A) quark - smallest particle known. The only thing that could be smaller would be strings (String Theory), but our microscopes are not powerful enough to detect them. Here are some articles from Wikipedia on quarks, and string theory:
Quark
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For other uses, see Quark (disambiguation).
These are the six flavors of quarks and their most likely decay modes. Mass decreases moving from right to left.In particle physics, quarks are one of the two basic constituents of matter (the other are the leptons). Quarks are the only fundamental particles that interact through all four of the fundamental forces. The word was originally coined by Murray Gell-Mann as a nonsense word rhyming with "walk". Later, he found the same word in James Joyce's book Finnegans Wake, where seabirds give "three quarks", akin to three cheers (probably onomatopoetically imitating a seabird call, like "quack" for ducks, as well as making a pun on the relationship between Munster and its provincial capital, Cork) in the passage "Three quarks for Muster Mark!/Sure he hasn't got much of a bark/And sure any he has it's all beside the mark.". Further explanation for the use of the word "quark" may be derived from the fact that, at the time, there were only three known quarks in existence.
Quarks come in six flavors, and their names (up, down, strange, charm, bottom, and top) were also chosen arbitrarily based on the need to name them something that could be easily remembered and used.
Antiparticles of quarks are called antiquarks.
Isolated quarks are never found naturally; they are almost always found in groups of two (mesons) or groups of three (baryons) called hadrons. This is a direct consequence of confinement, explained below.
Contents [hide]
1 Free quarks
2 Confinement and quark properties
3 Flavor
4 Spin
5 Color
6 Quark masses
6.1 Current quark mass
6.2 Valence quark mass
6.3 Heavy quark masses
7 Properties of quarks
8 Antiquarks
9 Substructure
10 History
11 See also
12 References and external links
12.1 Primary and secondary sources
12.2 Other references
[edit] Free quarks
1974 discovery photograph of a possible charmed baryon, now identified as the Σc++No search for free quarks or fractional electric charges has returned convincing evidence. The absence of free quarks has therefore been incorporated into the notion of confinement, which, it is believed, the theory of quarks must possess.
Confinement began as an experimental observation, and is expected to follow from the modern theory of strong interactions, called quantum chromodynamics (QCD). Although there is no mathematical derivation of confinement in QCD, it is easy to show using lattice gauge theory.
However, it may be possible to change the confinement by creating dense or hot quark matter. These new phases of QCD matter have been predicted theoretically, and experimental searches for them have now started.
[edit] Confinement and quark properties
Every subatomic particle is completely described by a small set of observables such as mass m and quantum numbers, such as spin J and parity P. Usually these properties are directly determined by experiments. However, confinement makes it impossible to measure these properties of quarks. Instead, they must be inferred from measurable properties of the composite particles which are made up of quarks. Such inferences are usually most easily made for certain additive quantum numbers called flavors.
The composite particles made of quarks and antiquarks are the hadrons. These include the mesons which get their quantum numbers from a quark and an antiquark, and the baryons, which get theirs from three quarks. The quarks (and antiquarks) which impart quantum numbers to hadrons are called valence quarks. Apart from these, any hadron may contain an indefinite number of virtual quarks, antiquarks and gluons which together contribute nothing to their quantum numbers. Such virtual quarks are called sea quarks.
[edit] Flavor
Each quark is assigned a baryon number, B = 1/3, and a vanishing lepton number L = 0. They have fractional electric charge, Q, either Q = +2/3 or Q = â1/3. The former are called up-type quarks, the latter, down-type quarks. Each quark is assigned a weak isospin: Tz = +1/2 for an up-type quark and Tz = â1/2 for a down-type quark. Each doublet of weak isospin defines a generation of quarks. There are three generations, and hence six flavors of quarks — the up-type quark flavors are up, charm and top; the down-type quark flavors are down, strange, and bottom (each list is in the order of increasing mass).
The number of generations of quarks and leptons are equal in the standard model. The number of generations of leptons with a light neutrino is strongly constrained by experiments at the LEP in CERN and by observations of the abundance of helium in the universe. Precision measurement of the lifetime of the Z boson at LEP constrains the number of light neutrino generations to be three. Astronomical observations of helium abundance give consistent results. Results of direct searches for a fourth generation give limits on the mass of the lightest possible fourth generation quark. The most stringent limit comes from analysis of results from the Tevatron collider at Fermilab, and shows that the mass of a fourth-generation quark must be greater than 190 GeV. Additional limits on extra quark generations come from measurements of quark mixing performed by the experiments Belle and BaBar.
Each flavor defines a quantum number which is conserved under the strong interactions, but not the weak interactions. The magnitude of flavor changing in the weak interaction is encoded into a structure called the CKM matrix. This also encodes the CP violation allowed in the Standard Model. The flavor quantum numbers are described in detail in the article on flavor.
[edit] Spin
Quantum numbers corresponding to non-Abelian symmetries like rotations require more care in extraction, since they are not additive. In the quark model one builds mesons out of a quark and an antiquark, whereas baryons are built from three quarks. Since mesons are bosons (having integer spins) and baryons are fermions (having half-integer spins), the quark model implies that quarks are fermions. Further, the fact that the lightest baryons have spin-1/2 implies that each quark can have spin J = 1/2. The spins of excited mesons and baryons are completely consistent with this assignment.
