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Superstring theory
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String theory is a still-developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling Bosonic string theory is the original version of String theory, developed in the late 1960s In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified In non-technical terms M-theory presents an idea about the basic substance of the universe In Theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions In Theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. In Physics, a heterotic string is a peculiar mixture (or hybrid of the bosonic string and the Superstring (the adjective heterotic comes from In Theoretical physics, string field theory is a proposal to define String theory in such a way that the Background independence is respected The holographic principle is a physical property of Quantum gravity theories proposed by Gerard 't Hooft and Leonard Susskind, which resolves the Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world A string is one of the main objects of study in String theory, a branch of Theoretical physics. Unlike the point particles in quantum field theories like the standard model of particle physics, strings interact in a way that is almost uniquely specified by mathematical self-consistency, forming an apparently valid quantum theory of gravity. A point particle (or point-like, often spelled pointlike) is an idealized object heavily used in Physics. In quantum field theory (QFT the forces between particles are mediated by other particles The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature
Since its birth as the dual resonance model which described the strongly interacting hadrons as strings, the term string theory has changed to include any of a group of related superstring theories and larger frameworks such as M-theory, which unite them. A dual resonance model is a term used in Theoretical physics which refers to the early investigation (1968-1974 on Strong interactions of string theory In Particle physics, a hadron ( from the ἁδρός hadrós, " stout, thick " ( See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified A shared property of all these theories is the holographic principle. The holographic principle is a physical property of Quantum gravity theories proposed by Gerard 't Hooft and Leonard Susskind, which resolves the
String theorists have not yet completely described these theories, nor have they determined if these theories relate to the physical universe or how. [1] The logical coherence of the approach, however, and the fact that string theory can include all older theories of physics, have led many physicists to believe that such a connection is possible. In particular, string theory is the first candidate theory of everything, a way to describe all the known natural forces (gravitational, electromagnetic, weak and strong) and matter (quarks and leptons) in a mathematically complete system. A theory of everything ( TOE) is a putative Theory of Theoretical physics that fully explains and links together all known physical phenomena In Physics, a fundamental interaction or fundamental force is a mechanism by which particles interact with each other and which cannot be explained in terms Gravitation is a natural Phenomenon by which objects with Mass attract one another Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. Leptons are a family of fundamental Subatomic particles comprising the Electron, the Muon, and the Tauon (or tau particle as well as their On the other hand, many detractors criticise string theory because it has not yet provided experimentally testable predictions.
Like any other quantum theory of gravity, it is widely believed that testing the theory experimentally would be prohibitively expensive, requiring feats of engineering on a solar-system scale. Although string theory, like any other scientific theory, is falsifiable in principle, critics maintain that it is unfalsifiable for the foreseeable future, and so should not be called science.
Work on string theory is made interesting because of the mathematics involved, and because of the large number of forms that the theories can take. String theory strongly suggests that spacetime has eleven dimensions [2], not the usual three space and one time; but the theory can easily describe universes with four observable spacetime dimensions too. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS [3]
String theories include objects more general than strings, called branes. In Theoretical physics, a membrane, brane, or p -brane is a spatially extended mathematical concept that appears in String theory These are black-holes charged with a differential form vector potential which has more than one index, a different type of electricity and magnetism where the fundamental objects are extended. In the mathematical fields of Differential geometry and Tensor calculus, differential forms are an approach to Multivariable calculus which is In Vector calculus, a vector potential is a Vector field whose curl is a given vector field By studying certain p-branes and identifying them with D-branes, endpoints for strings, certain types of string theory are shown to be equivalent to certain types of more traditional gauge theory. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations Research on this equivalence has led to new insights on quantum chromodynamics, the fundamental theory of the strong nuclear force. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and [4][5][6][7]
Contents |
Overview
- See also: Quantum gravity
The overarching physical insight behind string theory is the holographic principle, which states that the description of the oscillations of the surface of a black hole must also describe the space-time around it. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature The holographic principle is a physical property of Quantum gravity theories proposed by Gerard 't Hooft and Leonard Susskind, which resolves the A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Holography demands that a low-dimensional theory describing the fluctuations of a horizon will end up describing everything that can fall through, which can be anything at all. So a theory of a black hole horizon is a theory of everything.
A-priori, finding even one consistent holographic description seems like a long-shot, because it would be a disembodied nonlocal description of quantum gravity. In string theory, not only is there one such description, there are several different ones, each describing fluctuations of horizons with different charges and dimensions, and all of them logically fit together. So the same physical objects and interactions can be described by the fluctuations of one-dimensional black hole horizons, or by three dimensional horizons, or by zero-dimensional horizons. A dual resonance model is a term used in Theoretical physics which refers to the early investigation (1968-1974 on Strong interactions of string theory For the relation of the AdS/CFT correspondence to the general context of string theory see String theory. In Physics, matrix string theory is the first known set of equations that describe Superstring theory in a non-perturbatively complete and consistent framework The fact that these different descriptions describe the same physics is overwhelming evidence that string theory is consistent.
An ordinary astronomical black hole does not have a convenient holographic description, because it has a Hawking temperature. Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes String theories are formulated on cold black holes, which are those which have as much charge as possible. The first holographic theory discovered described the scattering of one-dimensional strings, tiny loops of vibrating horizon charged with a two-form vector potential which makes a charged black hole a one-dimensional line. In the mathematical fields of Differential geometry and Tensor calculus, differential forms are an approach to Multivariable calculus which is Fluctuations of this line horizon describe all matter, so every elementary particle can be described by a mode of oscillation of a very small segment or loop of string. In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made A string is one of the main objects of study in String theory, a branch of Theoretical physics. The string-length is approximately the Planck length, but can be significantly bigger when the strings are weakly interacting. The Planck length, denoted by \scriptstyle\ell_P \, is the unit of Length approximately 1
All string theories predict the existence of degrees of freedom which are usually described as extra dimensions. For information on degrees of freedom in other sciences see Degrees of freedom. String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings Without fermions, bosonic strings can vibrate in a flat but unstable 26 dimensional space time. In a superstring theory with fermions, the weak-coupling (no-interaction) limit describes a flat stable 10 dimensional space time. See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling Interacting superstring theories are best thought of as configurations of an 11 dimensional supergravity theory called M-theory where one or more of the dimensions are curled up so that the line-extended charged black holes become long and light. In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified
Long light strings can vibrate at different resonant frequencies, and each resonant frequency describes a different type of particle. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's Frequency is a measure of the number of occurrences of a repeating event per unit Time. [8] So in string limits, any elementary particle should be thought of as a tiny vibrating line, rather than as a point. The string can vibrate in different modes just as a guitar string can produce different notes, and every mode appears as a different particle: electron, photon, gluon, etc. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the
The only way in which strings can interact is by splitting and combining in a smooth way. It is impossible to introduce arbitrary extra matter, like point particles which interact with strings by collisions, because the particles can fall into the black hole, so holography demands that it must show up as a mode of oscillation. The only way to introduce new matter is to find gravitational backgrounds where strings can scatter consistently, or to add boundary conditions, endpoints for the strings. Some of the backgrounds are called NS-branes, which are extreme-charged black hole sheets of different dimensions. In Theoretical physics, the NS5-brane is a five-dimensional object (a P-brane) in String theory that carries a magnetic charge under the B-field the field Other charged black-sheet backgrounds are the D-branes, which have an alternate description as planes where strings can end and slide. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named When the strings are long and light, the branes are classical and heavy. In other limits where the strings become heavy, some of the branes can become light.
