Advanced Theory - A State Of Mind (2) - String Theory (Vinyl)
Edward Witten and others observed this chirality property cannot be readily derived by compactifying from eleven dimensions. In the first superstring revolution inmany physicists turned to string theory as a unified theory of particle physics and quantum gravity.
Unlike supergravity theory, string theory was able to accommodate the chirality of the standard model, and it provided a theory of gravity consistent with quantum effects. In ordinary particle theories, one can consider any collection of elementary particles whose classical behavior is described by an arbitrary Lagrangian.
In string theory, the possibilities are much more constrained: by the s, physicists had argued that there were only five consistent supersymmetric versions of the theory. Although there were only a handful of consistent superstring theories, it remained a mystery why there was not just one consistent formulation. They found that a system of strongly interacting strings can, in some cases, be viewed as a system of weakly interacting strings.
This phenomenon is known as S-duality. It was studied by Ashoke Sen in the context of heterotic strings in four dimensions   and by Chris Hull and Paul Townsend in the context of the type IIB theory. This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent. 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.
InEric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes. Shortly after this discovery, Michael DuffPaul Howe, Takeo Inami, and Kellogg Stelle considered a particular compactification of eleven-dimensional supergravity with one of the dimensions curled up into a circle.
If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime. Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory.
Speaking at a string theory conference inEdward Witten made the surprising suggestion that all five superstring theories were in fact just different limiting cases of a single theory in eleven spacetime dimensions.
Witten's announcement drew together all of the previous results on S- and T-duality and the appearance of higher-dimensional branes in string theory. 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.
In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way.
A matrix model describes the behavior of a set of matrices within the framework of quantum mechanics. This theory describes the behavior of a set of nine large matrices.
In their original paper, these authors showed, among other things, that the low energy limit of this matrix model is described by eleven-dimensional supergravity. The BFSS matrix model can therefore be used as a prototype for a correct formulation of M-theory and a tool for investigating the properties of M-theory in a relatively simple setting. The development of the matrix model formulation of M-theory has led physicists to consider various connections between string theory and a branch of mathematics called noncommutative geometry.
This subject is a generalization of ordinary geometry in which mathematicians define new geometric notions using tools from noncommutative algebra. Douglasand Albert Schwarz showed that some aspects of matrix models and M-theory are described by a noncommutative quantum field theorya special kind of physical theory in which spacetime is described mathematically using noncommutative geometry.
It quickly led to the discovery of other important links between noncommutative geometry and various physical theories. In general relativity, a black hole is defined as a region of spacetime in which the gravitational field is so strong that no particle or radiation can escape. In the currently accepted models of stellar evolution, black holes are thought to arise when massive stars undergo gravitational collapseand many galaxies are thought to contain supermassive black holes at their centers.
Black holes are also important for theoretical reasons, as they present profound challenges for theorists attempting to understand the quantum aspects of gravity. String theory has proved to be an important tool for investigating the theoretical properties of black holes because it provides a framework in which theorists can study their thermodynamics. In the branch of physics called statistical mechanicsentropy is a measure of the randomness or disorder of a physical system. This concept was studied in the s by the Austrian physicist Ludwig Boltzmannwho showed that the thermodynamic properties of a gas could be derived from the combined properties of its many constituent molecules.
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. In addition, this perspective led him to give a precise definition of entropy as the natural logarithm of the number of different states of the molecules also called microstates that give rise to the same macroscopic features.
In the twentieth century, physicists began to apply the same concepts to black holes. In most systems such as gases, the entropy scales with the volume. In the s, the physicist Jacob Bekenstein suggested that the entropy of a black hole is instead proportional to the surface area of its event horizonthe boundary beyond which matter and radiation are lost to its gravitational attraction.
The Bekenstein—Hawking formula expresses the entropy S as. Like any physical system, a black hole has an entropy defined in terms of the number of different microstates that lead to the same macroscopic features. The Bekenstein—Hawking entropy formula gives the expected value of the entropy of a black hole, but by the s, physicists still lacked a derivation of this formula by counting microstates in a theory of quantum gravity.
Finding such a derivation of this formula was considered an important test of the viability of any theory of quantum gravity such as string theory. In a paper fromAndrew Strominger and Cumrun Vafa showed how to derive the Beckenstein—Hawking formula for certain black holes in string theory.
In other words, a system of strongly interacting D-branes in string theory is indistinguishable from a black hole. Strominger and Vafa analyzed such D-brane systems and calculated the number of different ways of placing D-branes in spacetime so that their combined mass and charge is equal to a given mass and charge for the resulting black hole.
The black holes that Strominger and Vafa considered in their original work were quite different from real astrophysical black holes.
