In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments.[21]. Their calculation reproduced the Bekenstein–Hawking formula exactly, including the factor of 1/4. [53], In the branch of physics called statistical mechanics, entropy is a measure of the randomness or disorder of a physical system. In this way, all of the different elementary particles may be viewed as vibrating strings. [45], Initially, some physicists suggested that the new theory was a fundamental theory of membranes, but Witten was skeptical of the role of membranes in the theory. 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. 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. The theory of cosmic inflation preserves the successes of the Big Bang while providing a natural explanation for some of the mysterious features of the universe. (2020, August 26). The structure of the graph is the data model defined by a vertex/edge/property topology. [138], Smolin goes on to offer a number of prescriptions for how scientists might encourage a greater diversity of approaches to quantum gravity research. Speculative scientific ideas fail not just when they make incorrect predictions, but also when they turn out to be vacuous and incapable of predicting anything. [34][35], Initially, many physicists hoped that by compactifying eleven-dimensional supergravity, it might be possible to construct realistic models of our four-dimensional world. One of the relationships that can exist between different string theories is called S-duality. [92], Generalizing this problem, one can ask how many lines can be drawn on a quintic Calabi–Yau manifold, such as the one illustrated above, which is defined by a polynomial of degree five. Other similar methods can be used to construct realistic or semi-realistic models of our four-dimensional world based on M-theory. [27], Branes are frequently studied from a purely mathematical point of view, and they are described as objects of certain categories, such as the derived category of coherent sheaves on a complex algebraic variety, or the Fukaya category of a symplectic manifold. [44] Today this flurry of work is known as the second superstring revolution. One can define the distance between points of this disk in such a way that all the triangles and squares are the same size and the circular outer boundary is infinitely far from any point in the interior. ", ThoughtCo uses cookies to provide you with a great user experience and for our. The largest sporadic group, the so-called monster group, has over 1053 elements, more than a thousand times the number of atoms in the Earth. "The Basics of String Theory." [75], The AdS/CFT correspondence resolves the black hole information paradox, at least to some extent, because it shows how a black hole can evolve in a manner consistent with quantum mechanics in some contexts. [128], One of the main criticisms of string theory from early on is that it is not manifestly background independent. According to Smolin, String theory is a powerful, well-motivated idea and deserves much of the work that has been devoted to it. At present, string theory has not successfully made any prediction which is not also explained through an alternative theory. This problem was solved by the nineteenth-century German mathematician Hermann Schubert, who found that there are exactly 2,875 such lines. [citation needed]. [55] When combined with ideas of the physicist Stephen Hawking,[56] Bekenstein's work yielded a precise formula for the entropy of a black hole. [13] Finally, there exist scenarios in which there could actually be more than 4D of spacetime which have nonetheless managed to escape detection. 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. [13], In quantum field theory, one typically computes the probabilities of various physical events using the techniques of perturbation theory. [22] In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions. It is closely related to hyperbolic space, which can be viewed as a disk as illustrated on the left. [e] Today mirror symmetry is an active area of research in mathematics, and mathematicians are working to develop a more complete mathematical understanding of mirror symmetry based on physicists' intuition. 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. [15] Unlike in quantum field theory, string theory does not have a full non-perturbative definition, so many of the theoretical questions that physicists would like to answer remain out of reach. It later developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. One of the problems was that the laws of physics appear to distinguish between clockwise and counterclockwise, a phenomenon known as chirality. [11] These problems have led some in the community to criticize these approaches to the unification of physics and question the value of continued research on these problems. Another reason is that it provides a general framework in which physicists can study and attempt to resolve the paradoxes of black holes. [137] Lee Smolin expresses a slightly different position in his critique, claiming that string theory grew out of a tradition of particle physics which discourages speculation about the foundations of physics, while his preferred approach, loop quantum gravity, encourages more radical thinking. Compactification is one way of modifying the number of dimensions in a physical theory. The study of D-branes in string theory has led to important results such as the AdS/CFT correspondence, which has shed light on many problems in quantum field theory. In the t-channel, the particles exchange intermediate states by emission and absorption. Jones, Andrew Zimmerman. M-theory was also foreshadowed in the work of Paul Townsend at approximately the same time. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle that appears in the theory, an obvious self-consistency condition, the lightest particle must be a tachyon. By the late 1970s, these two frameworks had proven to be sufficient to explain most of the observed features of the universe, from elementary particles to atoms to the evolution of stars and the universe as a whole. This is a theoretical result which implies that string theory is in some cases equivalent to a quantum field theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern. [31], In the 1970s, many physicists became interested in supergravity theories, which combine general relativity with supersymmetry. It is generally believed that finite groups are too diverse to admit a useful classification. [65] In collaboration with several other authors in 2010, he showed that some results on black hole entropy could be extended to non-extremal astrophysical black holes. As a result, physicists who study string theory are often guided by physical intuition to conjecture relationships between the seemingly different mathematical structures that are used to formalize different parts of the theory. ThoughtCo. [127], One of the fundamental properties of Einstein's general theory of relativity is that it is background independent, meaning that the formulation of the theory does not in any way privilege a particular spacetime geometry. String Theory, which is described as follows: 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. [135] In his book The Road to Reality, mathematical physicist Roger Penrose expresses similar views, stating "The often frantic competitiveness that this ease of communication engenders leads to bandwagon effects, where researchers fear to be left behind if they do not join in. [120] Weinberg suggested that there might be a huge number of possible consistent universes, each with a different value of the cosmological constant, and observations indicate a small value of the cosmological constant only because humans happen to live in a universe that has allowed intelligent life, and hence observers, to exist. Bosonic string theory was eventually superseded by theories called superstring theories. This is contrary to some popular models of dark energy such as Λ-CDM, which requires a positive vacuum energy. The AdS/CFT correspondence is example of a duality which relates string theory to a quantum field theory. This hypothesis, which is called the AdS/CFT correspondence, was further developed by Steven Gubser, Igor Klebanov and Alexander Polyakov,[69] and by Edward Witten,[70] and it is now well-accepted. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as M-theory. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. [30], Prior to 1995, theorists believed that there were five consistent versions of superstring theory (type I, type IIA, type IIB, and two versions of heterotic string theory). Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. A grammar G can be formally written as a 4-tuple (N, T, S, P) where − N or V N is a set of variables or non-terminal symbols. One of the goals of current research in string theory is to find a solution of the theory that reproduces the observed spectrum of elementary particles, with a small cosmological constant, containing dark matter and a plausible mechanism for cosmic inflation. While these approaches might eventually find support in observational data such as measurements of the cosmic microwave background, the application of string theory to cosmology is still in its early stages. [123] Many prominent theorists and critics have disagreed with Susskind's conclusions. For example, the type I theory includes both open strings (which are segments with endpoints) and closed strings (which form closed loops), while types IIA, IIB and heterotic include only closed strings. David Gross and Vipul Periwal discovered that string perturbation theory was divergent. The formulas that result from string theory predict more than four dimensions (10 or 11 in the most common variants, though one version requires 26 dimensions), but the extra dimensions are "curled up" within the Planck length. In addition to providing insights into the mathematical structure of string theory, the AdS/CFT correspondence has shed light on many aspects of quantum field theory in regimes where traditional calculational techniques are ineffective. [48], One important example of a matrix model is the BFSS matrix model proposed by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind in 1997. Typically, such models are based on the idea of compactification. The result was widely advertised by Murray Gell-Mann, leading Gabriele Veneziano to construct a scattering amplitude that had the property of Dolen–Horn–Schmid duality, later renamed world-sheet duality. So I think the real reason why people have got attracted by it is because there