of a circle of radius R. In this case there are two kinds of excitations to consider. The first, which is not special to string theory, are Kaluza--Klein momentum excitations on the circle, which contribute (n/R)2 to the energy squared, where n is an integer. Winding-mode excitations, due to a closed string winding m times around the circular dimension, are special to string theory denotes the string tension (energy per unit length), the contribution to the energy squared is Em=2pmRT. T duality exchanges these two kinds of excitations by exchanging m with n and This is part of an exact map between a T-dual pair A and B.
One implication is that usual geometric concepts break down at short distances, and classical geometry is replaced by "quantum geometry," which is described mathematically by 2D conformal field theory. It also suggests a generalization of the Heisenberg uncertainty principle according to which the best possible spatial resolution Dx is bounded below not only by the reciprocal of the momentum spread, Dp, but also by the string scale Lst. (Including non-perturbative effects, it may be possible to do a little better and reach the Planck scale.)
Two important examples of superstring theories that are T-dual when compactified on a circle are the IIA and IIB theories and the HE and HO theories. These two dualities reduce the number of distinct theories from five to three.

A Contract between TEM and de Broglie Waves

A clue to the nature of de Broglie waves (lambda=h/p) is that the period , lambda/c, is nearly equal to L/v (where L is the Compton wavelength and v is velocity). T he de Broglie "frequency" is c/lambda (approximately v/L), depends on "v", and suggests a Doppler origin. This can be understood, if (1) particles are not quiescent, but have charge elements, which oscillate internally, and (2) this oscillation creates EM waves unlike the TEM waves derived by Hertz. Charge oscillation leads to an E field directed along "v" and proportional to 1/r. There is also a cylindrical B field, proportional to 1/r^2, per the Biot- Savart law. The oscillating EM energy remains attached to the source. It is proposed that the frequency of internal motion is f=c/L=m0c^2/h=E/h, and is a fundamental property of matter. Modified by SR and split by the Doppler effect, the beat frequency (b.f.) leads directly to the de Broglie wavelength. The wave function Psi is identified with these b.f. waves, and is thought to be a mathematical simplification of the EM fields created by internal oscillations.
The wave-particle dilemma of the nature of light has troubled physicists of the 20th century. The experimental evidence shows that light has particle-l like properties, but no particles have been found to explain diffraction, interference, and coherence. The physics establishment remains convinced of the essential correctness of the transverse electromagnetic (TEM) wave theory of light, and the consensus seems to be that light is basically TEM wavelike even though the energy content is constrained to a small volume of space.
This all is not to be confused with the wave function. A wave function for any particle is simply a probability of what ever component is under discussion (ie. momentum) of being in a certain condition at a certain instant in time. As one will notice my theory follows that of the normally accepted TEM approach. It must also be stated that while particles have a wavelike nature. It is a field itself in the form of our proposed string structure that is in a wave motion and not an actual em field. But I do believe since this field set has a specific frequency and wavelength that all atomic elements could be effected by an simular em field.
Now, given the tube within a tube structure proposed herein. The de Broglie concept is inherent within the structure itself. As energy flows throughout this system from the outside to the inside and back an internalized oscillation is indeed generated. But the structure itself has an outward going wave and an inward going wave that also duplicates an older concept of the Standing wave concept. Also, given that the outward tube expands in a wave fashion along the length of the String. The Transverse Electromagnetic method is also present. It is the structure of these tubes that prevents our being able to duplicate by natural means TEM. The closest we ever come is in a wave-guide. If we could create one from a material that would exactly expand and collapse with its internal EM wave it is guiding. One could duplicate this same effect in a localized area.
Altering the TEM component should modify both the de Broglie and Standing Wave components. This is because an effect on one portion changes other aspects also. Now,more on this will be mentioned latter. But one aspect of this I wish to discuss in shot fasion has to do with the space-warp methods proposed by Miguel Alcubiere Moya in 1994. This method is as follows. In 1994, Miguel Alcubiere Moya, then at the University of Wales at Cardiff, discovered a solution to Einstein's equations that has many of the desired features of warp drive. It describes a space-time bubble that transports a starship at arbitrarily high speeds relative to observers outside the bubble, Calculations show that negative energy is required. "Warp drives might appear to violate Einstein's special theory of relativity. But special relativity says that you cannot outrun a light signal in a fair race in which you and the signal follow the same route. When space-time is warped, it might be possible to beat a light signal by taking a different route, a shortcut. The contraction of space-time in front of the bubble and the expansion behind it create such a shortcut. What I am proposing is that even though negative energy might be forbidden in the context of time reversed energy/matter. That if one follows the following proposed transtation method and its theoretical results another method of achieving the same effect is possible at far less energy requirements.
By using an EM wave of exactly opposite phase and equal wavelength to the particles included in the object, one was trying to warp, the outer tube component could be nullified. This nullification would remove the 4D space-time portion. As such, the remaining 6D component would expand in the given area of the transtation fields effects creating a zone in space devoid of gravity. Using a reverse of this process in front of the ship, with this process behind, would yield the same desired effect. The energy requirements for generating such a field would be vastly less than those of the original Alcubiere type.