Since string theory is widely believed to be a consistent theory of quantum gravity, many hope that it correctly describes our universe, making it a theory of everything. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature A theory of everything ( TOE) is a putative Theory of Theoretical physics that fully explains and links together all known physical phenomena There are known configurations which describe all the observed fundamental forces and matter but with a zero cosmological constant and some new fields. There are other configurations with different values of the cosmological constant, which are metastable but long-lived. Metastability is a general scientific concept which describes states of delicate equilibrium This leads many to believe that there is at least one metastable solution which is quantitatively identical with the standard model, with a small cosmological constant, which contains dark matter and a plausible mechanism for inflation. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles In Physical cosmology, cosmic inflation is the idea that the nascent Universe passed through a phase of exponential expansion that It is not yet known whether string theory has such a solution, nor how much freedom the theory allows to choose the details. Because of this, string theory has not yet made practically falsifiable predictions that would allow it to be experimentally tested. Falsifiability (or "refutability" is the logical possibility that an assertion can be shown false by an observation or a physical experiment
The full theory does not yet have a satisfactory definition in all circumstances, since the scattering of strings is most straightforwardly defined by a perturbation theory. In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system The complete quantum mechanics of high dimensional branes is not easily defined, and the behavior of string theory in cosmological settings (time-dependent backgrounds) is not fully worked out. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons It is also not clear if there is any principle by which string theory selects its vacuum state, the space-time configuration which determines the properties of our universe (see string theory landscape). In Quantum field theory, the vacuum state (also called the vacuum) is the Quantum state with the lowest possible Energy. The string theory landscape or anthropic landscape refers to the large number of possible false vacua in String theory.
Basic properties
String theory can be 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. In Physics, the action is a particular quantity in a Physical system that can be used to describe its operation The Nambu-Goto action is the simplest invariant action in Bosonic string theory. In Physics, the Polyakov action is the two-dimensional action of a Conformal field theory describing the Worldsheet of a string in String In the absence of external interactions, string dynamics are governed by tension and kinetic energy, which combine to produce oscillations. The quantum mechanics of strings implies these oscillations take on discrete vibrational modes, the spectrum of the theory. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons An energy spectrum is a distribution of Energy among a large assemblage of particles
On distance scales larger than the string radius, each oscillation mode behaves as a different species of particle, with its mass, spin and charge determined by the strings dynamics. Splitting and recombinations of string correspond to particle emission and absorption, giving rise to the interactions between particles.
An analogy for strings' modes of vibration is a guitar string's production of multiple but distinct musical notes. In the analogy, different notes correspond to different particles.
String theory includes both open strings, which have two distinct endpoints, and closed strings making a complete loop. The two types of string behave in slightly different ways, yielding two different spectra. A string is one of the main objects of study in String theory, a branch of Theoretical physics. 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. In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena 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 gauge theory). Bosonic string theory is the original version of String theory, developed in the late 1960s In Particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein Gravitation is a natural Phenomenon by which objects with Mass attract one another Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations 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. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that 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. See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified
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. Twine is a strong Thread or String composed of two or more smaller strands or Yarns twisted together 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. Werner Heisenberg (5 December 1901 in Würzburg &ndash1 February 1976 in Munich) was a German theoretical physicist best known for enunciating the In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain 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.
Worldsheet
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For more details on this topic, see Relationship between string theory and quantum field theory. Many first principles in Quantum field theory are explained or get further insight in String theory: Emission and absorption one of the most basic building blocks
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. In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS 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. A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be In String theory, the worldsheet is a two-dimensional Manifold which describes the embedding of the string in Spacetime. The different string modes (representing different particles, such as photon or graviton) are surface waves on this manifold. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework
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. A string is one of the main objects of study in String theory, a branch of Theoretical physics. In Mathematics, particularly in Complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional A surface S in the Euclidean space R 3 is orientable if a two-dimensional figure (for example) cannot be moved around the surface and back 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. In Mathematics, particularly in Complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional
Strings can split and connect. In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. A subatomic particle is an elementary or composite Particle smaller than an Atom. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles A string is one of the main objects of study in String theory, a branch of Theoretical physics. A string is one of the main objects of study in String theory, a branch of Theoretical physics. This is reflected by the form of their worldsheet (more accurately, by its topology). Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of 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 right). 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). In Geometry, a torus (pl tori) is a Surface of revolution generated by revolving a Circle in three dimensional space about an axis Coplanar 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 some versions of the bosonic string), strings can split and reconnect in an opposite orientation (as in a Möbius strip or a Klein bottle). In Theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions Bosonic string theory is the original version of String theory, developed in the late 1960s This article is about the mathematical object See Mobius Band (music group for the music group In Mathematics, the Klein bottle is a certain non- orientable Surface, i These theories are called unoriented. Formally, the worldsheet in these theories is a non-orientable surface. A surface S in the Euclidean space R 3 is orientable if a two-dimensional figure (for example) cannot be moved around the surface and back
Dualities
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 E8×E8). String duality is a class of symmetries in Physics that link different string theories, theories which assume that the fundamental building blocks of the In theoretical Physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory T-duality is a symmetry between small and large distances that is not present in Kaluza-Klein compactification of a Particle theory. U-duality is a symmetry of String theory or M-theory combining S-duality and T-duality transformations In Theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions In Theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. In Theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. In Physics, a heterotic string is a peculiar mixture (or hybrid of the bosonic string and the Superstring (the adjective heterotic comes from In Mathematics, the orthogonal group of degree n over a field F (written as O( n, F) is the group of n 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. A theory of everything ( TOE) is a putative Theory of Theoretical physics that fully explains and links together all known physical phenomena In Physics, compactification means changing a theory with respect to one of its Space-time dimensions 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). In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified 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. Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them 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, meaning 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. In Particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light |
| 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 (achiral) |
| 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 E8×E8 |
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). In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light In Mathematics, the orthogonal group of degree n over a field F (written as O( n, F) is the group of n In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light In Physics, a heterotic string is a peculiar mixture (or hybrid of the bosonic string and the Superstring (the adjective heterotic comes from In Mathematics, the orthogonal group of degree n over a field F (written as O( n, F) is the group of n In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light In Physics, a heterotic string is a peculiar mixture (or hybrid of the bosonic string and the Superstring (the adjective heterotic comes from In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named
Extra dimensions
Number of dimensions
An intriguing feature of string theory is that it involves the prediction of extra dimensions. The number of dimensions is not fixed by any consistency criterion, but flat spacetime solutions do exist in the so-called "critical dimension. In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity " Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions—more precisely different values of the "effective central charge," a count of degrees of freedom which reduces to dimensionality in weakly curved regimes—are related by dynamical transitions. [9]
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," and this number is fixed and independent of potential energy. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. String theory allows one to relate the number of dimensions to scalar potential energy. Technically, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. In Theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of Quantum mechanics —usually a One-loop diagram —that Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible.
This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations 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. In Physics, the Casimir effect and the Casimir-Polder force are physical forces arising from a quantized field. 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 in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions. [10]
When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation. [11] Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional space-time. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS
Compact dimensions
Two different ways have been proposed to resolve this apparent contradiction. In mathematics Calabi&ndashYau manifolds are compact Kähler manifolds whose Canonical bundle is trivial 3D projection is any method of mapping three-dimensional points to a two-dimensional plane The first is to compactify the extra dimensions; i. This article is on dimensional reduction in physics For the statistics concept see Dimensionality reduction. 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 mathematics Calabi&ndashYau manifolds are compact Kähler manifolds whose Canonical bundle is trivial In 7 dimensions, they are termed G2 manifolds. A G 2 manifold is a seven-dimensional Riemannian manifold with Holonomy group ''G''2. 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)!
