I posted a little something into Wikipedia as a holiday exercise. I really enjoy reading about String Theory as it is venturing into the realm of metaphysics. The academic purists will probably pull it out but someone might enjoy this while it lasts.
“Branes (multi-dimensional or hyperspace objects) are conceptually at the nexus point of physics and metaphysics. One might raise the question as to what a multi-dimensional solid would look like. (This issue is raised in Chapter 14 of How to Manage Your Destructive Impulses with Cyber-Kinetics.) Indeed a whole series of quasi scientific questions might be asked that could shed some light on practical applications of String Theory to evolutionary biology. Some thinkers, for example, have speculated that the "zero point" is the interface between multi-dimensional space and our commonly experienced four dimensions of height, width, depth and time. A question for further consideration might be: what kind of energy dynamics could cause a brane or multi-dimensional object (MDO) to directly affect four dimensional space and time? A corollary question would involve the vector dynamics of such an emergence or pressure into four dimensional space-time. Would, for example, the speed of light involve an actual slowing down of multi-dimensional solids assuming trans-light velocities for MDOs? What are the dynamics of such a precipitation? A question that impinges on the field of biology might relate to clues that molecular and other macro biological structures present. Is the double helix of DNA related to the vector dynamics of higher dimensional, evolutionary pressures?”
From Wikipedia
Note
- When
- A more serious problem: The name M-theory is slightly ambiguous. It can be used to refer to both the particular eleven-dimensional theory which
String theory
From Wikipedia, the free encyclopedia.
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String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that are the basis of the Standard Model of particle physics. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. Studies of string theories have revealed that they require not just strings but also higher-dimensional objects.
The basic idea is that the fundamental constituents of reality are strings of the Planck length (about 10-35 m) which vibrate at resonant frequencies. The tension of a string (8.9*1042 Newtons) is about 1041 times the tension of an average piano string (735 Newtons). The graviton (the proposed messenger particle of the gravitational force), for example, is predicted by the theory to be a string with wave amplitude zero. Another key insight provided by the theory is that no measurable differences can be detected between strings that wrap around dimensions smaller than themselves and those that move along larger dimensions (i.e., effects in a dimension of size R equal those whose size is 1/R). Singularities are avoided because the observed consequences of "big crunches" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of a string, at which point it would actually begin expanding.
Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. It is a possible solution of the quantum gravity problem, and in addition to gravity it can naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry. It is not yet known whether string theory is able to describe a universe with the precise collection of forces and matter that is observed, nor how much freedom to choose those details the theory will allow. String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various special corners of the theory are accessible to planned observations and experiments.
Work on string theory has led to advances in mathematics, mainly in algebraic geometry. String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment.
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History
String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. In particle-accelerator experiments, physicists observed that the spin of a hadron is never larger than a certain multiple of the square of its energy. No simple model of the hadron, such as picturing it as a set of smaller particles held together by spring-like forces, was able to explain these relationships. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. Veneziano found that a 200-year-old formula created by Swiss mathematician Leonhard Euler (the Euler beta function) perfectly matched modern data on the strong force. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked.
In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. But even after physicists understood the physical explanation for Veneziano’s insight, the string description of the strong force made many predictions that directly contradicted experimental findings. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened.
Then, in 1974, John Schwarz and Joel Scherk, and independently Tamiaki Yoneya, studied the messenger-like patterns of string vibration and found that their properties exactly matched those of the gravitational force’s hypothetical messenger particle — graviton. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope.
This led to the development of bosonic string theory, which is still the version first taught to many students. The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.
Bosonic string theory is formulated in terms of the Polyakov action, a mathematical quantity which can be used to predict how strings move through space and time. By applying the ideas of quantum mechanics to the Polyakov action — a procedure known as quantization — one can deduce that each string can vibrate in many different ways, and that each vibrational state appears to be a different particle. The mass the particle has, and the fashion with which it can interact, are determined by the way the string vibrates — in essence, by the "note" which the string sounds. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory.
These early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two spectra. Not all modern string theories use both types; some incorporate only the closed variety.
However, the bosonic theory has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. While bosons are a critical ingredient of the Universe, they are not its only constituents. Investigating how a string theory may include fermions in its spectrum led to supersymmetry, a mathematical relation between bosons and fermions which is now an independent area of study. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described.
Roughly between 1984 and 1986, physicists realized that string theory could describe all elementary particles and interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This first superstring revolution was started by a discovery of anomaly cancellation in type I string theory by Michael Green and John Schwarz in 1984. The anomaly is cancelled due to the Green-Schwarz mechanism. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985.
In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an unknown 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution. When
Many recent developments in the field relate to D-branes, objects which physicists discovered must also be included in any theory which includes open strings of the super string theory.
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Basic properties
The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'.
