In theoretical physics , type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and the only one which perturbatively contains not only closed strings , but also open strings . The terminology of type I and type II was coined by John Henry Schwarz in 1982 to classify the three string theories known at the time.
128-613: M-theory is a theory in physics that unifies all consistent versions of superstring theory . Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution . Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories initially appeared to be very different, work by many physicists showed that
256-499: A Platonist by Stephen Hawking , a view Penrose discusses in his book, The Road to Reality . Hawking referred to himself as an "unashamed reductionist" and took issue with Penrose's views. Mathematics provides a compact and exact language used to describe the order in nature. This was noted and advocated by Pythagoras , Plato , Galileo, and Newton. Some theorists, like Hilary Putnam and Penelope Maddy , hold that logical truths, and therefore mathematical reasoning, depend on
384-411: A disk as illustrated on the left. This image shows a tessellation of a disk by triangles and squares. 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. Now imagine a stack of hyperbolic disks where each disk represents the state of the universe at
512-488: A frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with motion in the absence of gravitational fields and the general theory of relativity with motion and its connection with gravitation . Both quantum theory and the theory of relativity find applications in many areas of modern physics. While physics itself aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking,
640-477: 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. 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. This theory describes
768-465: A noncommutative quantum field theory , a special kind of physical theory in which the coordinates on spacetime do not satisfy the commutativity property. This established a link between matrix models and M-theory on the one hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various physical theories. The application of quantum mechanics to physical objects such as
896-484: A supergravity theory . A theory of strings that incorporates the idea of supersymmetry is called a superstring theory . There are several different versions of superstring theory which are all subsumed within the M-theory framework. At low energies , superstring theories are approximated by one of the three supergravities in ten dimensions, known as type I , type IIA , and type IIB supergravity. Similarly, M-theory
1024-560: A surface , one obtains a four-dimensional quantum field theory, and there is a duality known as the AGT correspondence which relates the physics of this theory to certain physical concepts associated with the surface itself. More recently, theorists have extended these ideas to study the theories obtained by compactifying down to three dimensions. Physics Physics is the scientific study of matter , its fundamental constituents , its motion and behavior through space and time , and
1152-455: A basic awareness of the motions of the Sun, Moon, and stars. The stars and planets, believed to represent gods, were often worshipped. While the explanations for the observed positions of the stars were often unscientific and lacking in evidence, these early observations laid the foundation for later astronomy, as the stars were found to traverse great circles across the sky, which could not explain
1280-484: A brane. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes. Intuitively, these objects look like sheets or membranes propagating through the eleven-dimensional spacetime. Shortly after this discovery, Michael Duff , Paul Howe, Takeo Inami, and Kellogg Stelle considered a particular compactification of eleven-dimensional supergravity with one of
1408-400: A class of particles called fermions . Roughly speaking, fermions are the constituents of matter, while bosons mediate interactions between particles. In theories with supersymmetry, each boson has a counterpart which is a fermion, and vice versa. When supersymmetry is imposed as a local symmetry, one automatically obtains a quantum mechanical theory that includes gravity. Such a theory is called
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#17327649258561536-426: A four-dimensional spacetime , three spatial dimensions and one time dimension. In this framework, the phenomenon of gravity is viewed as a consequence of the geometry of spacetime. In spite of the fact that the universe is well described by four-dimensional spacetime, there are several reasons why physicists consider theories in other dimensions. In some cases, by modeling spacetime in a different number of dimensions,
1664-412: A garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling on the surface of the hose would move in two dimensions. Theories that arise as different limits of M-theory turn out to be related in highly nontrivial ways. One of
1792-473: A given time. The resulting geometric object is three-dimensional anti-de Sitter space. It looks like a solid cylinder in which any cross section is a copy of the hyperbolic disk. Time runs along the vertical direction in this picture. The surface of this cylinder plays an important role in the AdS/CFT correspondence. As with the hyperbolic plane, anti-de Sitter space is curved in such a way that any point in
1920-420: A hard-to-find physical meaning. The final mathematical solution has an easier-to-find meaning, because it is what the solver is looking for. Physics is a branch of fundamental science (also called basic science). Physics is also called " the fundamental science" because all branches of natural science including chemistry, astronomy, geology, and biology are constrained by laws of physics. Similarly, chemistry
2048-545: A key property of these models, shown by A. Sagnotti in 1992, is that in general the Green–Schwarz mechanism takes a more general form, and involves several two forms in the cancellation mechanism. The relation between the type IIB string theory and the type I string theory has a large number of surprising consequences, both in ten and in lower dimensions, that were first displayed by the String Theory Group at
2176-446: A large coupling constant is equivalent via S-duality to the same theory with small coupling constant. Theorists also found that different string theories may be related by T-duality. This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent. String theory extends ordinary particle physics by replacing zero-dimensional point particles by one-dimensional objects called strings. In
2304-496: A mystery why there was not just one consistent formulation. However, as physicists began to examine string theory more closely, they realized that these theories are related in intricate and nontrivial ways. In the late 1970s, Claus Montonen and David Olive had conjectured a special property of certain physical theories. A sharpened version of their conjecture concerns a theory called N = 4 supersymmetric Yang–Mills theory , which describes theoretical particles formally similar to