Brane-world scenario
Another possibility is that we are "stuck" in a 3+1 dimensional (i. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Physics and Chemistry, wave–particle duality is the concept that all Matter and Energy exhibits both Wave -like and 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. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named Brane cosmology refers to several theories in Particle physics and cosmology motivated by but not exclusively derived from Superstring theory and Many people believe that some combination of the two ideas — compactification and branes — will ultimately yield the most realistic theory.
Effect of the hidden dimensions
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 four 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 mathematics Calabi&ndashYau manifolds are compact Kähler manifolds whose Canonical bundle is trivial 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. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles 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.
D-branes
Another key feature of string theory is the existence of D-branes. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named 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. In String theory, the worldsheet is a two-dimensional Manifold which describes the embedding of the string in Spacetime. For a different notion of boundary related to Manifolds see that article 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). In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling In Physics, a charge may refer to one of many different quantities such as the Electric charge in Electromagnetism or the Color charge in
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). Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations In Particle physics, gauge bosons are Bosonic particles that act as carriers of the fundamental forces of nature 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). An abelian group, also called a commutative group, is a group satisfying the additional requirement that the product of elements does not depend on their order (the In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena If there are multiple parallel D-branes there will be multiple types of gauge bosons, giving rise to a non-Abelian gauge theory. Non-abelian may describe Non-abelian group, in mathematics a group that is not abelian (commutative Non-abelian gauge theory, in physics
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. In Physics, two systems are coupled if they are interacting with each other Gravitation is a natural Phenomenon by which objects with Mass attract one another
Gauge-gravity duality
Gauge-gravity duality is a conjectured duality between a quantum theory of gravity in certain cases and gauge theory in a lower number of dimensions. Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations This means that each predicted phenomenon and quantity in one theory has an analogue in the other theory, with a "dictionary" translating from one theory to the other.
Description of the 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. Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations In Physics, two systems are coupled if they are interacting with each other Gravitation is a natural Phenomenon by which objects with Mass attract one another In Physics, a fundamental interaction or fundamental force is a mechanism by which particles interact with each other and which cannot be explained in terms 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. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named 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.
Examples and intuition
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). In Theoretical physics, supergravity ( supergravity theory) is a field theory that combines the principles of Supersymmetry and General relativity In Topology and related areas of Mathematics, a product space is the Cartesian product of a family of Topological spaces equipped with a natural In Mathematics and Physics, n -dimensional anti de Sitter space, sometimes written AdS_n is a maximally symmetric Lorentzian manifold In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe [12] This is known as the AdS/CFT correspondence, a name often used for Gauge / gravity duality in general. For the relation of the AdS/CFT correspondence to the general context of string theory see String theory.
This duality can be thought of as follows: suppose there is a spacetime with a gravitational source, for example an extremal black hole. In Theoretical physics, an extremal black hole is a Black hole with the minimal possible mass that can be compatible with the given charges and Angular When particles are far away from this source, they are described by closed strings (i. e. a gravitational theory, or usually supergravity). In Theoretical physics, supergravity ( supergravity theory) is a field theory that combines the principles of Supersymmetry and General relativity 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. In Quantum chromodynamics, or more generally Quantum gauge theories with a connection which are confining, stringlike degrees of freedom called In Particle physics, gauge bosons are Bosonic particles that act as carriers of the fundamental forces of nature Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations 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 General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot
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. In Physics, particularly in Quantum field theory, configurations of a physical system that satisfy classical Equations of motion are called on shell In Physics, particularly in Quantum field theory, configurations of a physical system that satisfy classical Equations of motion are called on shell Correlation functions contain information about the distribution of points or events or things across some space/time 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. In quantum field theory (QFT the forces between particles are mediated by other particles 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. Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations 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. Dilaton is an Hypothetical particle that appears in Kaluza-Klein theory and String theory. In Physics, two systems are coupled if they are interacting with each other In Physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles such as Quarks, becomes arbitrarily e. its coupling will grow weaker in high energies.
Contact with experiment
This branch of string theory may lead to new insights on quantum chromodynamics, a gauge theory which is the fundamental theory of the strong nuclear force. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and To this end, it is hoped that a gravitational theory dual to quantum chromodynamics will be found. [13]
In fact, a vague contact with experiment has already been claimed to have been achieved[14][15][16][17], though currently the alternative, Lattice QCD, is doing a much better job and has already made contact with experiments in various fields with good results,[18] though the computations are numerical rather than analytic. In Physics, lattice quantum chromodynamics (lattice QCD is a theory of Quarks and Gluons formulated on a space-time lattice. Numerical analysis is the study of Algorithms for the problems of continuous mathematics (as distinguished from Discrete mathematics)
Problems and controversy
Although historically string theory is an outgrowth of physics, some contend that string theory should (strictly speaking) be classified as something other than science. This is a list of some of the major unsolved problems in Physics. See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified A theory of everything ( TOE) is a putative Theory of Theoretical physics that fully explains and links together all known physical phenomena For a scientific theory to be valid it must be corroborated empirically, i. In Philosophy, empiricism is a theory of Knowledge which asserts that knowledge arises from Experience. e. through experiment or observation. In scientific inquiry an experiment ( Latin: Ex- periri, "to try out" is a method of investigating particular types of research questions or Observation is either an activity of a living being (such as a Human) which senses and assimilates the Knowledge of a Phenomenon, or the recording of data Few avenues for such contact with experiment have been claimed. [19] With the construction of the Large Hadron Collider in CERN some scientists hope to produce relevant data, though it is widely believed that any theory of quantum gravity would require much higher energies to probe directly. The European Organization for Nuclear Research (Organisation Européenne pour la Recherche Nucléaire known as CERN Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature Moreover, string theory as it is currently understood has a huge number of equally possible solutions. [20] Thus it has been claimed by some scientists that string theory may not be falsifiable and may have no predictive power. Falsifiability (or "refutability" is the logical possibility that an assertion can be shown false by an observation or a physical experiment The predictive power of a Scientific theory refers to its ability to generate testable predictions [21][22][23][24]
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. The energy scales at which it would be possible to see the stringy nature of particles is much greater than that experimentally accessible. It possesses many features of mathematical interest and naturally incorporates all the gross features of the Standard Model, such as non-abelian gauge groups and chiral fermions. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles Because string theory may not be tested in the foreseeable future, some scientists[25] have asked if it even deserves to be called a scientific theory; it is not falsifiable in the sense of Popper. The word theory has many distinct meanings in different fields of Knowledge, depending on their methodologies and the context of discussion. Falsifiability (or "refutability" is the logical possibility that an assertion can be shown false by an observation or a physical experiment Sir Karl Raimund Popper ( July 28 1902 &ndash September 17 1994) was an Austrian and British Philosopher and a professor
It has also been suggested that string theory is better thought of as a framework for building models, in the same way that quantum field theory is a framework. In quantum field theory (QFT the forces between particles are mediated by other particles [26]
Ideas from string theory have had a major influence on proposals for physics beyond the Standard Model. For example, while supersymmetry is 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. However, 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, when observing stars during a solar eclipse, the sun's gravity had not deflected light by the predicted amount, then Einstein's general relativity theory would have been proven wrong. A solar eclipse occurs when the Moon passes between the Sun and the Earth so that the Sun is wholly or partially obscured General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916
On a more mathematical level, another problem is that, like many quantum field theories, much of string theory is still only formulated perturbatively (i. In quantum field theory (QFT the forces between particles are mediated by other particles In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system 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. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS In Mathematics and Physics, a non-perturbative function or process is one that cannot be accurately described by Perturbation theory.