Lets compare the force calculated as due to the diverging EM field - with Newton's Law for a force between two hydrogen atoms. The gravity force between two hydrogen atoms can be calculated as follows:
Fg=Gm1m2/R2
Is gravity simply a pseudo-force caused by the relativistic effects of moving charges - calculated as the divergent EM field? Perhaps gravitation may due to the fact that we do not have the right coordinate system? Curiously, the divergent atomic EM field does have all the characteristics of gravity, such as a non-shieldable force that follows the inverse square of distance law. Atoms that generate an EM field will give rise to nearby electrostatic fields that are set up to counter balance anything that is polarized by such EM fields. If we ignore the effects of particle spin, it means that there are no net forces on a single charged elementary particle suspended in a gravitational field - that is, if it is located inside a closed box of normal matter. We can predict that a single positive or negative elementary particle will "float" in a gravitational field, as if with no weight. However, a dielectric (such as a neutral atom) will fall in the same situation
It may be argued that elementary particles have no weight at all - and that they only have only inertia and mass. Interpretation of results from a free fall experiment of electrons at Stanford University may suggest that elementary single particles do not have weight. The results from Stanford University showed that the gravitational acceleration of electrons in a metal tube was close to zero (measured to within 9%). The scientists explained this unusual result as the effect of the earth gravitational pull on free electrons in metal. It was argued that each electron and nucleus in the metal were acted on by an average electrical field (set up by a slight displacement of charges), polarizing the metal and exactly counteracting the free floating electrons inside the tube.
According to the divergent EM field theory, the experiments at Stanford, could be explained by understanding that there are no forces on non-dielectric charged particles (such as an electron) located in cavity immersed in an EM field. The electrostatic field, setup inside the cavity to counteract to the EM field, will exactly cancels the EM field because of separation of charges. Understanding this, a single electron will behave as having no weight, since EM - Es = 0, and the electron will appear to have no acceleration in a gravitational field.
But, given the TEM nature of particles it is possible that what is being observed there is what I have chosen to term a transtation effect. The above cavity was immersed in an EM field. Even though the frequency is not equal in wavelength to that of an electron. The two waves would either be additive or subtractive depending upon the phase differences. If it was subtractive, and given that the gravity field generated by elemental particles is so small to begin with there might have simply occurred a canceling of the inertia field completely or to such an extent that the electron did behave as if it had no weight.
It is also known that Particles have a diameter roughly equal to the incident wavelength. Which I believe is accountable for a stretching of the basic string so that its net tension is increased and thus its frequency and wavelength are increased. This stretching would be accountable due to effects from 6D Higgs space-time. There is a stable solution to Maxwell's equations which is equivalent to a continuous standing electromagnetic wave arranged concentrically about a point. Standing waves of intermediate sizes explain the Rydberg constant and the fine and superfine structures of spectral lines. Some particles and all atoms are expected to be composites of different sized waves within each other.
Actually there are a whole set of solutions to Maxwell's equations which take this basic form. They all have the same nodal structure and property that the energy is distributed as the inverse square of the distance from the center, but the differences are due to the possible different polarization schemes for the light in the wave. It is not possible for all of the light in the wave to be unpolarized. This is the same situation as the ball of fur which has to have at least two places where there is a crown. To put it another way, if the wave is considered to be a displacement of space (as an alternative explanation to Maxwell's equations) then any rotation of a spherical shell must leave two points unmoved. The point here is that given a certain restraining medium (ie String Tubes) one can set this same effect up in a given small localized space.