While understanding the details of string and superstring theories requires considerable mathematical sophistication, some qualitative properties of quantum strings can be understood in a fairly intuitive fashion. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. The tension of a quantum string is closely related to its size. Consider a closed loop of string, left to move through space without external forces. Its tension will tend to contract it into a smaller and smaller loop. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". Consequently, the minimum size of a string must be related to the string tension.
Before 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and type IIB, and the two heterotic string theories (SO(32) and E8×E8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the theory whose low energy limit, with ten dimensions spacetime compactified down to four, matched the physics observed in our world today. But now it is known that this naive picture was wrong, and that the the five superstring theories are connected to one another as if they are each a special case of some more fundamental theory, of which there is only one. These theories are related by transformations that are called dualities. If two theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theory. The two theories are then said to be dual to one another under that kind of transformation.
These dualities link quantities that were also thought to be separate. Large and small distance scales, strong and weak coupling strengths – these quantities have always marked very distinct limits of behavior of a physical system, in both classical field theory and quantum particle physics. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related.
Suppose we're in ten spacetime dimensions, which means we have nine space and one time. Take one of those nine space dimensions and make it a circle of radius R, so that traveling in that direction for a distance L = 2πR takes you around the circle and brings you back to where you started. A particle traveling around this circle will have a quantized momentum around the circle, and this will contribute to the total energy of the particle. But a string is very different, because in addition to traveling around the circle, the string can wrap around the circle. The number of times the string winds around the circle is called the winding number, and that is also quantized. Now the weird thing about string theory is that these momentum modes and the winding modes can be interchanged, as long as we also interchange the radius R of the circle with the quantity 
, where Lst is the string length. If R is very much smaller than the string length, then the quantity is going to be very large. So exchanging momentum and winding modes of the string exchanges a large distance scale with a small distance scale.
This type of duality is called T-duality. T-duality relates type IIA superstring theory to type IIB superstring theory. That means if we take type IIA and Type IIB theory and compactify them both on a circle, then switching the momentum and winding modes, and switching the distance scale, changes one theory into the other. The same is also true for the two heterotic theories.
On the other hand, every force has a coupling constant. For electromagnetism, the coupling constant is proportional to the square of the electric charge. When physicists study the quantum behavior of electromagnetism, they can't solve the whole theory exactly, so they break it down to little pieces, and each little piece that they can solve has a different power of the coupling constant in front of it. At normal energies in electromagnetism, the coupling constant is small, and so the first few little pieces make a good approximation to the real answer. But if the coupling constant gets large, that method of calculation breaks down, and the little pieces become worthless as an approximation to the real physics.
This also can happen in string theory. String theories have a coupling constant. But unlike in particle theories, the string coupling constant is not just a number, but depends on one of the oscillation modes of the string, called the dilaton. Exchanging the dilaton field with minus itself exchanges a very large coupling constant with a very small one. This symmetry is called S-duality. If two string theories are related by S-duality, then one theory with a strong coupling constant is the same as the other theory with weak coupling constant. The theory with strong coupling cannot be understood by means of expanding in a series, but the theory with weak coupling can. So if the two theories are related by S-duality, then we just need to understand the weak theory, and that is equivalent to understanding the strong theory.
Superstring theories related by S-duality are: type I superstring theory with heterotic SO(32) superstring theory, and type IIB theory with itself.
Unsolved problems in physics: Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a "theory of everything," or just a blind alley?
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Extra dimensions
One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand". The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926.
Instead, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. This is roughly like saying that if an observer measures the distance between two points, then rotates by some angle and measures again, the observed distance only stays the same if the universe has a particular number of dimensions.
The only problem is that when the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time), but twenty-six. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. In bosonic string theories, the 26 dimensions come from the Polyakov equation ![Z=\int D^F \left [\rho \left (\xi \right ) \right ] \exp \left ( {(26 - D) \over 12 \pi} \int_\xi \left [ {1 \over 2} {\left (\partial_a \rho \right )^2 \over \rho^2} \right ] + \int_\xi \mu_R^2 \rho^2 \right )](cid:image003.gif@01C60D47.805AA0E0)
(see technical details in the preprint "Quantum Geometry of Bosonic Strings - Revisited").
However, these models appear to contradict observed phenomena. Physicists usually solve this problem in one of two different ways. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G2 manifolds. Essentially these extra dimensions are compactified by causing them to loop back upon themselves.
A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. This "extra dimension" is only visible within a relatively close range to the hose, just as the extra dimensions of the Calabi-Yau space are only visible at extremely small distances, and thus are not easily detected.
(Of course, everyday garden hoses exist in three spatial dimensions, but for the purpose of the analogy, its thickness is neglected and only motion on the surface of the hose is considered. A point on the hose's surface can be specified by two numbers, a distance along the hose and a distance along the circumference, just as points on the Earth's surface can be uniquely specified by latitude and longitude. In either case, the object has two spatial dimensions. Like the Earth, garden hoses have an interior, a region that requires an extra dimension; however, unlike the Earth, a Calabi-Yau space has no interior.)