Yet another central problem of string theory is that the best understood backgrounds of string theory preserve much of the supersymmetry of the underlying theory, which results in time-invariant space-times: currently string theory cannot deal well with time-dependent, cosmological backgrounds.
The previous two issues are related to a more profound problem: string theory might not be truly fundamental in its present formulation because it is background-dependent — string theory describes perturbative expansions about fixed spacetime backgrounds. Some see background independence as a fundamental requirement of a theory of quantum gravity, particularly since General Relativity is already background independent. Background independence is a condition in theoretical physics especially in Quantum gravity (QG that requires the defining equations of a theory to be independent of the actual General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 In response to this criticism, some string theorists disagree that background-independence should be a guiding principle, while others hope that M-theory, or a non-perturbative treatment of string theory (such as string field theory) will turn out to be background-independent, giving as solutions the many different versions of string theory with the different backgrounds. In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified In Mathematics and Physics, a non-perturbative function or process is one that cannot be accurately described by Perturbation theory. In Theoretical physics, string field theory is a proposal to define String theory in such a way that the Background independence is respected
Another problem is that the vacuum structure of the theory, called the string theory landscape, is not well understood. The string theory landscape or anthropic landscape refers to the large number of possible false vacua in String theory. As string theory is presently understood, it appears to contain a large number of distinct, meta-stable vacua, perhaps 10500 or more. Each of these corresponds to a different universe, with a different collection of particles and forces. [20] 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. In Physics and Cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical A physical Constant is a Physical quantity that is generally believed to be both universal in nature and constant in time In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification [27][28] However, such explanations are not usually regarded as scientific in the Popperian sense. Sir Karl Raimund Popper ( July 28 1902 &ndash September 17 1994) was an Austrian and British Philosopher and a professor
String theory does predict, at least perturbatively, that at sufficiently high energies—which are probably near the quantum gravity scale—the string-like nature of particles should be apparent. For example, there should be heavier copies of all particles corresponding to higher string harmonics. However, it is unclear what these energies are. In the limiting case, these energies would be one million billion (ten followed by fourteen zeros) times higher than those accessible in the newest accelerator, the LHC.
Following the appearance of two books claiming string theory is a failure,[21][24] a hot media debate evolved in 2007. [29][30]
- "For more than a generation, physicists have been chasing a will-o’-the-wisp called string theory. The beginning of this chase marked the end of what had been three-quarters of a century of progress. Dozens of string-theory conferences have been held, hundreds of new Ph. D. s have been minted, and thousands of papers have been written. Yet, for all this activity, not a single new testable prediction has been made, not a single theoretical puzzle has been solved. In fact, there is no theory so far—just a set of hunches and calculations suggesting that a theory might exist. And, even if it does, this theory will come in such a bewildering number of versions that it will be of no practical use: a Theory of Nothing. " [31]
History
Some of the structures reintroduced by string theory arose for the first time much earlier as part of the program of classical unification started by Albert Einstein. 1943-1958 S-Matrix String theory is an outgrowth of a research program begun by Werner Heisenberg in 1943 picked up and advocated by many prominent theorists starting Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical The first person to add a fifth dimension to general relativity was German mathematician Theodor Kaluza in 1919, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. In Physics and Mathematics, a sequence of N numbers can be understood to represent a location in an N -dimensional General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Theodor Franz Eduard Kaluza ( November 9, 1885 &ndash January 19, 1954) was a German Mathematician and Physicist In 1926, the Swedish physicist Oskar Klein gave a physical interpretation of the unobservable extra dimension--- it is wrapped into a small circle. Oskar Benjamin Klein ( September 15 1894 - February 5 1977) was a Swedish theoretical Physicist. In Physics, Kaluza–Klein theory (or KK theory, for short is a model that seeks to unify the two fundamental forces of Gravitation and Einstein introduced a geometrical antisymmetric tensor for purely aesthetic reasons, while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they are demanded by consistency conditions.
String theory was originally developed during the late 1960s and early 1970s as a never completely successful theory of hadrons, the subatomic particles like the proton and neutron which feel the strong interaction. In Particle physics, a hadron ( from the ἁδρός hadrós, " stout, thick " ( A subatomic particle is an elementary or composite Particle smaller than an Atom. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and In the 1960s, Geoffrey Chew and Steven Frautschi discovered that the mesons make families called Regge trajectories with masses related to spins in a way that was later understood by Yoichiro Nambu and Leonard Susskind to be the relationship expected from rotating strings. Geoffrey Chew (born 1924 is an American Theoretical physicist. Steven Frautschi (born 1933 is an American Theoretical physicist, Professor of Physics at the California Institute of Technology. In Particle physics, a meson is a strongly interacting Boson &mdashthat is a Hadron with integer spin. In Quantum physics, Regge theory is the study of the analytic properties of scattering as a function of angular momentum where the angular momentum is not restricted to be an is a Japan -born American Physicist, currently a Professor at the University of Chicago. Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and Chew advocated making a theory for the interactions of these trajectories which did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix. In Physics, the term bootstrap model is used for a class of theories that use very general Consistency criteria to determine the form of a quantum theory from some Scattering matrix redirects here For the meaning in linear electrical networks see Scattering parameters. The S-matrix approach was started by Werner Heisenberg in the 1940s as a way of constructing a theory which did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale. Werner Heisenberg (5 December 1901 in Würzburg &ndash1 February 1976 in Munich) was a German theoretical physicist best known for enunciating the While the scale was off by many orders of magnitude, the approach he advocated was ideally suited for a theory of quantum gravity.
Working with experimental data, R. Dolen, D. Horn and C. Schmidt developed some sum rules for hadron exchange. Sum rule may refer to Sum rule in differentiation Sum rule in integration Rule of sum, a counting principle in combinatorics When a particle and antiparticle scatter, virtual particles can be exchanged in two qualitatively different ways. In the s-channel, the two particles annihilate to make temporary intermediate states which fall apart into the final state particles. In the t-channel, the particles exchange intermediate states by emission and absorption. In field theory, the two contributions add together, one giving a continuous background contribution, the other giving peaks at certain energies. In the data, it was clear that the peaks were stealing from the background--- the authors interpreted this as saying that the t-channel contribution was dual to the s-channel one, meaning both described the whole amplitude and included the other.
The result was widely advertised by Murray Gell-Mann, leading Gabriele Veneziano to construct a scattering amplitude which had the property of Dolen-Horn-Schmidt duality, later renamed world-sheet duality. Murray Gell-Mann (born September 15, 1929) is an American Physicist who received the 1969 Nobel Prize in physics for his work Gabriele Veneziano (born 1942, Florence, Italy) is an Italian theoretical physicist and a founder of String theory. The amplitude needed poles where the particles appear, on straight line trajectories, and there is a special mathematical function whose poles are evenly spaced on half the real line--- the Gamma function--- which was widely used in Regge theory. In Mathematics, the Gamma function (represented by the capitalized Greek letter '''&Gamma''') is an extension of the Factorial function By manipulating combinations of Gamma functions, Veneziano was able to find a consistent scattering amplitude with poles on straight lines, with mostly positive residues, which obeyed duality and had the appropriate Regge scaling at high energy. The amplitude could fit near-beam scattering data as well as other Regge type fits, and had a suggestive integral representation which could be used for generalization.