One difference was that Strominger and Vafa considered only extremal black holes in order to make the calculation tractable. These are defined as black holes with the lowest possible mass compatible with a given charge.
Although it was originally developed in this very particular and physically unrealistic context in string theory, the entropy calculation of Strominger and Vafa has led to a qualitative understanding of how black hole entropy can be accounted for in any theory of quantum gravity.
Indeed, inStrominger argued that the original result could be generalized to an arbitrary consistent theory of quantum gravity without relying on strings or supersymmetry. This is a theoretical result which implies that string theory is in some cases equivalent to a quantum field theory. It is closely related to hyperbolic spacewhich can be viewed as a disk as illustrated on the left. 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.
One can imagine a stack of hyperbolic disks where each disk represents the state of the universe at a given time. The resulting geometric object is three-dimensional anti-de Sitter space. Time runs along the vertical direction in this picture.
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. This construction describes a hypothetical universe with only two space dimensions and one time dimension, but it can be generalized to any number of dimensions. Indeed, hyperbolic space can have more than two dimensions and one can "stack up" copies of hyperbolic space to get higher-dimensional models of anti-de Sitter space.
An important feature of anti-de Sitter space is its boundary which looks like a cylinder in the case of three-dimensional anti-de Sitter space. One property of this boundary is that, within a small region on the surface around any given point, it looks just like Minkowski spacethe model of spacetime used in nongravitational physics.
The claim is that this quantum field theory is equivalent to a gravitational theory, such as string theory, in the bulk anti-de Sitter space in the sense that there is a "dictionary" for translating entities and calculations in one theory into their counterparts in the other theory.
For example, a single particle in the gravitational theory might correspond to some collection of particles in the boundary theory. In addition, the predictions in the two theories are quantitatively identical so that if two particles have a 40 percent chance of colliding in the gravitational theory, Advanced Theory - A State Of Mind (2) - String Theory (Vinyl) the corresponding collections in the boundary theory would also have a 40 percent chance of colliding.
One reason for this is that the correspondence provides a formulation of string theory in terms of quantum field theory, which is well understood by comparison.
Another reason is that it provides a general framework in which physicists can study and attempt to resolve the paradoxes of black holes. InStephen Hawking published a calculation which suggested that black holes are not completely black but emit a dim radiation due to quantum effects near the event horizon. This property is usually referred to as unitarity of time evolution. The apparent contradiction between Hawking's calculation and the unitarity postulate of quantum mechanics came to be known as the black hole information paradox.
This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies. The physics of the quark—gluon plasma is governed by a theory called quantum chromodynamicsbut this theory is mathematically intractable in problems involving the quark—gluon plasma. 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.
Inthe predicted value of this ratio for the quark-gluon plasma was confirmed at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. Over the decades, experimental condensed matter physicists have discovered a number of exotic states of matter, including superconductors and superfluids.
These states are described using the formalism of quantum field theory, but some phenomena are difficult to explain using standard field theoretic techniques.
So far some success has been achieved in using string theory methods to describe the transition of a superfluid to an insulator. A superfluid is a system of electrically neutral atoms that flows without any friction. Such systems are often produced in the laboratory using liquid heliumbut recently experimentalists have developed new ways of producing artificial superfluids by pouring trillions of cold atoms into a lattice of criss-crossing lasers.
These atoms initially behave as a superfluid, but as experimentalists increase the intensity of the lasers, they become less mobile and then suddenly transition to an insulating state. During the transition, the atoms behave in an unusual way. For example, the atoms slow to a halt at a rate that depends on the temperature and on Planck's constantthe fundamental parameter of quantum mechanics, which does not enter into the description of the other phases.
This behavior has recently been understood by considering a dual description where properties of the fluid are described in terms of a higher dimensional black hole. 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.
Phenomenology is the branch of theoretical physics in which physicists construct realistic models of nature from more abstract theoretical ideas. String phenomenology is the part of string theory that attempts to construct realistic or semi-realistic models based on string theory.
Partly because of theoretical and mathematical difficulties and partly because of the extremely high energies needed to test these theories experimentally, there is so far no experimental evidence that would unambiguously point to any of these models being a correct fundamental description of nature. This has led some in the community to criticize these approaches to unification and question the value of continued Advanced Theory - A State Of Mind (2) - String Theory (Vinyl) on these problems.
The currently accepted theory describing elementary particles and their interactions is known as the standard model of particle physics. This theory provides a unified description of three of the fundamental forces of nature: electromagnetism and the strong and weak nuclear forces. Advanced Theory - A State Of Mind (2) - String Theory (Vinyl) its remarkable success in explaining a wide range of physical phenomena, the standard model cannot be a complete description of reality.