GRAVITY WAVES

Gravity waves were postulated by Einstein's theory of gravitation, wherein accelerated masses also produce signals (gravitational waves) that travel only at the speed of light. And, just as electromagnetic waves can make their presence known by the pushing to and fro of electrically charged bodies, so can gravitational waves be detected, in principle, by the tugging to and fro of massive bodies. However, because the coupling of gravitational forces to masses is intrinsically much weaker than the coupling of electromagnetic forces to charges, the generation and detection of gravitational radiation are much more difficult than those of electromagnetic radiation. Indeed, since the time of Einstein's invention of general relativity in 1916, there has yet to be a single instance of the detection of gravitational waves that is direct and undisputed.
There are, however, some indirect pieces of evidence that accelerated astronomical masses do emit gravitational radiation. The most convincing concerns radio-timing observations of a pulsar located in a binary star system with an orbital period of 7.75 hours. This object, discovered in 1974, has a pulse period of about 59 milliseconds that varies by about one part in 1,000 every 7.75 hours. Interpreted as Doppler shifts, these variations imply orbital velocities on the order of 1/1000 the speed of light. The non-sinusoidal shape of the velocity curve with time allows a deduction that the orbit is quite noncircular (indeed, an ellipse of eccentricity 0.62 whose long axis precesses in space by 4.2 per year). It is now believed that the system is composed of two neutron stars, each having a mass of about 1.4 solar masses, with a semi-major axis separation of only 2.8 solar radii. According to Einstein's theory of general relativity, such a system ought to be losing orbital energy through the radiation of gravitational waves at a rate that would cause them to spiral together on a time scale of about 3 108 years. The observed decrease in the orbital period in the years since the discovery of the binary pulsar does indeed indicate that the two stars are spiraling toward one another at exactly the predicted rate.
Gravitational waves have a polarization pattern that causes objects to expand in one direction, while contracting in the perpendicular direction. That is, they have spin two. This is because gravity waves are fluctuations in the tensor metric of space-time. All oscillating radiation fields can be quantized, and in the case of gravity, the intermediate boson is called the "graviton" in analogy with the photon. But quantum gravity is hard, for several reasons:

· The quantum field theory of gravity is hard, because gauge interactions of spin-two fields are not renormalizable. See Cheng and Li, Gauge Theory of Elementary Particle Physics (search for "power counting").

· There are conceptual problems - what does it mean to quantize geometry, or space-time?
It is possible to quantize weak fluctuations in the gravitational field. This gives rise to the spin-2 graviton. But full quantum gravity has so far escaped formulation. It is not likely to look much like the other quantum field theories. In addition, there are models of gravity which include additional bosons with different spins. Some are the consequence of non-Einsteinian models, such as Brans-Dicke which has a spin-0 component. Others are included by hand, to give "fifth force" components to gravity. For example, if you want to add a weak repulsive short range component, you will need a massive spin-1 boson. (Even-spin bosons always attract. Odd-spin bosons can attract or repel.) If antigravity is real, then this has implications for the boson spectrum as well.
The spin-two polarization provides the method of detection. Most experiments to date use a "Weber bar." This is a cylindrical, very massive, bar suspended by fine wire, free to oscillate in response to a passing graviton. A high-sensitivity, low noise, capacitive transducer can turn the oscillations of the bar into an electric signal for analysis. So far such searches have failed. But they are expected to be insufficiently sensitive for typical radiation intensity from known types of sources.
A more sensitive technique uses very long baseline laser interferometry. This is the principle of LIGO (Laser Interferometric Gravity wave Observatory). This is a two-armed detector, with perpendicular laser beams each travelling several km before meeting to produce an interference pattern which fluctuates if a gravity wave distorts the geometry of the detector. To eliminate noise from seismic effects as well as human noise sources, two detectors separated by hundreds to thousands of miles are necessary. A coincidence measurement then provides evidence of gravitational radiation. In order to determine the source of the signal, a third detector, far from either of the first two, would be necessary. Timing differences in the arrival of the signal to the three detectors would allow triangulation of the angular position in the sky of the signal.
The speed of gravitational radiation (Cgw) depends upon the specific model of Gravitation that you use. There are quite a few competing models (all consistent with all experiments to date) including of course Einstein's but also Brans-Dicke and several families of others. All metric models can support gravity waves. But not all predict radiation travelling at Cgw = Cem. (Cem is the speed of electromagnetic waves.) There is a class of theories with "prior geometry", in which, as I understand it, there is an additional metric which does not depend only on the local matter density. In such theories, Cgw != Cem in general.
However, there is good evidence that Cgw is in fact at least almost Cem. We observe high energy cosmic rays in the 1020 to 1021 eV region. Such particles are travelling at up to (1-10-18)*Cem. If Cgw < Cem, then particles with Cgw < v < Cem will radiate Cherenkov gravitational radiation into the vacuum, and decelerate from the back reaction. So evidence of these very fast cosmic rays is good evidence that Cgw >= (1-10-18)*Cem, very close indeed to Cem. Bottom line: in a purely Einsteinian universe, Cgw = Cem. However, a class of models not yet ruled out experimentally does make other predictions.

I was recently Emailed a most interesting question on the subject of groupoids and transitions. I have lost who exactly Emailed this question. But the person was from Bangor Maine. So I thought I would post his question here and a partial answer.