Over the next years, hundreds of physicists worked to complete the bootstrap program for this model, with many surprises. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle which appears in the theory, an obvious self-consistency condition, the lightest particle must be a tachyon. A tachyon (from the Greek, takhyónion, from, takhýs, ie swift fast is any hypothetical particle that travels at Faster-than-light Miguel Virasoro and Joel Shapiro found a different amplitude now understood to be that of closed strings, while Ziro Koba and Holger Nielsen generalized Veneziano's integral representation to multiparticle scattering. Miguel Angel Virasoro is an Argentinian physicist who did most of his work in Italy Holger Bech Nielsen (born 25 August, 1941) is a Danish theoretical physicist, professor at the Niels Bohr Institute, at the Veneziano and Sergio Fubini introduced an operator formalism for computing the scattering amplitudes which was a forerunner of world-sheet conformal theory, while Virasoro understood how to remove the poles with wrong-sign residues using a constraint on the states. Claud Lovelace calculated a loop amplitude, and noted that there is an inconsistency unless the dimension of the theory is 26. Charles Thorn, Peter Goddard and Richard Brower went on to prove that there are no wrong-sign propagating states in dimensions less than or equal to 26. Charles Thorn is a Professor of Physics at University of Florida in Gainesville Florida. Peter Goddard (born 3 September 1945) is a mathematical physicist who works in String theory and Conformal field theory, and proved
In 1969 Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind recognized that the theory could be given a description in space and time in terms of strings. is a Japan -born American Physicist, currently a Professor at the University of Chicago. Holger Bech Nielsen (born 25 August, 1941) is a Danish theoretical physicist, professor at the Niels Bohr Institute, at the Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and The scattering amplitudes were derived systematically from the action principle by Peter Goddard, Jeffrey Goldstone, Claudio Rebbi and Charles Thorn, giving a space-time picture to the vertex operators introduced by Veneziano and Fubini and a geometrical interpretation to the Virasoro conditions. Peter Goddard (born 3 September 1945) is a mathematical physicist who works in String theory and Conformal field theory, and proved Jeffrey Goldstone (born 3 September 1933) is a British -born theoretical Physicist and an emeritus physics faculty at MIT Center Charles Thorn is a Professor of Physics at University of Florida in Gainesville Florida. In Mathematics, the Virasoro algebra (named after the physicist Miguel Angel Virasoro) is a complex Lie algebra, given as a central extension
In 1970, Pierre Ramond added fermions to the model, which led him to formulate a two-dimensional supersymmetry to cancel the wrong-sign states. Pierre Ramond (b 31 January 1943 in Neuilly-sur-Seine, France) is a Distinguished Professor of Physics at University of Florida John Schwarz and André Neveu added another sector to the fermi theory a short time later. John Henry Schwarz (born 1941) is an American theoretical physicist. André Neveu (born 1946 is a French Physicist working on String theory and Quantum field theory who coinvented the Neveu-Schwarz algebra In the fermion theories, the critical dimension was 10. Stanley Mandelstam formulated a world sheet conformal theory for both the bose and fermi case, giving a two-dimensional field theoretic path-integral to generate the operator formalism. Stanley Mandelstam (b 1928 Johannesburg) is a South African born theoretical physicist
In 1974, Tamiaki Yoneya discovered that all the known string theories included a massless spin two particle which obeyed the correct Ward identities to be a graviton. Tamiaki Yoneya is a Physicist. Independently of Joel Scherk and John H In Quantum field theory, a Ward-Takahashi identity is an identity between Correlation functions that follows from the global or gauged symmetries of the John Schwarz and Joel Scherk came to the same conclusion and made the bold leap to suggest that string theory was a theory of gravity, not a theory of hadrons. Joël Scherk (often cited as Joel Scherk was a physicist who studied String theory and Supergravity. They reintroduced Kaluza Klein theory as a way of making sense of the extra dimensions. At the same time, quantum chromodynamics was recognized as the correct theory of hadrons, shifting the attention of physicists and apparently leaving the bootstrap program in the dustbin of history. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the The expression ash heap of history (or often dustbin of history) was coined by Leon Trotsky in response to the Mensheviks walking out of the Second
String theory eventually made it out of the dustbin, but for the following decade all work on the theory was completely ignored. Still, the theory continued to develop at a steady pace thanks the work of a handful of devotees. Ferdinando Gliozzi, Joel Scherk, and David Olive realized in 1976 that the original Ramond and Neveu Schwarz strings were separately inconsistent and needed to be combined. The resulting theory did not have a tachyon, and was proven to have space-time supersymmetry by John Schwarz and Michael Green in 1981. Michael Green may refer to Sports Michael Green (Australian rules footballer Michael Green (field hockey (born 1972 The same year, Alexander Polyakov gave the theory a modern path integral formulation, and went on to develop conformal field theory extensively. Alexander M Polyakov (born 27 September 1945) is a theoretical Physicist, formerly at the Landau Institute in Moscow, currently In 1979, Daniel Friedan showed that the equations of motions of string theory, which are generalizations of the Einstein equations of General Relativity, emerge from the Renormalization group equations for the two dimensional field theory. Daniel Friedan is an American theoretical physicist and is one of two sons of Betty Friedan. The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 In Theoretical physics, renormalization group (RG refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views Schwarz and Green discovered T-duality, and constructed two different superstring theories--- IIA and IIB related by T-duality, and type I theories with open strings. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices.
In the early 1980s, Edward Witten discovered that most theories of quantum gravity could not accommodate chiral fermions like the neutrino. Edward Witten (born August 26, 1951) is an American Theoretical physicist and Professor at the Institute for Advanced Study This led him, in collaboration with Luiz Alvarez-Gaume to study violations of the conservation laws in gravity theories with anomalies, concluding that type I string theories were inconsistent. Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaume had missed, which restricted the gauge group of the type I string theory to be SO(32). In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate. Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution. In Physics, the first superstring revolution is a period of important discoveries in String theory roughly between 1984 and 1986.
During this period, David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm discovered heterotic strings. David Jonathan Gross (born February 19, 1941 in Washington DC Jeffrey A Harvey is a Professor of Physics and string theorist at University of Chicago. Emil Martinec is an American Theoretical physicist born in 1958 The gauge group of these closed strings was two copies of E8, and either copy could easily and naturally include the standard model. Philip Candelas, Gary Horowitz, Andrew Strominger and Edward Witten found that the Calabi-Yau manifolds are the compactifications which preserve a realistic amount of supersymmetry, while Lance Dixon and others worked out the physical properties of orbifolds, distinctive geometrical singularities allowed in string theory. Andrew Strominger (born 1955 is an American theoretical physicist who works on String theory and son of Jack L Cumrun Vafa generalized T-duality from circles to arbitrary manifolds, creating the mathematical field of mirror symmetry. Cumrun Vafa کامران وفا væˈfɔː}} (born 1960 in Tehran) is an Iranian-American leading string theorist from Harvard Mirror symmetry may refer to Mirror symmetry (string theory, a relation between two Calabi-Yau manifolds in string theory Homological mirror David Gross and Vipul Periwal discovered that string perturbation theory was divergent in a way that suggested that new non-perturbative objects were missing. David Jonathan Gross (born February 19, 1941 in Washington DC
In the 1990s, Joseph Polchinski discovered that the theory requires higher-dimensional objects, called D-branes and identified these with the black-hole solutions of supergravity. Joseph Polchinski (born on May 16, 1954 in White Plains, New York) is a Physicist working on String theory. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named These were understood to be the new objects suggested by the perturbative divergences, and they opened up a new field with rich mathematical structure. It quickly became clear that D-branes and other p-branes, not just strings, formed the matter content of the string theories, and the physical interpretation of the strings and branes was revealed--- they are a type of black hole. Leonard Susskind had incorporated the holographic principle of Gerardus 't Hooft into string theory, identifying the long highly-excited string states with ordinary thermal black hole states. Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and The holographic principle is a physical property of Quantum gravity theories proposed by Gerard 't Hooft and Leonard Susskind, which resolves the Gerardus 't Hooft (xeːrɑrt ət hoːft (born July 5, 1946, Den Helder) is a professor in Theoretical physics at Utrecht University As suggested by 't Hooft, the flucutations of the black hole horizon, the world-sheet or world-volume theory, describes not only the degrees of freedom of the black hole, but all nearby objects too.