2432-439: A quantum theory of gravity. It describes a force just like the familiar gravitational force subject to the rules of quantum mechanics. In everyday life, there are three familiar dimensions of space: height, width and depth. Einstein's general theory of relativity treats time as a dimension on par with the three spatial dimensions; in general relativity, space and time are not modeled as separate entities but are instead unified to
2560-503: A similar result which suggested that strongly interacting strings in ten dimensions might have an equivalent description in terms of weakly interacting five-dimensional branes. Initially, physicists were unable to prove this relationship for two important reasons. On the one hand, the Montonen–Olive duality was still unproven, and so Strominger's conjecture was even more tenuous. On the other hand, there were many technical issues related to
2688-462: A single force. This idea was improved by physicist Oskar Klein , who suggested that the additional dimension proposed by Kaluza could take the form of a circle with radius around 10 cm. The Kaluza–Klein theory and subsequent attempts by Einstein to develop unified field theory were never completely successful. In part this was because Kaluza–Klein theory predicted a particle (the radion ), that has never been shown to exist, and in part because it
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#17327649258562816-465: A specific practical application as a goal, other than the deeper insight into the phenomema themselves. Applied physics is a general term for physics research and development that is intended for a particular use. An applied physics curriculum usually contains a few classes in an applied discipline, like geology or electrical engineering. It usually differs from engineering in that an applied physicist may not be designing something in particular, but rather
2944-426: A speed much less than the speed of light. These theories continue to be areas of active research today. Chaos theory , an aspect of classical mechanics, was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Newton (1642–1727). These central theories are important tools for research into more specialized topics, and any physicist, regardless of their specialization,
3072-399: A subfield of mechanics , is used in the building of bridges and other static structures. The understanding and use of acoustics results in sound control and better concert halls; similarly, the use of optics creates better optical devices. An understanding of physics makes for more realistic flight simulators , video games, and movies, and is often critical in forensic investigations. With
3200-466: A substantial treatise on " Physics " – in the 4th century BC. Aristotelian physics was influential for about two millennia. His approach mixed some limited observation with logical deductive arguments, but did not rely on experimental verification of deduced statements. Aristotle's foundational work in Physics, though very imperfect, formed a framework against which later thinkers further developed
3328-558: A system of strongly interacting particles (large coupling constant) has an equivalent description as a system of weakly interacting particles (small coupling constant) and vice versa by spin-moment. In the 1990s, several theorists generalized Montonen–Olive duality to the S-duality relationship, which connects different string theories. Ashoke Sen studied S-duality in the context of heterotic strings in four dimensions. Chris Hull and Paul Townsend showed that type IIB string theory with
3456-471: A theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily. There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics . Finally, there exist scenarios in which there could actually be more than four dimensions of spacetime which have nonetheless managed to escape detection. One notable feature of string theory and M-theory
3584-478: A tool for investigating the properties of M-theory in a relatively simple setting. In geometry, it is often useful to introduce coordinates . For example, in order to study the geometry of the Euclidean plane , one defines the coordinates x and y as the distances between any point in the plane and a pair of axes . In ordinary geometry, the coordinates of a point are numbers, so they can be multiplied, and
3712-563: Is approximated at low energies by supergravity in eleven dimensions. In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension p , these are called p -branes. Branes are dynamical objects which can propagate through spacetime according to
3840-413: Is clear-cut, but not always obvious. For example, mathematical physics is the application of mathematics in physics. Its methods are mathematical, but its subject is physical. The problems in this field start with a " mathematical model of a physical situation " (system) and a "mathematical description of a physical law" that will be applied to that system. Every mathematical statement used for solving has
3968-419: Is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies not subject to an acceleration), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics ),
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4096-400: Is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in particle accelerators . On this scale, ordinary, commonsensical notions of space, time, matter, and energy are no longer valid. The two chief theories of modern physics present a different picture of
4224-428: Is eleven. In the same year, Eugène 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. Initially, many physicists hoped that by compactifying eleven-dimensional supergravity, it might be possible to construct realistic models of our four-dimensional world. The hope
4352-425: Is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics , electromagnetism , and special relativity. Classical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics , optics , thermodynamics, and electromagnetism. Classical mechanics
4480-429: Is generally concerned with matter and energy on the normal scale of observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on a very large or very small scale. For example, atomic and nuclear physics study matter on the smallest scale at which chemical elements can be identified. The physics of elementary particles is on an even smaller scale since it
4608-430: 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 space , the model of spacetime used in nongravitational physics. One can therefore consider an auxiliary theory in which "spacetime" is given by the boundary of anti-de Sitter space. This observation