Another possibility is that we are stuck in a 3+1 dimensional subspace of the full universe, where the "3+1" reminds us that time is a different kind of dimension than space. Because it involves mathematical objects called D-branes, this is known as a braneworld theory.
In either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility.
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Problems
String theory remains to be verified. No version of string theory has yet made a prediction which differs from those made by other theories—at least, not in a way that could be checked by a currently feasible experiment. In this sense, string theory is still in a "larval stage": it possesses many features of mathematical interest, and it may yet become supremely important in our understanding of the Universe, but it requires further developments before it is accepted or falsified. Since string theory may not be tested in the foreseeable future, some scientists[1] have asked if it even deserves to be called a scientific theory: it is not yet falsifiable in the sense of Popper.
It is by no means the only theory currently being developed which suffers from this difficulty; any new development can pass through a stage of uncertainty before it becomes conclusively accepted or rejected. As Richard Feynman noted in The Character of Physical Law, the key test of a scientific theory is whether its consequences agree with the measurements taken in experiments. It does not matter who invented the theory, "what his name is", or even how aesthetically appealing the theory may be—"if it disagrees with experiment, it's wrong." (Of course, there are subsidiary issues: something may have gone wrong with the experiment, or perhaps the person computing the consequences of the theory made a mistake. All these possibilities must be checked, which may take a considerable time.) These developments may be in the theory itself, such as new methods of performing calculations and deriving predictions, or they may be advances in experimental science, which make formerly ungraspable quantities measurable.
Since the influence of quantum effects upon gravity only become significant at distances many orders of magnitude smaller than human beings have the technology to observe (or at roughly the Planck length, about 10-35 meters), string theory, or any other candidate theory of quantum gravity, will be very difficult to test experimentally. Eventually, scientists may be able to test string theory by observing cosmological phenomena which may be sensitive to string physics.
In the early 2000s, string theorists revived interest in an older concept, the cosmic string. Originally discussed in the 1980s, cosmic strings are a different type of object than the entities of superstring theories. For several years, cosmic strings were a popular model for explaining various cosmological phenomena, such as the way galaxies formed in the early Universe. However, further experiments — and in particular the detailed measurements of the cosmic microwave background — failed to support the cosmic-string model's predictions, and the cosmic string fell out of vogue. If such objects did exist, they must be few and far between. Several years later, it was pointed out that the expanding Universe could have stretched a "fundamental" string (the sort which superstring theory considers) until it was of intergalactic size. Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. Furthermore, modern superstring theories offer other objects which could feasibly resemble cosmic strings, such as highly elongated one-dimensional D-branes (known as "D-strings"). As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Older proposals for detecting cosmic strings could now be used to investigate superstring theory. For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing.
Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability.
While intriguing, these cosmological proposals fall short in one respect: testing a theory requires that the test be capable, at least in principle, of falsifying the theory. For example, if observing the Sun during a solar eclipse had not shown that the Sun's gravity deflected light, Einstein's general relativity theory would have been proven wrong. Not finding cosmic strings would not demonstrate that string theory is fundamentally wrong — merely that the particular idea of highly stretched strings acting "cosmic" is in error. While many measurements could in principle be made that would suggest that string theory is on the right track, scientists have not at present devised a stringent "test".
On a more mathematical level, another problem is that, like quantum field theory, much of string theory is still only formulated perturbatively (i.e., as a series of approximations rather than as an exact solution). Although nonperturbative techniques have progressed considerably — including conjectured complete definitions in space-times satisfying certain asymptotics — a full nonperturbative definition of the theory is still lacking.
Background
It was shown in the early 1990s that the various superstring theories were related by dualities, which allowed physicists to relate the description of an object in one string theory to the description of a different object in another theory. These relationships imply that each of the string theories is a different aspect of a single underlying theory, which has been named "M-theory".
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The Theory
It was believed before 1995 that there were exactly five consistent superstring theories, which are called, respectively, the Type I string theory, the Type IIA string theory, the Type IIB string theory, the heterotic SO(32) string theory, and the heterotic E8xE8 string theory. As the names suggest, some of these string theories are related to each other. In the early 1990s, string theorists discovered that these relations were so strong that they could be thought of as an identification. The Type IIA string theory and the Type IIB string theory are connected by T-duality; this means, essentially, that the IIA string theory description of a circle of radius R is exactly the same as the IIB description of a circle of radius 1/R.