This is because the standard model fails to incorporate the force of gravity and because of problems such as the hierarchy problem and the inability to explain the structure of fermion masses or dark matter. String theory has been used to construct a variety of models of particle physics going beyond the standard model.
Typically, such models are based on the idea of compactification. Starting with the ten- or eleven-dimensional spacetime of string or M-theory, physicists postulate a shape for the extra dimensions. By choosing this shape appropriately, they can construct models roughly similar to the standard model of particle physics, together with additional undiscovered particles. Such compactifications offer many ways of extracting realistic physics from string theory. Other similar methods can be used to construct realistic or semi-realistic models of our four-dimensional world based on M-theory.
The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution. Despite its success in explaining many observed features of the universe including galactic redshiftsthe relative abundance of light elements such as hydrogen and heliumand the existence of a cosmic microwave backgroundthere are several questions that remain unanswered. For example, the standard Big Bang model does not explain why the universe appears to be the same in all directions, why it appears flat on very large distance scales, or why certain hypothesized particles such as magnetic Advanced Theory - A State Of Mind (2) - String Theory (Vinyl) are not observed in experiments.
Currently, the leading candidate for a theory going beyond the Big Bang is the theory of cosmic inflation. Developed by Alan Guth and others in the s, inflation postulates a period of extremely rapid accelerated expansion of the universe prior to the expansion described by the standard Big Bang theory. 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.
In the theory of inflation, the rapid initial expansion of the universe is caused by a hypothetical particle called the inflaton. The exact properties of this particle are not fixed by the theory but should ultimately be derived from a more fundamental theory such as string theory.
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. In addition to influencing research in theoretical physicsstring theory has stimulated a number of major developments in pure mathematics.
Like many developing ideas in theoretical physics, string theory does not at present have a mathematically rigorous formulation in which all of its concepts can be defined precisely.
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. These conjectures are later proved by mathematicians, and in this way, string theory serves as a source of new ideas in pure mathematics.
After Calabi—Yau manifolds had entered physics as a way to compactify extra dimensions in string theory, many physicists began studying these manifolds. In the late s, several physicists noticed that given such a compactification of string theory, it is not possible to reconstruct uniquely a corresponding Calabi—Yau manifold.
In this situation, the manifolds are called mirror manifolds, and the relationship between the two physical theories is called mirror symmetry. Regardless of whether Calabi—Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences.
The Calabi—Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in enumerative geometrya branch of mathematics concerned with counting the numbers of solutions to geometric questions. Enumerative geometry studies a class of geometric objects called algebraic varieties which are defined by the vanishing of polynomials.
For example, the Clebsch cubic illustrated on the right is an algebraic variety defined using a certain polynomial of degree three in four variables. A celebrated result of nineteenth-century mathematicians Arthur Cayley and George Salmon states that there are exactly 27 straight lines that lie entirely on such a surface. 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.
This problem was solved by the nineteenth-century German mathematician Hermann Schubertwho found that there are exactly 2, such lines. Ingeometer Sheldon Katz proved that the number of curves, such as circles, that are defined by polynomials of degree two and lie entirely in the quintic isBy the yearmost of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish.
Originally, these results of Candelas were justified on physical grounds. However, mathematicians generally prefer rigorous proofs that do not require an appeal to physical intuition. Inspired by physicists' work on mirror symmetry, mathematicians have therefore constructed their own arguments proving the enumerative predictions of mirror symmetry.
Group theory is the branch of mathematics that studies the concept of symmetry. For example, one can consider a geometric shape such as an equilateral triangle. There are various operations that one can perform on this triangle without changing its shape. Each of these operations is called a symmetryand the collection of these symmetries satisfies certain technical properties making it into what mathematicians call a group.
In this particular example, the group is known as the dihedral group of order 6 because it has six elements. A general group may describe finitely many or infinitely many symmetries; if there are only finitely many symmetries, it is called a finite group. Mathematicians often strive for a classification or list of all mathematical objects of a given type. It is generally believed that finite groups are too diverse to admit a useful classification.
A more modest but still challenging problem is to classify all finite simple groups. These are finite groups that 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. This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family. The latter groups are called the "sporadic" groups, and each one owes its existence to a remarkable combination of circumstances.
The largest sporadic group, the so-called monster grouphas over 10 53 elements, more than a thousand times the number of atoms in the Earth. A seemingly unrelated construction is the j -function of number theory. This object belongs to a special class of functions called modular functionswhose graphs form a certain kind of repeating pattern.