[edit] Color
Since quarks are fermions, the Pauli exclusion principle implies that the three valence quarks must be in an antisymmetric combination in a baryon. However, the charge Q = 2 baryon, Î++ (which is one of four isospin Iz = 3/2 baryons) can only be made of three u quarks with parallel spins. Since this configuration is symmetric under interchange of the quarks, it implies that there exists another internal quantum number, which would then make the combination antisymmetric. This is given the name "color", although it has nothing to do with the perception of the frequency (or wavelength) of light, which is the usual meaning of color. This quantum number is the charge involved in the gauge theory called quantum chromodynamics (QCD).
The only other colored particle is the gluon, which is the gauge boson of QCD. Like all other non-Abelian gauge theories (and unlike quantum electrodynamics) the gauge bosons interact with one another by the same force that affects the quarks.
Color is a gauged SU(3) symmetry. Quarks are placed in the fundamental representation, 3, and hence come in three colors (red, green, and blue). Gluons are placed in the adjoint representation, 8, and hence come in eight varieties. For more on this, see the article on color charge.
[edit] Quark masses
Although one speaks of quark mass in the same way as the mass of any other particle, the notion of mass for quarks is complicated by the fact that quarks cannot be found free in nature. As a result, the notion of a quark mass is a theoretical construct, which makes sense only when one specifies exactly the procedure used to define it.
[edit] Current quark mass
The approximate chiral symmetry of quantum chromodynamics, for example, allows one to define the ratio between various (up, down and strange) quark masses through combinations of the masses of the pseudo-scalar meson octet in the quark model through chiral perturbation theory, giving
The fact that the up quark has mass is important, since there would be no strong CP problem if it were massless. The absolute values of the masses are currently determined from QCD sum rules (also called spectral function sum rules) and lattice QCD. Masses determined in this manner are called current quark masses. The connection between different definitions of the current quark masses needs the full machinery of renormalization for its specification.
[edit] Valence quark mass
Another, older, method of specifying the quark masses was to use the Gell-Mann-Nishijima mass formula in the quark model, which connect hadron masses to quark masses. The masses so determined are called constituent quark masses, and are significantly different from the current quark masses defined above. The constituent masses do not have any further dynamical meaning.
[edit] Heavy quark masses
The masses of the heavy charm and bottom quarks are obtained from the masses of hadrons containing a single heavy quark (and one light antiquark or two light quarks) and from the analysis of quarkonia. Lattice QCD computations using the heavy quark effective theory (HQET) or non-relativistic quantum chromodynamics (NRQCD) are currently used to determine these quark masses.
The top quark is sufficiently heavy that perturbative QCD can be used to determine its mass. Before its discovery in 1995, the best theoretical estimates of the top quark mass are obtained from global analysis of precision tests of the Standard Model. The top quark, however, is unique amongst quarks in that it decays before having a chance to hadronize. Thus, its mass can be directly measured from the resulting decay products. This can only be done at the Tevatron which is the only particle accelerator energetic enough to produce top quarks in abundance.
[edit] Properties of quarks
The following table summarizes the key properties of the six known quarks:
Generation Weak
Isospin Flavor Name Symbol Charge / e Mass / MeV·c-2 Antiparticle Symbol
1 +½ Iz=+½ Up u +â
1.5 – 4.0 Antiup
1 -½ Iz=-½ Down d -â
4 – 8 Antidown
2 -½ S=-1 Strange s -â
80 – 130 Antistrange
2 +½ C=1 Charm c +â
1150 – 1350 Anticharm
3 -½ B'=-1 Bottom b -â
4100 – 4400 Antibottom
3 +½ T=1 Top t +â
170900 ± 1800[1] Antitop
Top quark mass from the Tevatron Electroweak Working Group
Other quark masses from Particle Data Group; these masses are given in the MS-bar scheme.
The quantum numbers of the top and bottom quarks are sometimes known as truth and beauty respectively, as an alternative to topness and bottomness.
[edit] Antiquarks
The additive quantum numbers of antiquarks are equal in magnitude and opposite in sign to those of the quarks. CPT symmetry forces them to have the same spin and mass as the corresponding quark. Tests of CPT symmetry cannot be performed directly on quarks and antiquarks, due to confinement, but can be performed on hadrons. Notation of antiquarks follows that of antimatter in general: an up quark is denoted by , and an anti-up quark is denoted by .
[edit] Substructure
Some extensions of the Standard Model begin with the assumption that quarks and leptons have substructure. In other words, these models assume that the elementary particles of the Standard Model are in fact composite particles, made of some other elementary constituents. Such an assumption is open to experimental tests, and these theories are severely constrained by data. At present there is no evidence for such substructure. For more details see the article on preons.
[edit] History
The notion of quarks evolved out of a classification of hadrons developed independently in 1961 by Murray Gell-Mann and Kazuhiko Nishijima, which nowadays goes by the name of the quark model. The scheme grouped together particles with isospin and strangeness using a unitary symmetry derived from current algebra, which we today recognise as part of the approximate chiral symmetry of QCD. This is a global flavor SU(3) symmetry, which should not be confused with the gauge symmetry of QCD.