This is a profound result. First, it is an intrinsically quantum mechanical result; the identification is not true classically. Second, because we can build up any space by gluing circles together in various ways, it would seem that any space described by the IIA string theory can also be seen as a different space described by the IIB theory. This means that we can actually identify the IIA string theory with the IIB string theory; any object which can be described with the IIA theory has an equivalent although seemingly different description in terms of the IIB theory. This means that the IIA theory and the IIB theory are really aspects of the same underlying theory. It might be said at this point that we have reduced our count of fundamental string theories by one.
There are other dualities between the other string theories. The heterotic SO(32) and heterotic E8xE8 theories are also related by T-duality; the heterotic SO(32) description of a circle of radius R is exactly the same as the heterotic E8xE8 description of a circle of radius 1/R. There are then really only three superstring theories, which might be called (for discussion) the Type I theory, the Type II theory, and the heterotic theory.
There are still more dualities, however. The Type I string theory is related to the heterotic SO(32) theory by S-duality; this means that the Type I description of weakly interacting particles can also be seen as the heterotic SO(32) description of very strongly interacting particles. This identification is somewhat more subtle, in that it identifies only extreme limits of the respective theories. String theorists have found strong evidence that the two theories are really the same, even away from the extremely strong and extremely weak limits, but they do not yet have a proof strong enough to satisfy mathematicians. However, it has become clear that the two theories are related in some fashion; they appear as different limits of a single underlying theory.
At this point, there are only two string theories: The heterotic string theory (which is also the type I string theory) and the Type II theory. There are relations between these two theories as well, and these relations are in fact strong enough to allow them to be identified.
This last step, however, is the most difficult and most mysterious. It is best explained first in a certain limit. In order to describe our world, strings must be extremely tiny objects. So when one studies string theory at low energies, it becomes difficult to see that strings are extended objects—they become effectively zero-dimensional (pointlike). Consequently, the quantum theory describing the low energy limit is a theory which describes the dynamics of particles moving in spacetime, rather than strings. Such theories are called quantum field theories. However, since string theory also describes gravitational interactions, one expects the low-energy theory to describe particles moving in gravitational backgrounds. Finally, since superstring string theories are supersymmetric, one expects to see supersymmetry appearing in the low-energy approximation. These three facts imply that the low-energy approximation to a superstring theory is a supergravity theory.
The possible supergravity theories were classified by W. Nahm in the 1970s. In 10 dimensions, there are only two supergravity theories, which are denoted Type IIA and Type IIB. This is not a coincidence. The Type IIA string theory has the Type IIA supergravity theory as its low-energy limit. Likewise, the Type IIB string theory gives rise to Type IIB supergravity. More interestingly, however, the heterotic SO(32) and heterotic E8xE8 string theories also reduce to Type IIA and Type IIB supergravity in the low-energy limit. This suggests that there may indeed be a relation between the heterotic/Type I theories and the Type II theories.
In 1995, Edward Witten outlined the following relationship: The Type IIA supergravity (corresponding to the heterotic SO(32) and Type IIA string theories) can be obtained by dimensional reduction from the single unique eleven-dimensional supergravity theory. This means that if one studied supergravity on an eleven-dimensional spacetime that looks like the product of a ten-dimensional spacetime with another very small one-dimensional manifold, one gets the Type IIA supergravity theory. (And the Type IIB supergravity theory can be obtained by using T-duality.) However, eleven-dimensional supergravity is not consistent on its own. It does not make sense at extremely high energy, and likely requires some form of completion. It seems plausible then, that there is some quantum theory—which Witten dubbed M-theory—in eleven-dimensions which gives rise at low energies to eleven-dimensional supergravity, and is related to ten-dimensional string theory by dimensional reduction. Dimensional reduction to a circle yields the Type IIA string theory, and dimensional reduction to a line segment yields the heterotic SO(32) string theory.
Taking seriously the notion that all of the different string theories should be different limits and/or different presentations of the same underlying theory, then the concept of string theory must be expanded. But little is known about this underlying theory. The bonus is that all of the different string theories may now be thought of as different limits of a single underlying theory.
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Naming conventions, or What does M stand for?
There are two issues to be dealt with here:
- When
- A more serious problem: The name M-theory is slightly ambiguous. It can be used to refer to both the particular eleven-dimensional theory which
M-theory in the following descriptions refers to the more general theory, and will be specified when used in its more limited sense.
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M-theory in various backgrounds
Please improve this section according to the posted request for expansion.
Although no complete description of M-theory (in the more general sense) exists, it can be formulated in certain limits.
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Membranes
A (mem)brane is a multidimensional object usually called p-brane referring to its spatial dimensionality p (for example, a string is a 1-brane and a flat surface is a 2-brane). There are different forms of branes: p-brane, D-brane, and black brane. P-branes are membrane-like structures of one to eleven dimensions that arise in equations of M-theory. These branes are said to float in an eleven-dimensional space and contain universes, including our own.
Please improve this section according to the posted request for expansion.
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Matrix Theory
Please improve this section according to the posted request for expansion
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