is no other game in town. [39], At around the same time, as many physicists were studying the properties of strings, a small group of physicists were examining the possible applications of higher dimensional objects. This observation is the starting point for AdS/CFT correspondence, which states that the boundary of anti-de Sitter space can be regarded as the "spacetime" for a quantum field theory. Daniel Friedan, Emil Martinec and Stephen Shenker further developed the covariant quantization of the superstring using conformal field theory techniques. For example, Montonen–Olive duality is example of an S-duality relationship between quantum field theories. The gauge group of these closed strings was two copies of E8, and either copy could easily and naturally include the standard model. Each of these operations is called a symmetry, and the collection of these symmetries satisfies certain technical properties making it into what mathematicians call a group. These calculations led them to propose that the BFSS matrix model is exactly equivalent to M-theory. In this particular example, the group is known as the dihedral group of order 6 because it has six elements. The other is quantum mechanics, a completely different formulation, which uses known probability principles to describe physical phenomena at the micro-level. [5] This is a theoretical result which relates string theory to other physical theories which are better understood theoretically. [23], Another approach to reducing the number of dimensions is the so-called brane-world scenario. [82] One popular way of deriving realistic physics from string theory is to start with the heterotic theory in ten dimensions and assume that the six extra dimensions of spacetime are shaped like a six-dimensional Calabi–Yau manifold. [124] According to Woit, "in this case [anthropic reasoning] is nothing more than an excuse for failure. In some "braneworld scenarios," our universe is actually "stuck" inside of a 3-dimensional brane (called a 3-brane). The different theories allow different types of strings, and the particles that arise at low energies exhibit different symmetries. This property is usually referred to as unitarity of time evolution. Veneziano and Sergio Fubini introduced an operator formalism for computing the scattering amplitudes that 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. [88], In addition to influencing research in theoretical physics, string theory has stimulated a number of major developments in pure mathematics. A theoretical physics model is a mathematical framework that, in order to make predictions, requires that certain parameters are set. John Schwarz and Joël 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. This phenomenon is known as S-duality. 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 in essence united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called M-theory. String theory is a candidate for a unified theory of the four fundamental forces of nature: electromagnetism, the weak force, the strong force, and gravity.Particles in string theory are identified with particular patterns of vibration of a one-dimensional elementary object called a string.String theory is a quantum theory in that the mass spectrum of strings is discrete, so string theory … If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. [133], Several other high-profile theorists and commentators have expressed similar views, suggesting that there are no viable alternatives to string theory.[134]. [7], So far some success has been achieved in using string theory methods to describe the transition of a superfluid to an insulator. In his book criticizing string theory, Peter Woit views the status of string theory research as unhealthy and detrimental to the future of fundamental physics. [112] In 1998, Borcherds was awarded the Fields medal for his work. [26], In string theory and other related theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices. Whereas general relativity makes sense in any number of dimensions, supergravity places an upper limit on the number of dimensions. [1] The general theory of relativity is formulated within the framework of classical physics, whereas the other fundamental forces are described within the framework of quantum mechanics. Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory. The hope was that such models would provide a unified description of the four fundamental forces of nature: electromagnetism, the strong and weak nuclear forces, and gravity. In particle physics, quantum field theories form the basis for our understanding of elementary particles, which are modeled as excitations in the fundamental fields. The number of times the string winds around a circle is called the winding number. In addition to being an idea of considerable theoretical interest, string theory provides a framework for constructing models of real world physics that combine general relativity and particle physics. One of the deepest problems in modern physics is the problem of quantum gravity. Some recent versions of string theory have predicted that the strings could have a longer length, up to nearly a millimeter in size, which would mean they're in the realm that experiments could detect them. Such collisions cause the quarks that make up atomic nuclei to deconfine at temperatures of approximately two trillion kelvin, conditions similar to those present at around 10−11 seconds after the Big Bang. [35], In the first superstring revolution in 1984, many physicists turned to string theory as a unified theory of particle physics and quantum gravity. String theory describes how these strings propagate through space and interact with each other. If it has so far failed, the principal reason is that its intrinsic flaws are closely tied to its strengths—and, of course, the story is unfinished, since string theory may well turn out to be part of the truth. 