In 1995, at the annual conference of string theorists at the University of Southern California (USC), Edward Witten gave a speech on string theory that essentially united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called M-theory. Edward Witten (born August 26, 1951) is an American Theoretical physicist and Professor at the Institute for Advanced Study In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified M-theory was also foreshadowed in the work of Paul Townsend at approximately the same time. The flurry of activity which began at this time is sometimes called the second superstring revolution. The second superstring revolution was the intense wave of breakthroughs in String theory that took place approximately between 1994 and 1997.
During this period, Tom Banks, Willy Fischler Stephen Shenker and Leonard Susskind formulated a full holographic description of M-theory on IIA D0 branes, the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. Thomas Banks, Tom Banks, or Tommy Banks may refer to Thomas Banks (1735-1805 English sculptor Tom Banks (Physicist Willy Fischler born in 1949 in Antwerpen, Belgium is a theoretical physicist and string theorist. Stephen Shenker is an American theoretical physicist who works on String theory. Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and The holographic principle is a physical property of Quantum gravity theories proposed by Gerard 't Hooft and Leonard Susskind, which resolves the Andrew Strominger and Cumrun Vafa calculated the entropy of certain configurations of D-branes and found agreement with the semi-classical answer for extreme charged black holes. Andrew Strominger (born 1955 is an American theoretical physicist who works on String theory and son of Jack L Cumrun Vafa کامران وفا væˈfɔː}} (born 1960 in Tehran) is an Iranian-American leading string theorist from Harvard Petr Horava and Edward Witten found the eleven dimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Petr Hořava is a Czech string theorist. He is well-known for his articles written with Edward Witten about the Horava-Witten domain walls in Witten noted that the effective description of the physics of D-branes at low energies is by a supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and Nathan Seiberg had earlier discovered in terms of the location of the branes. Nathan "Nati" Seiberg, born in 1956 is an Israel-born American Theoretical physicist who works on String theory.
In 1997 Juan Maldacena noted that the low energy excitations of a theory near a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an anti de Sitter space. Juan Martín Maldacena (born September 10, 1968) is a theoretical Physicist born in Buenos Aires, Argentina. In Mathematics and Physics, n -dimensional anti de Sitter space, sometimes written AdS_n is a maximally symmetric Lorentzian manifold He noted that in this limit the gauge theory describes the string excitations near the branes. So he hypothesized that string theory on a near-horizon extreme-charged black-hole geometry, an anti-deSitter space times a sphere with flux, is equally well described by the low-energy limiting gauge theory, the N=4 supersymmetric Yang-Mills theory. Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations This hypothesis, complemented by converging work due to Steven Gubser, Igor Klebanov and Alexander Polyakov, is called the AdS/CFT correspondence and it is now well-accepted. Igor R Klebanov is a Theoretical physicist whose research is centered on relations between String theory and quantum gauge field theory. Alexander M Polyakov (born 27 September 1945) is a theoretical Physicist, formerly at the Landau Institute in Moscow, currently For the relation of the AdS/CFT correspondence to the general context of string theory see String theory. 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. The holographic principle is a physical property of Quantum gravity theories proposed by Gerard 't Hooft and Leonard Susskind, which resolves the A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e In Physics, the principle of locality is that distant objects cannot have direct influence on one another an object is influenced directly only by its immediate surroundings Information as a concept has a diversity of meanings from everyday usage to technical settings Through this relationship, string theory has been shown to be related to gauge theories like quantum chromodynamics and this has led to more quantitative understanding of the behavior of hadrons, bringing string theory back to its roots. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the In Particle physics, a hadron ( from the ἁδρός hadrós, " stout, thick " (
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. The Elegant Universe Superstrings Hidden Dimensions and the Quest for the Ultimate Theory (ISBN 0-375-70811-1 is a Book by Brian Greene published in Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. Columbia University is a private University in the United States and a member of the Ivy League. Nova is a Popular science Television series from the US produced by WGBH Boston It was also shown by Discovery Channel on Indian television, as well as in Australia on SBS. Discovery Channel is an American Satellite and Cable TV channel (also delivered via IPTV, Terrestrial television and India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country
- String Theory is also a trilogy of novels based on the Star Trek: Voyager television series. String Theory is a trilogy of novels set in the Star Trek universe
- 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. Quantum teleportation, or entanglement-assisted teleportation, is a technique used to transfer information on a Quantum level usually from one Particle Olympos sequel on for example the true nature of Setebos the voynix or Odysseus' changing Olympos, Dan Simmons ' novel published in 2005 is the sequel to Ilium and final part of Ilium/Olympus duology Dan Simmons (born April 4, 1948 in Peoria, Illinois) is an American Author most widely known for his Hugo Award 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. The multiverse (or meta-universe) is the hypothetical set of multiple possible Universes (including our universe that together comprise all of Reality. A gravitational singularity (sometimes spacetime singularity) is approximately a place where quantities which are used to measure the Gravitational field become A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e In Physics, a wormhole is a hypothetical topological feature of Spacetime that is fundamentally a 'shortcut' through Space and Time
- In "H. P. Lovecraft's Dreams in the Witch-House", an episode of the Showtime series Masters of Horror (based on a story by H. P. Lovecraft and directed by Stuart Gordon), a young grad student from Miskatonic University studies interdimensional string theory in his run-down apartment and discovers the intersection of two separate realities. H P Lovecraft's Dreams in the Witch House is the second episode of the first season of Masters of Horror, directed by Stuart Gordon Showtime is a subscription television Brand used by a number of channels and platforms around the world but primarily refers to a group of channels in the United Masters of Horror is an American Television series created by director Mick Garris for the Showtime cable network "The Dreams in the Witch House" is a short story by H Stuart Gordon (born August 11, 1947) in Chicago Illinois) is a director, writer and producer of Films and Miskatonic University is a fictional university located in the equally fictitious Arkham, set in the real-world Essex County Massachusetts.
- String theory and its related philosophy features prominently in River of Gods, a science-fiction novel by Ian McDonald set in futuristic India. River of Gods is a Science fiction Novel by Ian McDonald. It is one of the first works in popular fiction to imagine a futuristic India Ian McDonald may refer to Ian McDonald (cricketer (born 1923 Australian first-class cricketer Ian McDonald (musician (born 1946 member
- On "The Big Bang Theory" in the episode "The Jerusalem Duality", Sheldon indicates that his research is in string theory. The Big Bang Theory is an American Situation comedy created and executive produced by Chuck Lorre and Bill Prady, which premiered
- Lupe Fiasco mentions the string theory in his song "Hurt Me Soul". Wasalu Muhammad Jaco (born February 16 1982 better known by his Stage name Lupe Fiasco, is a Grammy -winning American rapper. " Hurt Me Soul " is a satirical song written by rapper Lupe Fiasco.