In this scheme the lightest mesons (spin-0) and baryons (spin-½) are grouped together into octets, 8, of flavor symmetry. A classification of the spin-3/2 baryons into the representation 10 yielded a prediction of a new particle, Ωâ, the discovery of which in 1964 led to wide acceptance of the model. The missing representation 3 was identified with quarks.
This scheme was called the eightfold way by Gell-Mann, a clever conflation of the octets of the model with the eightfold way of Buddhism. He also chose the name quark and attributed it to the sentence “Three quarks for Muster Mark” in James Joyce's Finnegans Wake [1]. The negative results of quark search experiments caused Gell-Mann to hold that quarks were mathematical fiction.
Analysis of certain properties of high energy reactions of hadrons led Richard Feynman to postulate substructures of hadrons, which he called partons (since they form part of hadrons). A scaling of deep inelastic scattering cross sections derived from current algebra by James Bjorken received an explanation in terms of partons. When Bjorken scaling was verified in an experiment in 1969, it was immediately realized that partons and quarks could be the same thing. With the proof of asymptotic freedom in QCD in 1973 by David Gross, Frank Wilczek and David Politzer the connection was firmly established.
The charm quark was postulated by Sheldon Glashow, Iliopoulos and Maiani in 1970 to prevent unphysical flavor changes in weak decays which would otherwise occur in the standard model. The discovery in 1975 of the meson which came to be called the J/Ï led to the recognition that it was made of a charm quark and its antiquark.
The existence of a third generation of quarks was predicted by Kobayashi and Maskawa in 1973 who realized that the observed violation of CP symmetry by neutral kaons could not be accommodated into the Standard Model with two generations of quarks. The bottom quark was discovered in 1977 and the top quark in 1996 at the Tevatron collider in Fermilab.
[edit] See also
Quark model
Fundamental forces and strong interactions
Gluons
Quantum chromodynamics, the quark model and partons.
Confinement, deconfinement, quark matter and asymptotic freedom
Standard model overview and details, the CKM matrix and CP symmetry.
[edit] References and external links
^ Summary of Top Mass Results - March 2007.
[edit] Primary and secondary sources
Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.
Povh, Bogdan (1995). Particles and Nuclei: An Introduction to the Physical Concepts. Springer-Verlag. ISBN 0-387-59439-6.
Particle Data Group on quarks
A schematic model of baryons and mesons, by Murray Gell-Mann (1964)
Observation of the top quark at Fermilab
NanoReisen-A very educational site on Quarks and many other things beyond the nanoscale.
[edit] Other references
Quark dance
A Positron Named Priscilla — A description of CERN’s experiment to count the families of quarks
The original English word quark and its adaptation to particle physics
An elementary popular introduction
v • d • e Particles in physics - elementary particles
Fermions: Quarks: (Up · Down · Strange · Charm · Bottom · Top) | Leptons: (Electron · Muon · Tau · Neutrinos)
Gauge bosons: Photon | W and Z bosons | Gluons
Not yet observed: Higgs boson | Graviton | Other hypothetical particles
Retrieved from "http://en.wikipedia.org/wiki/Quark"
Categories: Quarks | Fundamental physics concepts
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String theory
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theoryString theory v • d • e
bosonic string theory
superstring theory
type I string
type II string
heterotic string
M-theory (simplified)
string field theory
strings
branes
Related topics
quantum field theory
gauge theory
conformal field theory
topological field theory
supersymmetry
supergravity
general relativity
quantum gravity
See also
string theory topics
String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the Standard Model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. String theorists are attempting to adjust the Standard Model by removing the assumption in quantum mechanics that particles are point-like. By removing this assumption and replacing the point-like particles with strings, it appears that a sensible quantum theory of gravity naturally emerges. Moreover, string theory may be able to "unify" the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. (See Theory of everything)
Very few avenues for experimental verification of the theory have been claimed (see [2]), thus leading some experts to turn to one of several alternate models, such as Loop quantum gravity. With the construction of the Large Hadron Collider in Geneva, Switzerland some scientists hope to produce relevant data. However, it is likely that any theory of quantum gravity would require much higher energies to probe.
There are different versions of string theory, depending on factors such as the type of strings used (open or closed) and whether or not supersymmetry is incorporated into the formulation.
Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory) spacetime dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory[1]; however the theory can describe universes with four effective (observable) spacetime dimensions by a variety of methods.
Contents [hide]
1 Overview
2 Basic properties
2.1 Worldsheet
2.2 Dualities
2.3 Extra dimensions
2.4 D-branes
3 Gauge-gravity duality
4 Problems and controversy
5 History
6 Popular culture
7 See also
8 References
9 Further Reading
9.1 Popular books and articles
9.2 Textbooks
10 External links
[edit] Overview
The basic idea behind all string theories is that the most basic constituents of reality are strings of extremely small size (possibly of the order of the Planck length, about 10â35 m) which vibrate at specific resonant frequencies.[2] Thus, any particle should be thought of as a tiny vibrating object, rather than as a point. This object can vibrate in different modes (just as a guitar string can produce different notes), with every mode appearing as a different particle (electron, photon, etc.). Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.
In addition to strings, this theory also includes objects of higher dimensions, such as D-branes and NS-branes. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions. String theory is thought to include some 10, 11, or 26 dimensions, depending on the specific theory and on the point of view.