Question: Thanks for the reference. It would be marvellous if some expert could makea use of these multiple groupoids in string theory, as has been suggested to me. A. Connes in his book on `Non commutative geometry' (Academic Press, 1994) suggests that Heisenberg invented quangtum mechanics by passing from a group of symmetry to the groupoid of transitions of the hydrogen spectrum (and considering the convolution algebra of this). So my *very* naive question is what can be invented in physics by passing from groupoids to multiple groupoids (of interacting multiple transitions?)? I hope that putting the question will at some stage suggest a good idea to someone. I have a lot to do in thew areas I know something about!

Answer: Some of the most significant developments in mathematics in the past year stem from a breakthrough achieved by Vladimir Voevodsky, and from work by Voevodsky and Andrei Suslin which builds on this breakthrough. Providing bridges across different areas of mathematics, this work constitutes a significant step toward resolving some questions that had eluded mathematicians for several decades. Voevodsky has been invited to present a plenary lecture about his work at the International Congress of Mathematicians, the most important meeting in the mathematical world which takes place every four years and will next be held in Berlin in August 1998.
On its most general level, the work of Voevodsky provides a new link between two circles of ideas in mathematics: the algebraic and the topological. The term algebra as used here refers to a much broader and deeper field than that studied by high school students. What mathematicians mean by algebra is, roughly speaking, a theory for studying the general structure of sets endowed with algebraic operations, like addition and multiplication of the integers {...-3, -2, -1, 0,1, 2, 3,...}.
There are many different kinds of algebraic objects, the most basic one being an abelian group. An abelian group is a set together with an operation on the elements of the set, where the operation has all the properties of addition of the integers. More complicated structures, such as commutative rings and fields, arise when one considers more than one operation and how the operations interact. The simplest example of a ring is the integers, together with the two operations of addition and multiplication. If one introduces a third operation, division, one obtains the rational numbers, i.e., fractions, and such a structure is formalized in the notion of a field. Other examples of rings are the sets of polynomials (in any number of variables) whose coefficients belong to a given field. For any finite set of polynomials one can look at the common zeros of those polynomials. This set of zeros is called the algebraic variety defined by the polynomials. Adding more polynomials will often cut down the size of the common zero set, yielding sub-varieties of the algebraic variety. Sub-varieties are sometimes referred to as algebraic cycles on the variety.
Now, a lot of symmetry theory and work with guage fields deals with non-abelian type groups or sets. Since these groups do not commute they require a different algebraic form to solve for them. One good example that comes to mind is those involved in QCD and QED. It is interesting to note that just one portion of the math involved in QED involves no less than 7 pages. Yet, this theory is the single most experimentally proved theory within the limits of error.
In the 1960s, mathematicians discovered a remarkable link between singular cohomology and another set of groups which are collectively referred to as K-theory. A cornerstone of topological K-theory is the Atiyah-Hirzebruch spectral sequence, developed by Michael Atiyah and Friedrich Hirzebruch, which provides a catalog of isomorphisms between certain cohomology groups of a topological space and its K-groups. In fact, more is true. The collection of all the cohomology groups of a space forms a ring, and the same is true of the K-groups. These two rings are isomorphic, meaning that both addition and multiplication in cohomology and K-theory are preserved by the isomorphism between them. This isomorphism is known as the Chern character, after S. S. Chern. These results were very surprising, because the definitions of cohomology and of K-theory are very different and they arise in widely separated contexts. Cohomology arises from cutting up a space into smaller pieces, whereas K-theory arises from consideration of larger objects called vector bundles over the space.
To a certain extent M-Theory evolved along simular lines as a means of studying the localized effects of those Strings upon space-time. Here they dwelt with the different Brane states. One of these, the D-Brane has already been used to study Blackholes of near-extremal type. It was that which recently proved Hawkin's theory about blackholes radiating energy as correct.
One of the reasons I mention on my site the desire to use modeling is to find if either, any new apllications can be derived, or if there are special effects in the structure of space-time that one could look for as a signature of further proof the theory is correct. Finding something of a signature would be vastly a step beyond the proofs I have offered thus far.
However, it must be remembered that the tube within a tube field structure I have proposed in my Modification is something new. It has taken the membrane and expanded it back into something more akin with the older point particle. But on a scale that avoids infinities. That was also why I had that statement about if we take the particle as the smeared out wave function. Then a lot of the problems with Uncertanity have been removed. Because a particles position and momentum then becomes that of the group or wave function as a whole when you remove the outside reflection type waves from the equation. This was why I said that a particle in the old 2 slit experiment actually does take a specific path through the slit. The other is simply a false pattern that is formed by virtual particles.

FOR A MORE COMPLETE LOOK AT THIS THEORY AND ITS BACKGROUND TRY:

http://65.108.189.168/Docs/The%20Revised%20Modification%20To%20M-Theory%20Model.pdf

THE FORMAT HERE IS A COMPLETE EBOOK.