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
- Zeta function regularization
References
- ^ Peter Woit (2006). For the relation of the AdS/CFT correspondence to the general context of string theory see String theory. A conformal field theory (CFT is a Quantum field theory (or Statistical mechanics model at the Critical point) that is Invariant under F-theory is a branch of String theory developed by Cumrun Vafa. In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework In Physics, Kaluza–Klein theory (or KK theory, for short is a model that seeks to unify the two fundamental forces of Gravitation and This is a list of String theory topics. See also List of mathematical topics in quantum theory. Loop quantum gravity (LQG, also known as loop gravity and Quantum geometry, is a proposed quantum theory of Spacetime which attempts to reconcile the theories In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature Many first principles in Quantum field theory are explained or get further insight in String theory: Emission and absorption one of the most basic building blocks String duality is a class of symmetries in Physics that link different string theories, theories which assume that the fundamental building blocks of the The string theory landscape or anthropic landscape refers to the large number of possible false vacua in String theory. In Theoretical physics, supergravity ( supergravity theory) is a field theory that combines the principles of Supersymmetry and General relativity See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that A theory of everything ( TOE) is a putative Theory of Theoretical physics that fully explains and links together all known physical phenomena In Mathematics and Theoretical physics, zeta-function regularization is a type of regularization or Summability method that assigns finite values Not even wrong: the failure of string theory and the search for unity in physical law. New York: Basic Books. ISBN 0465092756.
- ^ 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
- ^ Polchinski, Joseph (1998). String Theory, Cambridge University Press.
- ^ H. Nastase The RHIC fireball as a dual black hole BROWN-HET-1439, ArXiv: hep-th/0501068, January 2005,
- ^ H. Nastase More on the RHIC fireball and dual black holes BROWN-HET-1466, ArXiv: hep-th/0603176, March 2006,
- ^ H. Liu, K. Rajagopal, U. A. Wiedemann An AdS/CFT Calculation of Screening in a Hot Wind, MIT-CTP-3757, July 2006,
- ^ H. Liu, K. Rajagopal, U. A. Wiedemann Calculating the Jet Quenching Parameter from AdS/CFT, Phys. Rev. Lett. 97:182301,2006
- ^ 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 Planck length, denoted by \scriptstyle\ell_P \, is the unit of Length approximately 1 Geometry, a diameter of a Circle is any straight Line segment that passes through the center of the circle and whose Endpoints are on the History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny Proxima Centauri ( Latin la ''proximus proxima proximum'' meaning 'next to' or 'nearest to' is a Red dwarf Star approximately 4 A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 The Sun (Sol is the Star at the center of the Solar System. The tension of a string (8. In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object 9×1042 newtons) is about 1041 times the tension of an average piano string (735 newtons). The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The piano is a Musical instrument played by means of a keyboard that produces sound by striking steel strings with Felt covered hammers
- ^ Simeon Hellerman, Ian Swanson: "Dimension-changing exact solutions of string theory". e-Print: hep-th/0612051; Ofer Aharony, Eva Silverstein: "Supercritical stability, transitions and (pseudo)tachyons". Physical Review D 75:046003, 2007. e-Print: hep-th/0612031
- ^ 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. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally This is known as the linear dilaton or non-critical string. The non-critical string theory describes the relativistic string without enforcing the critical dimension The non-critical string theory describes the relativistic string without enforcing the critical dimension
- ^ "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" (subscription required). Phys. Rept. 323: 183–386. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. . For other examples see: [1]
- ^ For example: T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113:843-882,2005, ArXiv: hep-th/0412141, December 2004
- ^ H. Nastase The RHIC fireball as a dual black hole BROWN-HET-1439, ArXiv: hep-th/0501068, January 2005,
- ^ H. Nastase More on the RHIC fireball and dual black holes BROWN-HET-1466, ArXiv: hep-th/0603176, March 2006,
- ^ H. Liu, K. Rajagopal, U. A. Wiedemann An AdS/CFT Calculation of Screening in a Hot Wind, MIT-CTP-3757, July 2006,
- ^ H. Liu, K. Rajagopal, U. A. Wiedemann Calculating the Jet Quenching Parameter from AdS/CFT, Phys. Rev. Lett. 97:182301,2006
- ^ See for example Recent Results of the MILC research program, taken from the MILC Collaboration homepage
- ^ M. R. Douglas,Are There Testable Predictions of String Theory? February 2007 Texas A&M
- ^ a b S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, de Sitter Vacua in String Theory, Phys. Rev. D68:046005,2003
- ^ a b Peter Woit's Not Even Wrong weblog
- ^ P. Woit (Columbia University) String theory: An Evaluation,February 2001, e-Print: physics/0102051
- ^ P. Woit, Is String Theory Testable? INFN Rome March 2007
- ^ a b Lee Smolin's The Trouble With Physics webpage
- ^ 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. Philip Warren Anderson (born December 13, 1923) is an American Physicist. Sheldon Lee Glashow (born December 5, 1932) is an American physicist. ' 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)
- ^ David Gross, Perspectives, String Theory: Achievements and Perspectives - A conference
- ^ N. Lawrence M Krauss (born May 27, 1954) is Foundation Professor in the School of Earth and Space Exploration and the Physics Department and Director Peter Woit is a mathematical physicist at Columbia University. Carlo Rovelli is an Italian physicist and cosmologist who has worked in Italy the USA and France Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive Landscapes and New Physics at a TeV, SLAC-PUB-10928, HUTP-05-A0001, SU-ITP-04-44, January 2005
- ^ L. Susskind The Anthropic Landscape of String Theory, February 2003
- ^ John Baez and responses on the group weblog The n-Category Cafe
- ^ John Baez weblog
- ^ [2]
Further reading
Popular books and articles
- Davies, Paul; Julian R. Paul Charles William Davies (born April 22, 1946) is a British-born Physicist, Writer and broadcaster, presently a professor 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. New Scientist is a weekly International science magazine and website covering recent developments in science and technology for a general English -speaking 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. Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and The multiverse (or meta-universe) is the hypothetical set of multiple possible Universes (including our universe that together comprise all of Reality.
- Green, Michael (September 1986). For other people with this name see Michael Green. Michael Boris Green (born 22 May 1946 Superstrings. Scientific American. Scientific American is a Popular science magazine, published (first weekly and later monthly since August 28, 1845, making it Retrieved on December 19, 2005.
- Greene, Brian (October 20 2003). Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Reissue edition, New York: W. The Elegant Universe Superstrings Hidden Dimensions and the Quest for the Ultimate Theory (ISBN 0-375-70811-1 is a Book by Brian Greene published in W. Norton & Company, 464. ISBN 0-393-05858-1.
- Greene, Brian (2004). Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. The Fabric of the Cosmos: Space, Time, and the Texture of Reality. The Fabric of the Cosmos: Space Time and the Texture of Reality ( 2004) is the second book on Theoretical physics, New York: Alfred A. Knopf, 569. ISBN 0-375-41288-3.
- Gribbin, John (1998). John R Gribbin (born 1946 is a British science writer and a visiting Fellow in astronomy at the University of Sussex. The Search for Superstrings, Symmetry, and the Theory of Everything. London: Little Brown and Company, 224. ISBN 0-316-32975-4.
- Halpern, Paul (2004). Paul Halpern is Professor of Mathematics and Physics, and Fellow in the Humanities at the University of the Sciences in Philadelphia The Great Beyond: Higher Dimensions, Parallel Universes, and the Extraordinary Search for a Theory of Everything. Hoboken, New Jersey: John Wiley & Sons, Inc. , 326. ISBN 0-471-46595-X.