Interest in string theory is driven largely by the hope that it will prove to be a consistent theory of quantum gravity or even a theory of everything. It can also naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry, a conjectured (but unobserved) symmetry of nature. It is not yet known whether string theory will be able to describe a universe with the precise collection of forces and particles that is observed, nor how much freedom the theory allows to choose those details.
String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various planned observations and experiments could confirm some essential aspects of the theory, such as supersymmetry and extra dimensions. In addition, the full theory is not yet understood. For example, the theory does not yet have a satisfactory definition outside of perturbation theory; the quantum mechanics of branes (higher dimensional objects than strings) is not understood; the behavior of string theory in cosmological settings (time-dependent backgrounds) is still being worked out; finally, the principle by which string theory selects its vacuum state is a hotly contested topic (see string theory landscape).
String theory is thought to be a certain limit of another, more fundamental theory - M-theory - which is only partly defined and is not well understood.
[3]
[edit] Basic properties
String theory is formulated in terms of an action principle, either the Nambu-Goto action or the Polyakov action, which describes how strings move through space and time. Like springs, the strings want to minimize their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion with which it can interact, are determined by the way the string vibrates — the string can vibrate in many different modes, just like a guitar string can produce different notes. The different modes, each corresponding to a different kind of particle, make up the "spectrum" of the theory.
Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.
String theory includes 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 different spectra. For example, in most string theories, one of the closed string modes is the graviton, and one of the open string modes is the photon. Because the two ends of an open string can always meet and connect, forming a closed string, there are no string theories without closed strings.
The earliest string model — the bosonic string, which incorporated only bosons, describes — in low enough energies — a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge fields such as the photon (or, more generally, any Yang-Mills theory). However, this model has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay (at least partially) of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described, but all are now thought to be different limits of M-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 is related to the string tension.
[edit] Worldsheet
For more details on this topic, see Relationship between string theory and quantum field theory.
A point-like particle's motion may be described by drawing a graph of its position (in one or two dimensions of space) against time. The resulting picture depicts the worldline of the particle (its 'history') in spacetime. By analogy, a similar graph depicting the progress of a string as time passes by can be obtained; the string (a one-dimensional object — a small line — by itself) will trace out a surface (a two-dimensional manifold), known as the worldsheet. The different string modes (representing different particles, such as photon or graviton) are surface waves on this manifold.
A closed string looks like a small loop, so its worldsheet will look like a pipe, or - more generally - as a Riemannian surface (a two-dimensional oriented manifold) with no boundaries (i.e. no edge). An open string looks like a short line, so its worldsheet will look like a strip, or — more generally — as a Riemann surface with a boundary.
Strings can split and connect. This is reflected by the form of their worldsheet (more accurately, by its topology). For example, if a closed string splits, its worldsheet will look like a single pipe splitting (or connected) to two pipes (often referred to as a pair of pants — see drawing at the top of this page). If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes (one representing the ingoing string, and the other — the outgoing one). An open string doing the same thing will have its worldsheet looking like a ring connected to two strips.
Note that the process of a string splitting (or strings connecting) is a global process of the worldsheet, not a local one: locally, the worldsheet looks the same everywhere and it is not possible to determine a single point on the worldsheet where the splitting occurs. Therefore these processes are an integral part of the theory, and are described by the same dynamics that controls the string modes.
In some string theories (namely, closed strings in Type I and string in some version of the bosonic string), strings can split and reconnect in an opposite orientation (as in a Möbius strip or a Klein bottle). These theories are called unoriented. Formally, the worldsheet in these theories is an non-orientable surface.
[edit] Dualities
Main articles: String duality, S-duality, T-duality, and U-duality
Before the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories (SO(32) and E8ÃE8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today. It is now known that this picture was naïve, and that the five superstring theories are connected to one another as if they are each a special case of some more fundamental theory (thought to be M-theory). 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. Put differently, the two theories are mathematically different descriptions of the same phenomena.
These dualities link quantities that were also thought to be separate. Large and small distance scales, as well as strong and weak coupling strengths, are quantities that 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. T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.
Before the "duality revolution" there were believed to be five distinct versions of string theory, plus the (unstable) bosonic and gluonic theories.
String Theories
Type Spacetime dimensions
Details
Bosonic 26 Only bosons, no fermions means only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory.
I 10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32)
IIA 10 Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions spin both ways (nonchiral)
IIB 10 Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions only spin one way (chiral)
HO 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO(32)
HE 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8ÃE8
Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the bulk), while open strings have their ends attached to D-branes, which are membranes of lower dimensionality (their dimension is odd - 1,3,5,7 or 9 - in type IIA and even - 0,2,4,6 or 8 - in type IIB, including the time direction).
[edit] Extra dimensions
An artist's impression of a Calabi-Yau manifold. Made for Nova.One intriguing feature of string theory is that it predicts the possible number of dimensions in the universe. 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 general relativity was 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 (see Kaluza–Klein theory).
Unlike general relativity, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because, for a different number of dimensions, the theory has a gauge anomaly. This can be understood by noting that in a consistent theory which includes a photon (technically, a particle carrying a force related to an unbroken gauge symmetry), it must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon will be massless — and the theory consistent — only for a particular number of dimensions.[4]
When the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time). 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.[5] However, these results appear to contradict the observed four dimensional space-time.