In the late s, 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. InRichard Borcherds constructed a bridge between the theory of modular functions and finite groups and, in the process, explained the observations of McKay and Thompson.
Since the s, the connection between string theory and moonshine has led to further results in mathematics and physics. Harvey proposed a generalization of this moonshine phenomenon called umbral moonshine and their conjecture was proved mathematically by Duncan, Michael Griffin, and Ken Ono. 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.
Thereafter, German mathematician Theodor Kaluza combined the fifth dimension with general relativityand only Kaluza is usually credited with the idea. Inthe Swedish physicist Oskar Klein gave a physical interpretation of the unobservable extra dimension—it is wrapped into a small circle. Einstein introduced a non-symmetric metric tensorwhile 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 s and early s as a never completely successful theory of hadronsthe subatomic particles like the proton and neutron that feel the strong interaction. In the s, 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 NambuHolger Bech Nielsen and Leonard Susskind to be the relationship expected from rotating strings.
Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix. The S-matrix approach was started by Werner Heisenberg in the s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale.
While the scale was off by many orders Advanced Theory - A State Of Mind (2) - String Theory (Vinyl) magnitude, the approach he advocated was ideally suited for a theory of quantum gravity. Working with experimental data, R.
Dolen, D. Horn and C. Schmid developed some Advanced Theory - A State Of Mind (2) - String Theory (Vinyl) rules for hadron exchange. 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 that 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-Mannleading Gabriele Veneziano to construct a scattering amplitude that had the property of Dolen—Horn—Schmid duality, later renamed world-sheet duality.
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. 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 that could be used for generalization. Natural theories of mind: Evolution, development and simulation of everyday mindreading, 1 Cognition, 21 1 Bernstein, D. Theory of mind through the ages: Older and middle-aged adults exhibit more errors than do younger adults on a continuous false belief task.
Experimental Aging Research, 37 5 Call, J. Distinguishing intentional from accidental actions in orangutans Pongo pygmaeuschimpanzees Pan troglodytes and human children Homo sapiens. Journal of Comparative Psychology, 2 Callaghan, T.
Synchrony in the onset of mental-state reasoning: Evidence from five cultures. Psychological Science, 16 5 Callejas, A.
False belief vs. Frontiers in psychology, 2 Castelli, F. Autism, Asperger syndrome and brain mechanisms for the attribution of mental states to animated shapes. Brain, 8 Charman, T. Testing joint attention, imitation, and play as infancy precursors to language and theory of mind. Cognitive development, 15 4 Dennett, D. Brainstorms: Philosophical essay on mind and psychology. Montgomery, AL: Harvester Press. Behavioral and Brain Sciences, 6 3 Dodell-Feder, D.
T he neural basis of theory of mind and its relationship to social functioning and social anhedonia in individuals with schizophrenia. NeuroImage: Clinical, 4 Fine, C. Dissociation between theory of mind and executive functions in a patient with early left amygdala damage. Brain, 2 Flombaum, J. Rhesus monkeys attribute perceptions to others. Current Biology, 15 5 Gallagher, H. Trends in cognitive sciences, 7 2 Gopnik, A.
Child Development, 6298— Children's understanding of representational change and its relation to the understanding of false belief and the appearance-reality distinction. Child development Hare, B. Chimpanzees know what conspecifics do and do not see. Animal Behaviour, 59 4 Happe, F. Evidence from a PET scan study of Asperger syndrome. Neuroreport, 8 1 Hynes, C. Differential role of the orbital frontal lobe in emotional versus cognitive perspective-taking.
Neuropsychologia, 44 3 Keysar, B. Limits on theory of mind use in adults. Cognition, 89 1 Krachun, C. A new change-of-contents false belief test: Children and chimpanzees compared.
International Journal of Comparative Psychology, 23 2. Luchkina, E. More than just making it go: Toddlers effectively integrate causal efficacy and intentionality in selecting an appropriate causal intervention. Cognitive Development, 45 Meltzoff, A.
Imitation as a mechanism of social cognition: Origins of empathy, theory of mind, and the representation of action. Blackwell handbook of childhood cognitive development Milligan, K. Child development, 78 2 Moore, C. Children's understanding of the modal expression of speaker certainty and uncertainty and its relation to the development of a representational theory of mind.
Child development, 61 3 Moran, J. Lifespan development: The effects of typical aging on theory of mind. Behavioural brain research, Nelson, P. Developmental science, 11 6 Nickerson, R. Superior and modest. Created and creator. All in one. And one for all. Degiheugi - Endless Smile by Degiheugi. So stoked for this LE vinyl! Sinner's Syndrome by Moderator. Hypnotizing and head-nodding at the same time.
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