- Hooper, Dan (2006). Dark Cosmos: In Search of Our Universe's Missing Mass and Energy. New York: HarperCollins, 240. ISBN 978-0-06-113032-8.
- Kaku, Michio (April 1994). Dr Michio Kaku (b January 24, 1947) is an American theoretical physicist specializing in String field theory, and a Futurist 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). Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus 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). Lisa Randall (born June 18 1962 is an American Theoretical physicist and a leading expert on Particle physics and Cosmology. Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. New York: Ecco Press, 512. ISBN 0-06-053108-8.
- Smolin, Lee (2006). Lee Smolin (born 1955 in New York City) is an American Theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. New York: Houghton Mifflin Co. , 392. ISBN 0-618-55105-0.
- Susskind, Leonard (December 2006). Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. New York: Hachette Book Group/Back Bay Books, 403. ISBN 0-316-01333-1.
- Taubes, Gary (November 1986). Gary Taubes (born April 30, 1956) is an American science writer "Everything's Now Tied to Strings. " Discover Magazine vol 7, #11. (Popular article, probably the first ever written, on the first superstring revolution. In Physics, the first superstring revolution is a period of important discoveries in String theory roughly between 1984 and 1986. )
- Vilenkin, Alex (2006). Alexander Vilenkin is Professor of Physics and Director of the Institute of Cosmology at Tufts University. Many Worlds in One: The Search for Other Universes. New York: Hill and Wang, 235. ISBN 0-8090-9523-8.
- Witten, Edward (June 2002). Edward Witten (born August 26, 1951) is an American Theoretical physicist and Professor at the Institute for Advanced Study The Universe on a String. Astronomy Magazine. Astronomy ( ISSN 0091-6358 is a monthly American magazine about Astronomy. Retrieved on December 19, 2005. – An easy article for everybody outside physics wanting to understand the very basics of the theory.
- Woit, Peter (2006). Peter Woit is a mathematical physicist at Columbia University. Not Even Wrong - The Failure of String Theory And the Search for Unity in Physical Law. London: Jonathan Cape &: New York: Basic Books, 290. ISBN 0-224-07605-1 & ISBN 978-0-465-09275-8.
Textbooks
- Binétruy, Pierre (2007). Supersymmetry: Theory, Experiment, and Cosmology, Oxford University Press. ISBN 978-0-19-850954-7.
- Dine, Michael (2007). Supersymmetry and String Theory: Beyond the Standard Model, Cambridge University Press. ISBN 0-521-85841-0.
- Paul H. Frampton (1974). Paul Howard Frampton (born October 31, 1943, in England) is a Theoretical physicist and notable model builderin particle phenomenology Dual Resonance Models. Frontiers in Physics. ISBN 0-805-32581-6.
- Gasperini, Maurizio (2007). Elements of String Cosmology, Cambridge University Press. ISBN 978-0-521-86875-4.
- Michael Green, John H. Schwarz and Edward Witten (1987). For other people with this name see Michael Green. Michael Boris Green (born 22 May 1946 John Henry Schwarz (born 1941) is an American theoretical physicist. Edward Witten (born August 26, 1951) is an American Theoretical physicist and Professor at the Institute for Advanced Study 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.
- Kiritsis, Elias (2007). String Theory in a Nutshell, Princeton University Press. ISBN 978-0-691-12230-4.
- Polchinski, Joseph (1998). Joseph Polchinski (born on May 16, 1954 in White Plains, New York) is a Physicist working on String theory. 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). Barton Zwiebach (born Oct 4 1954) is a string theorist and professor at the Massachusetts Institute of Technology, born in Lima, 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). John Henry Schwarz (born 1941) is an American theoretical physicist. String Theory and M-Theory: A Modern Introduction , Cambridge University Press. ISBN 0-521-86069-5
- Leonard Susskind, (2006). Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and The Cosmic Landscape: String Theory And The Illusion Of Intelligent Design, Little, Brown & Company ISBN 0-316-15579-9
- Szabo, Richard J. (Reprinted 2007). An Introduction to String Theory and D-brane Dynamics, Imperial College Press. ISBN 978-1-86094-427-7.
External links
- Superstring Theory Perimeter Institute for Theoretical Physics
- 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. Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. Events 306 - Maxentius is proclaimed Roman Emperor. 312 - Battle of Milvian Bridge: Constantine m. and November 4, 8-9 p. Events 1333 - Flood of the Arno River, causing massive damage in Florence as recorded by the Florentine chronicler Giovanni Villani 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, Luboš; Screiber, Urs. Luboš Motl (born 5 December 1973) is a Czech theoretical physicist who worked on String theory and conceptual problems of Quantum 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). John Henry Schwarz (born 1941) is an American theoretical physicist. 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. The North Atlantic Treaty See also Culture of the Virgin Islands Music of the Virgin Islands Virgin Islands Creole Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them
- Witten, Edward (1998). Edward Witten (born August 26, 1951) is an American Theoretical physicist and Professor at the Institute for Advanced Study 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). Thomas Walter Bannerman Kibble is a senior research investigator at The Blackett Laboratory at Imperial College London, UK 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. Events 1176 - The Battle of Myriokephalon is fought 1462 - The Battle of Świecino (or Battle of Żarnowiec "MMIV" redirects here For the Modest Mouse album see " Baron von Bullshit Rides Again "
- 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). Peter Woit is a mathematical physicist at Columbia University. Is string theory even wrong?. American Scientist. American Scientist (ISSN 0003-0996 (not to be confused with Scientific American) is an illustrated bimonthly Magazine about Science and Retrieved on December 16, 2005. – A criticism of string theory.
- Woit, Peter (2004). Peter Woit is a mathematical physicist at Columbia University. 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, <http://www.sciam.com/article.cfm?chanID=sa006&articleID=00042F0D-1A0E-1085-94F483414B7F0000>
- McKie, Robin (2006-10-09), “Setback as string theory of the universe is de-bunked”, The Hindu, <http://www.hindu.com/thehindu/holnus/008200610091240.htm>
- Harris, Richard (2006-11-07). Gabriele Veneziano (born 1942, Florence, Italy) is an Italian theoretical physicist and a founder of String theory. Scientific American is a Popular science magazine, published (first weekly and later monthly since August 28, 1845, making it The Hindu is a single-edition English-language Indian newspaper Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 1492 - The Ensisheim Meteorite the oldest Meteorite with a known date of impact strikes the Earth around noon in a Wheat Short of 'All,' String Theorists Accused of Nothing. National Public Radio. Retrieved on 2007-03-05. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 363 - Roman Emperor Julian moves from Antioch with an army of 90000 to attack the Sassanid Empire, in a
- A website dedicated to creative writing inspired by string theory.
- George Gardner (2007-01-24). "Theory of everything put to the test". tech.blorge.com. (Web link). Retrieved on 2007-03-03. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1284 - Statute of Rhuddlan incorporated the Principality of Wales into England 1575 - Indian
- Minkel, J. R. (2006-03-02), “A Prediction from String Theory, with Strings Attached”, Scientific American, <http://www.sciam.com/article.cfm?chanId=sa003&articleId=1475A684-E7F2-99DF-355B95296BE6031C>
- Chalmers, Matthew (2007-09-03). Scientific American is a Popular science magazine, published (first weekly and later monthly since August 28, 1845, making it Stringscape. Physics World. Retrieved on September 6, 2007. — An up-to-date and thorough review of string theory in a popular way.
Dictionary
string theory
-noun
- (physics) A candidate unified theory of all physical forces and particles; a theory which suggests that subatomic particles are one-dimensional strings rather than zero-dimensional points. It also suggests that space-time can have up to nine dimensions, plus the dimension of time.
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