Calabi-Yau manifold (3D projection)Two different ways have been proposed to resolve this apparent contradiction. 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. In order to retain the supersymmetric properties of string theory, these spaces must be very special. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G2 manifolds. 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. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only visible at extremely small distances, or by experimenting with particles with extremely small wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave-particle duality).
Another possibility is that we are stuck in a 3+1 dimensional (i.e. three spatial dimensions plus the time dimension) subspace of the full universe. This subspace is supposed to be a D-brane, hence this is known as a braneworld theory. Many people believe that some combination of the two ideas – compactification and branes – will ultimately yield the most realistic theory.
In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. 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. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.
[edit] D-branes
Main article: D-brane
Another key feature of string theory is the existence of D-branes. These are membranes of different dimensionality (anywhere from a zero dimensional membrane — which is in fact a point — and up, including 2-dimensional membranes, 3-dimensional volumes and so on).
D-branes are defined by the fact that worldsheet boundaries are attached to them. Thus D-branes can emit and absorb closed strings; therefore they have mass (since they emit gravitons) and — in superstring theories — charge as well (since they emit closed strings which are gauge bosons).
From the point of view of open strings, D-branes are objects to which the ends of open strings are attached. The open strings attached to a D-brane are said to "live" on it, and they give rise to gauge theories "living" on it (since one of the open string modes is a gauge boson such as the photon). In the case of one D-brane there will be one type of a gauge boson and we will have an Abelian gauge theory (with the gauge boson being the photon). If there are multiple parallel D-branes there will be multiple types of gauge bosons, giving rise to a non-Abelian gauge theory.
D-branes are thus gravitational sources, on which a gauge theory "lives". This gauge theory is coupled to gravity (which is said to exist in the bulk), so that normally each of these two different viewpoints is incomplete.
[edit] Gauge-gravity duality
In certain cases the gauge theory on the D-branes is decoupled from the gravity living in the bulk; thus open strings attached to the D-branes are not interacting with closed strings. Such a situation is termed a decoupling limit.
In those cases, the D-branes have two independent alternative descriptions. As discussed above, from the point of view of closed strings, the D-branes are gravitational sources, and thus we have a gravitational theory on spacetime with some background fields. From the point of view of open strings, the physics of the D-branes is described by the appropriate gauge theory. Therefore in such cases it is often conjectured that the gravitational theory on spacetime with the appropriate background fields is dual (i.e. physically equivalent) to the gauge theory on the boundary of this spacetime (since the subspace filled by the D-branes is the boundary of this spacetime). So far, this duality has not been proven in any cases, so there is also disagreement among string theorists regarding how strong the duality applies to various models.
The most well-known example and the first one to be studied is the duality between Type IIB supergravity on AdS5 * S5 (a product space of a five-dimensional Anti de Sitter space and a five-sphere) on one hand, and N = 4 supersymmetric Yang-Mills theory on the four-dimensional boundary of the Anti de Sitter space (either a flat four-dimensional spacetime R3,1 or a three-sphere with time S3* R).[6] This is known as the AdS/CFT correspondence, a name often used for Gauge / gravity duality in general.
This duality can be thought of as follows: suppose there is a spacetime with a gravitational source, for example an extremal black hole. When particles are far away from this source, they are described by closed strings (i.e. a gravitational theory, or usually supergravity). As the particles approach the gravitational source, they can still be described by closed strings; alternatively, they can be described by objects similar to QCD strings, which are made of gauge bosons (gluons) and other gauge theory degrees of freedom. So if one is able (in a decoupling limit) to describe the gravitational system as two separate regions - one (the bulk) far away from the source, and the other close to the source - then the latter region can also be described by a gauge theory on D-branes. This latter region (close to the source) is termed the near-horizon limit, since usually there is an event horizon around (or at) the gravitational source.
In the gravitational theory, one of the directions in spacetime is the radial direction, going from the gravitational source and away (towards the bulk). The gauge theory lives only on the D-brane itself, so it does not include the radial direction: it lives in a spacetime with one less dimension compared to the gravitational theory (in fact, it lives on a spacetime identical to the boundary of the near-horizon gravitational theory). Let us understand how the two theories are still equivalent:
The physics of the near-horizon gravitational theory involves only on-shell states (as usual in string theory), while the field theory includes also off-shell correlation function. The on-shell states in the near-horizon gravitational theory can be thought of as describing only particles arriving from the bulk to the near-horizon region and interacting there between themselves. In the gauge theory these are "projected" onto the boundary, so that particles which arrive at the source from different directions will be seen in the gauge theory as (off-shell) quantum fluctuations far apart from each other, while particles arriving at the source from almost the same direction in space will be seen in the gauge theory as (off-shell) quantum fluctuations close to each other. Thus the angle between the arriving particles in the gravitational theory translates to the distance scale between quantum fluctuations in the gauge theory. The angle between arriving particles in the gravitational theory is related to the radial distance from the gravitational source at which the particles interact: the larger the angle, the closer the particles have to get to the source in order to interact with each other. On the other hand, the scale of the distance between quantum fluctuations in a quantum field theory is related (inversely) to the energy scale in this theory. So small radius in the gravitational theory translates to low energy scale in the gauge theory (i.e. the IR regime of the field theory) while large radius in the gravitational theory translates to high energy scale in the gauge theory (i.e. the UV regime of the field theory).