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. [33] In the same year, Eugene Cremmer, Bernard Julia, and Joël Scherk of the École Normale Supérieure showed that supergravity not only permits up to eleven dimensions but is in fact most elegant in this maximal number of dimensions. [90] Instead, two different versions of string theory, type IIA and type IIB, can be compactified on completely different Calabi–Yau manifolds giving rise to the same physics. "The Basics of String Theory." String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. Thereafter, German mathematician Theodor Kaluza combined the fifth dimension with general relativity, and only Kaluza is usually credited with the idea. 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. A general group may describe finitely many or infinitely many symmetries; if there are only finitely many symmetries, it is called a finite group. The calculation showed that the ratio of two quantities associated with the quark–gluon plasma, the shear viscosity and volume density of entropy, should be approximately equal to a certain universal constant. [12], The application of quantum mechanics to physical objects such as the electromagnetic field, which are extended in space and time, is known as quantum field theory. Black holes are also important for theoretical reasons, as they present profound challenges for theorists attempting to understand the quantum aspects of gravity. In compactification, some of the extra dimensions are assumed to "close up" on themselves to form circles. String theory is a mathematical theory that tries to explain certain phenomena which is not currently explainable under the standard model of quantum physics. [68] Important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov,[69] and by Edward Witten. [2] In addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of atomic nuclei, black holes, and the early universe. to be asymptotically anti-de Sitter. One physical system that has been studied using the AdS/CFT correspondence is the quark–gluon plasma, an exotic state of matter produced in particle accelerators. As with the hyperbolic plane, anti-de Sitter space is curved in such a way that any point in the interior is actually infinitely far from this boundary surface. M theory is now known to have countless solutions, often predicting things strange and unknown to exist. 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. The resulting theory did not have a tachyon, and was proven to have space-time supersymmetry by John Schwarz and Michael Green in 1984. [122] According to Susskind, the different vacuum states of string theory might be realized as different universes within a larger multiverse. [47], In mathematics, a matrix is a rectangular array of numbers or other data. Nordström attempted to unify electromagnetism with his theory of gravitation, which was however superseded by Einstein's general relativity in 1919. [19], In spite of the fact that the Universe is well described by 4D spacetime, there are several reasons why physicists consider theories in other dimensions. [130] Smolin has responded by saying that the AdS/CFT correspondence, as it is currently understood, may not be strong enough to resolve all concerns about background independence.[131]. A standard analogy for this is to consider a multidimensional object such as a garden hose. The resulting geometric object is three-dimensional anti-de Sitter space. [54], In the twentieth century, physicists began to apply the same concepts to black holes. Many critics of string theory have commented on this state of affairs. [71] It looks like a solid cylinder in which any cross section is a copy of the hyperbolic disk. The letter "D" in D-brane refers to a certain mathematical condition on the system known as the Dirichlet boundary condition. String theory describes how strings propagate through space and interact with each other. In his book Not Even Wrong, Peter Woit, a lecturer in the mathematics department at Columbia University, has argued that the large number of different physical scenarios renders string theory vacuous as a framework for constructing models of particle physics. Instead, many researchers have adopted a view that they are describing a vast string theory landscape of possible theoretical structures, many of which do not actually describe our universe. Two independent mathematical proofs of mirror symmetry were given by Givental, More precisely, a nontrivial group is called, anti-de Sitter/conformal field theory correspondence, Perimeter Institute for Theoretical Physics, "Top Cited Articles during 2010 in hep-th", "Solving Quantum Field Theories via Curved Spacetimes", "Collaborative physics: string theory finds a bench mate", "Supersymmetries and their representations", "Supermembranes and eleven-dimensional supergravity", "Forty Years of String Theory Reflecting on the Foundations", "Mathematicians chase moonshine's shadow", "Monstrous moonshine and Lie superalgebras", "Dark Energy May Be Incompatible With String Theory", "Response to review of The Trouble with Physics by Joe Polchinski", Numerical methods for ordinary differential equations, Numerical methods for partial differential equations, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Society for Industrial and Applied Mathematics, Japan Society for Industrial and Applied Mathematics, Société de Mathématiques Appliquées et Industrielles, International Council for Industrial and Applied Mathematics, https://en.wikipedia.org/w/index.php?title=String_theory&oldid=1003636473, All articles with specifically marked weasel-worded phrases, Articles with specifically marked weasel-worded phrases from February 2016, Articles with specifically marked weasel-worded phrases from November 2016, Articles with unsourced statements from September 2020, Articles with unsourced statements from June 2018, Creative Commons Attribution-ShareAlike License, This page was last edited on 29 January 2021, at 23:10. [129], Others have disagreed with Smolin's characterization of string theory. They found that a system of strongly interacting strings can, in some cases, be viewed as a system of weakly interacting strings. Such systems are often produced in the laboratory using liquid helium, but recently experimentalists have developed new ways of producing artificial superfluids by pouring trillions of cold atoms into a lattice of criss-crossing lasers. Boltzmann argued that by averaging the behaviors of all the different molecules in a gas, one can understand macroscopic properties such as volume, temperature, and pressure. These strings, the size of the Planck length (10-35 m), vibrate at specific resonant frequencies. 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. [7][81], The AdS/CFT correspondence has also been used to study aspects of condensed matter physics. [86], In the theory of inflation, the rapid initial expansion of the universe is caused by a hypothetical particle called the inflaton. A p-brane sweeps out a (p+1)-dimensional volume in spacetime called its worldvolume. In the late 1970s, mathematicians John McKay and John Thompson noticed that certain numbers arising in the analysis of the monster group (namely, the dimensions of its irreducible representations) are related to numbers that appear in a formula for the j-function (namely, the coefficients of its Fourier series). The Bekenstein–Hawking entropy formula gives the expected value of the entropy of a black hole, but by the 1990s, physicists still lacked a derivation of this formula by counting microstates in a theory of quantum gravity. [16], In theories of particle physics based on string theory, the characteristic length scale of strings is assumed to be on the order of the Planck length, or 10−35 meters, the scale at which the effects of quantum gravity are believed to become significant. A more modest but still challenging problem is to classify all finite simple groups. "[136] Penrose also claims that the technical difficulty of modern physics forces young scientists to rely on the preferences of established researchers, rather than forging new paths of their own. These are finite groups which may be used as building blocks for constructing arbitrary finite groups in the same way that prime numbers can be used to construct arbitrary whole numbers by taking products. [109], In 1992, Richard Borcherds constructed a bridge between the theory of modular functions and finite groups and, in the process, explained the observations of McKay and Thompson. The earliest version of string theory, bosonic string theory, incorporated only the class of particles known as bosons. "[46] In the absence of an understanding of the true meaning and structure of M-theory, Witten has suggested that the M should stand for "magic", "mystery", or "membrane" according to taste, and the true meaning of the title should be decided when a more fundamental formulation of the theory is known. They have mass and can have other attributes such as charge. The driving hope behind this work is that it will result in a "theory of everything," including a solution to the problem of quantum gravity, and to reconcile quantum physics with general relativity, thus reconciling the fundamental forces of physics. There are many versions of string theory, none quite successfully predicting the observational data explained by the Standard Model. [25], Another relationship between different string theories is T-duality. Ferdinando Gliozzi, Joël Scherk, and David Olive realized in 1977 that the original Ramond and Neveu Schwarz-strings were separately inconsistent and needed to be combined. [107] This relationship was further developed by John Horton Conway and Simon Norton[108] who called it monstrous moonshine because it seemed so far fetched. [7][8], Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it will eventually be developed to the point where it fully describes our universe, making it a theory of everything.

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