A simple example to this principle is that if in the gravitational theory there is a setup in which the dilaton field (which determines the strength of the coupling) is decreasing with the radius, then its dual field theory will be asymptotically free, i.e. its coupling will grow weaker in high energies.
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?
[edit] Problems and controversy
String theory remains to be confirmed. No version of string theory has yet made an experimentally verified prediction that differs from those made by other theories. In this sense, string theory is still in a "larval stage": it is not a proper physical theory. It possesses many features of mathematical interest and may yet become important in our understanding of the universe, but it requires further developments before it is accepted or discarded. Since string theory may not be tested in the foreseeable future, some scientists[7] have asked if it even deserves to be called a scientific theory; it is not falsifiable in the sense of Popper.
For example, while supersymmetry is now seen as a vital ingredient of string theory, supersymmetric models with no obvious connection to string theory are also studied. Therefore, if supersymmetry were detected at the Large Hadron Collider it would not be seen as a direct confirmation of the theory. More importantly, if supersymmetry were not detected, there are vacua in string theory in which supersymmetry would only be seen at much higher energies, so its absence would not falsify string theory. By contrast, if observing the Sun during a solar eclipse had not shown that the Sun's gravity deflected light by the predicted amount, Einstein's general relativity theory would have been proven wrong.
On a more mathematical level, another problem is that, like many quantum field theories, 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 non-perturbative definition of the theory is still lacking.
Philosophically, string theory cannot be truly fundamental in its present formulation because it is background-dependent: each string theory is built on a fixed spacetime background. Since a dynamic spacetime is the central tenet of general relativity, the hope is that M-theory will turn out to be background-independent, giving as solutions the many different versions of string theories, but no one yet knows how such a fundamental theory can be constructed. A related problem is that the best understood backgrounds of string theory preserve much of the supersymmetry of the underlying theory, and thus are time-invariant: string theory cannot yet deal well with time-dependent, cosmological backgrounds.
Another problem is that the vacuum structure of the theory, called the string theory landscape, is not well understood. As string theory is presently understood, it appears to contain a large number of distinct vacua, perhaps 10500 or more. Each of these corresponds to a different universe, with a different collection of particles and forces. What principle, if any, can be used to select among these vacua is an open issue. While there are no known continuous parameters in the theory, there is a very large discretuum (coined in contradistinction to continuum) of possible universes, which may be radically different from each other. Some physicists believe this is a benefit of the theory, as it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant. However, such explanations are not usually regarded as scientific in the Popperian sense.[citation needed]
"String theory —the hot topic in physics for the past 20 years—is a dead-end, says Smolin, one of the founders of Canada's Perimeter Institute of Theoretical Physics and himself a lapsed string theorist [3].
[edit] History
Main article: History of string theory
String theory v • d • e
bosonic string theory
superstring theory
type I string
type II string
heterotic string
M-theory (simplified)
string field theory
strings
branes
Related topics
quantum field theory
gauge theory
conformal field theory
topological field theory
supersymmetry
supergravity
general relativity
quantum gravity
See also
string theory topics
String theory was originally developed and explored during the late 1960s and early 1970s to explain some peculiarities of the behavior of hadrons (subatomic particles such as the proton and neutron which experience the strong nuclear force). In particular, Yoichiro Nambu (and later Lenny Susskind and Holger Nielsen) realized in 1970 that the dual resonance model of strong interactions could be explained by a quantum-mechanical model of strings. This approach was abandoned as an alternative theory, quantum chromodynamics, gained experimental support.
During the mid-1970s it was discovered that the same mathematical formalism can be used to describe a theory of quantum gravity. This led to the development of bosonic string theory, which is still the version first taught to many students.
Between 1984 and 1986, physicists realized that string theory could describe all elementary particles and the interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This is known as the first superstring revolution.
In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of a new 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution.
In the mid 1990s, Joseph Polchinski discovered that the theory requires the inclusion of higher-dimensional objects, called D-branes. These added an additional rich mathematical structure to the theory, and opened up many possibilities for constructing realistic cosmological models in the theory.
In 1997 Juan Maldacena conjectured a relationship between string theory and a gauge theory called N=4 supersymmetric Yang-Mills theory. This conjecture, called the AdS/CFT correspondence has generated a great deal of interest in the field and is now well-accepted. It is a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational interaction. Through this relationship, string theory may be related in the future to quantum chromodynamics and lead, eventually, to a better understanding of the behavior of hadrons, thus returning to its original goal.
Recently, the discovery of the string theory landscape, which suggests that string theory has an exponentially large number of different vacua, led to discussions of what string theory might eventually be expected to predict, and to the worry that the answer might continue to be nothing.
[edit] Popular culture
The book The Elegant Universe by Brian Greene, Professor of Physics at Columbia University, was adapted into a three-hour documentary for Nova and also shown on British television. It was also shown by Discovery Channel on Indian television, as well as in Australia on SBS.
String theory is also a series of books based in the Star Trek: Voyager universe.
In the TV series Angel, the character of Winifred Burkle (aka Fred) puts forward a theory about String Theory & Alternate Dimensions to the Physics Institute following her own experience of being trapped in one such delicate alternate dimension for five years. The episode which this is referenced to is "Supersymmetry".
Another theory named string theory was used in the science fiction television series Quantum Leap. In the series it relates to a theory of time travel, and is not related to accepted String Theory. It views a person's life as a string that moves from one end to the other. However, if it were possible to roll up this string into a ball it would be possible to leap from one section to another, as the main character of the show does.
Both the String Theory and the Calabi-Yau Model are mentioned in reference to teleportation in the popular video game Half-Life 2.
The Calabi-Yau space is mentioned in reference to a hypothetical matter quantum teleportation (QT for short) in the novels Ilium and Olympos, by Science Fiction writer Dan Simmons. In addition, several other hypothetical quantum-mechanics and string theory-related concepts are employed and to some extent explained or described in the books: Brane holes, parallel universes, singularities (black holes and wormholes), "quantum" morphing/shapeshifting devices and the intrinsic probabilistic nature of the quantum mechanical theory.
In an episode of Criminal Minds, a Schizophrenic hostage taker named Ted Bryar had completed a PhD in string theory in the '80s.
In an episode of Masters of Horror directed by Stuart Gordon, a young grad student from Miskatonic University studies interdimensional string theory in his run-down apartment. Based on the short story "Dreams in the Witch-House" by H.P. Lovecraft.
On the popular CBS drama, Numb3rs, one of the supporting characters, physicist professor Dr. Larry Fleinhardt (Peter MacNicol), actively researches string theory at 'Cal-Sci' (based on Caltech).
An episode of "Heroes (TV series)" is titled String Theory.
The book "Xenocide" by Orson Scott Card uses "ansibles", transmitors of information along strings
[edit] See also
AdS/CFT correspondence
Conformal field theory
F-theory
Fuzzballs
Graviton
Kaluza-Klein theory
List of string theory physicists
List of string theory topics
Loop quantum gravity
M-theory
Quantum gravity
Relationship between string theory and quantum field theory
String duality
String theory landscape
Supergravity
Superstring theory
Supersymmetry
Theory of everything
[edit] References
^ M. J. Duff, James T. Liu and R. Minasian Eleven Dimensional Origin of String/String Duality: A One Loop Test Center for Theoretical Physics, Department of Physics, Texas A&M University
^ To compare, the size of an atom is roughly 10-10 m and the size of a proton is 10-15 m. To imagine the Planck length: you can stretch along the diameter of an atom the same number of strings as the number of atoms you can line up to Proxima Centauri (the nearest star to Earth after the Sun). The tension of a string (8.9Ã1042 newtons) is about 1041 times the tension of an average piano string (735 newtons).
^ This is most vividly captured by T-duality, a result that demonstrates that it is impossible to tell the difference between dimensions smaller than the string length and those much larger: Physical processes in a dimension of size R in one theory match those in a dimension of size 1/R of a different theory.
^ The calculation of the number of dimensions can be circumvented by adding a degree of freedom which compensates for the "missing" quantum fluctuations. However, this degree of freedom behaves similar to spacetime dimensions only in some aspects, and the produced theory is not Lorentz invariant, and has other characteristics which don't appear in nature. This is known as the linear dilaton or non-critical string.
^ "Quantum Geometry of Bosonic Strings - Revisited"
^ Aharony, O.; S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz (2000). "Large N Field Theories, String Theory and Gravity". Phys. Rept. 323: 183-386. . For other examples see: [1]
^ Prominent critics include Philip Anderson ("string theory is the first science in hundreds of years to be pursued in pre-Baconian fashion, without any adequate experimental guidance", New York Times, 4 January 2005), Sheldon Glashow ("there ain't no experiment that could be done nor is there any observation that could be made that would say, `You guys are wrong.' The theory is safe, permanently safe", NOVA interview), Lawrence Krauss ("String theory [is] yet to have any real successes in explaining or predicting anything measurable", New York Times, 8 November 2005), Peter Woit (see his blog, article and book "Not Even Wrong", ISBN 0-224-07605-1) and Carlo Rovelli (see his Dialog on Quantum Gravity).
[edit] Further Reading
[edit] Popular books and articles
Davies, Paul; Julian R. Brown (Eds.) (July 31 1992). Superstrings: A Theory of Everything?, Reprint edition, Cambridge: Cambridge University Press, 244. ISBN 0-521-43775-X.
Gefter, Amanda (December 2005). Is string theory in trouble?. New Scientist. Retrieved on December 19, 2005. – An interview with Leonard Susskind, the theoretical physicist who discovered that string theory is based on one-dimensional objects and now is promoting the idea of multiple universes.
Green, Michael (September 1986). Superstrings. Scientific American. Retrieved on December 19, 2005.
Greene, Brian (October 20 2003). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Reissue edition, New York: W.W. Norton & Company, 464. ISBN 0-393-05858-1.
Gribbin, John (1998). The Search for Superstrings, Symmetry, and the Theory of Everything. London: Little Brown and Company, 224. ISBN 0-316-32975-4.
Kaku, Michio (April 1994). Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford: Oxford University Press, 384. ISBN 0-19-508514-0.
Penrose, Roger (February 22 2005). The Road to Reality: A Complete Guide to the Laws of the Universe. Knopf, 1136. ISBN 0-679-45443-8.
Randall, Lisa (September 1 2005). Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. New York: Ecco Press, 512. ISBN 0-06-053108-8.
Lee Smolin (2006). "The Trouble With Physics".
Taubes, Gary (November 1986). "Everything's Now Tied to Strings." Discover Magazine vol 7, #11. (Popular article, probably the first ever written, on the first superstring revolution.)
Witten, Edward (June 2002). The Universe on a String. Astronomy magazine. Retrieved on December 19, 2005. – An easy article for everybody outside physics wanting to understand the very basics of the theory.
Woit, Peter (2006). Not Even Wrong - The Failure of String Theory And the Search for Unity in Physical Law. Random House, 290. ISBN 0-224-07605-1.
[edit] Textbooks
Paul H. Frampton (1974). Dual Resonance Models. Frontiers in Physics. ISBN 0-805-32581-6.
Michael Green, John H. Schwarz and Edward Witten (1987). Superstring theory, Cambridge University Press. The original textbook.
Vol. 1: Introduction. ISBN 0-521-35752-7.
Vol. 2: Loop amplitudes, anomalies and phenomenology. ISBN 0-521-35753-5.
Polchinski, Joseph (1998). String Theory, Cambridge University Press. A modern textbook.
Vol. 1: An introduction to the bosonic string. ISBN 0-521-63303-6.
Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4.
Johnson, Clifford (2003). D-branes. Cambridge: Cambridge University Press. ISBN 0-521-80912-6.
Zwiebach, Barton (2004). A First Course in String Theory, Cambridge University Press. ISBN 0-521-83143-1. Errata are available
Katrin Becker, Melanie Becker and John H. Schwarz (2007). String Theory and M-Theory: A Modern Introduction , Cambridge University Press.
[edit] External links
Schwarz, Patricia (1998). The Official String Theory Web Site. Retrieved on December 16, 2005.
WGBH Educational Foundation (2003). The Elegant Universe. PBS Online, NOVA. Retrieved on December 16, 2005. – A Three-Hour Miniseries with Brian Greene by NOVA (original PBS Broadcast Dates: October 28, 8-10 p.m. and November 4, 8-9 p.m., 2003). Various images, texts, videos and animations explaining string theory.
Troost, Jan (2002). Beyond String Theory. Vrije Universiteit Brussel, Theoretical Physics (TENA). Retrieved on December 16, 2005. – An ongoing project by a string physicist, working for the French CNRS.
Pierre, John M. (1999). Superstrings! String Theory Home Page. Retrieved on December 16, 2005. – Online tutorial.
Motl, LuboÅ¡; Screiber, Urs. SCI.physics. STRINGS newsgroup. Harvard High Energy Theory Group. Retrieved on December 16, 2005. – A moderated newsgroup for discussion of string theory (a theory of quantum gravity and unification of forces) and related fields of high-energy physics.
Schwarz, John H. (2000). Introduction to Superstring Theory. arXiv.org e-Print archive. Retrieved on December 22, 2005. – Four lectures, presented at the NATO Advanced Study Institute on Techniques and Concepts of High Energy Physics, St. Croix, Virgin Islands, in June 2000, and addressed to an audience of graduate students in experimental high energy physics, survey basic concepts in string theory.
Witten, Edward (1998). Duality, Spacetime and Quantum Mechanics. Kavli Institute for Theoretical Physics. Retrieved on December 16, 2005. – Slides and audio from an Ed Witten lecture where he introduces string theory and discusses its challenges.
Kibble, Tom (2004). Cosmic strings reborn?. arXiv.org e-Print archive. Retrieved on December 16, 2005. – Invited Lecture at COSLAB 2004, held at Ambleside, Cumbria, United Kingdom, from 10 to 17 September 2004.
Marolf, Don (2004). Resource Letter NSST-1: The Nature and Status of String Theory. arXiv.org e-Print archive. Retrieved on December 16, 2005. – A guide to the string theory literature.
Ajay, Shakeeb, Wieland et al. (2004). The nth dimension. Retrieved on December 16, 2005. – A comprehensive compilation of materials concerning string theory. Created by an international team of students.
Woit, Peter (2002). Is string theory even wrong?. American Scientist. Retrieved on December 16, 2005. – A criticism of string theory.
Woit, Peter (2004). Not Even Wrong. Columbia University Mathematics Department. Retrieved on December 16, 2005. – A blog critical of string theory.
Veneziano, Gabriele (May 2004), "The Myth of the Beginning of Time", Scientific American
McKie, Robin (2006-10-09), "Setback as string theory of the universe is de-bunked", The Hindu
Harris, Richard (2006-11-07). Short of 'All,' String Theorists Accused of Nothing. National Public Radio. Retrieved on 2007-03-05.
A website dedicated to creative writing inspired by string theory.
A Flash Animation for the book "Imagining the Tenth Dimension" by Rob Bryanton
George Gardner (2007-01-24). "Theory of everything put to the test". tech.blorge.com. (Google Groups). Retrieved on 2007-03-03.
Minkel, J. R. (2006-03-02), "A Prediction from String Theory, with Strings Attached", Scientific American
Retrieved from "http://en.wikipedia.org/wiki/String_theory"
Categories: Unsolved problems in physics | Articles with unsourced statements since February 2007 | All articles with unsourced statements | Particle physics | Physical cosmology | Protoscience | String theory | Fundamental physics concepts
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