4736-460: Is not known, such a formulation should describe two- and five-dimensional objects called branes and should be approximated by eleven-dimensional supergravity at low energies . Modern attempts to formulate M-theory are typically based on matrix theory or the AdS/CFT correspondence . According to Witten, M should stand for "magic", "mystery" or "membrane" according to taste, and the true meaning of
4864-593: Is often called the central science because of its role in linking the physical sciences. For example, chemistry studies properties, structures, and reactions of matter (chemistry's focus on the molecular and atomic scale distinguishes it from physics ). Structures are formed because particles exert electrical forces on each other, properties include physical characteristics of given substances, and reactions are bound by laws of physics, like conservation of energy , mass , and charge . Fundamental physics seeks to better explain and understand phenomena in all spheres, without
4992-405: Is one way of modifying the number of dimensions in a physical theory. In compactification, some of the extra dimensions are assumed to "close up" on themselves to form circles. 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. A standard analogy for this is to consider a multidimensional object such as
5120-506: Is possible only in discrete steps proportional to their frequency. This, along with the photoelectric effect and a complete theory predicting discrete energy levels of electron orbitals , led to the theory of quantum mechanics improving on classical physics at very small scales. Quantum mechanics would come to be pioneered by Werner Heisenberg , Erwin Schrödinger and Paul Dirac . From this early work, and work in related fields,
5248-509: Is provided by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence . Proposed by Juan Maldacena in late 1997, the AdS/CFT correspondence is a theoretical result which implies that M-theory is in some cases equivalent to a quantum field theory. In addition to providing insights into the mathematical structure of string and M-theory, the AdS/CFT correspondence has shed light on many aspects of quantum field theory in regimes where traditional calculational techniques are ineffective. In
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5376-488: Is that these theories require extra dimensions of spacetime for their mathematical consistency. In string theory, spacetime is ten-dimensional (nine spatial dimensions, and one time dimension), while in M-theory it is eleven-dimensional (ten spatial dimensions, and one time dimension). In order to describe real physical phenomena using these theories, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments. Compactification
5504-411: 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. The claim is that this quantum field theory is equivalent to the gravitational theory on 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
5632-431: Is using physics or conducting physics research with the aim of developing new technologies or solving a problem. The approach is similar to that of applied mathematics . Applied physicists use physics in scientific research. For instance, people working on accelerator physics might seek to build better particle detectors for research in theoretical physics. Physics is used heavily in engineering. For example, statics,
5760-688: The S factor). In the real world, spacetime is four-dimensional, at least macroscopically, so this version of the correspondence does not provide a realistic model of gravity. Likewise, the dual theory is not a viable model of any real-world system since it describes a world with six spacetime dimensions. Nevertheless, the (2,0)-theory has proven to be important for studying the general properties of quantum field theories. Indeed, this theory subsumes many mathematically interesting effective quantum field theories and points to new dualities relating these theories. For example, Luis Alday, Davide Gaiotto, and Yuji Tachikawa showed that by compactifying this theory on
5888-473: The SO (32) heterotic string theory. Similarly, type IIB string theory is related to itself in a nontrivial way by S-duality. Another relationship between different string theories is T-duality . Here one considers strings propagating around a circular extra dimension. T-duality states that a string propagating around a circle of radius R is equivalent to a string propagating around a circle of radius 1/ R in
6016-536: The Industrial Revolution as energy needs increased. The laws comprising classical physics remain widely used for objects on everyday scales travelling at non-relativistic speeds, since they provide a close approximation in such situations, and theories such as quantum mechanics and the theory of relativity simplify to their classical equivalents at such scales. Inaccuracies in classical mechanics for very small objects and very high velocities led to
6144-660: The Latin physica ('study of nature'), which itself is a borrowing of the Greek φυσική ( phusikḗ 'natural science'), a term derived from φύσις ( phúsis 'origin, nature, property'). Astronomy is one of the oldest natural sciences . Early civilizations dating before 3000 BCE, such as the Sumerians , ancient Egyptians , and the Indus Valley Civilisation , had a predictive knowledge and
6272-426: 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. Years later, he would state, "I thought my colleagues would understand that it really stood for membrane. Unfortunately, it got people confused." In mathematics, a matrix is a rectangular array of numbers or other data. In physics,
6400-608: The Northern Hemisphere . Natural philosophy has its origins in Greece during the Archaic period (650 BCE – 480 BCE), when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause. They proposed ideas verified by reason and observation, and many of their hypotheses proved successful in experiment; for example, atomism
6528-637: The Scientific Revolution in the 17th century, these natural sciences branched into separate research endeavors. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry , and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in these and other academic disciplines such as mathematics and philosophy. Advances in physics often enable new technologies . For example, advances in
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#17327649258566656-619: The Standard Model of particle physics was derived. Following the discovery of a particle with properties consistent with the Higgs boson at CERN in 2012, all fundamental particles predicted by the standard model, and no others, appear to exist; however, physics beyond the Standard Model , with theories such as supersymmetry , is an active area of research. Areas of mathematics in general are important to this field, such as
6784-402: The University of Rome Tor Vergata in the early 1990s. It opened the way to the construction of entire new classes of string spectra with or without supersymmetry. Joseph Polchinski 's work on D-branes provided a geometrical interpretation for these results in terms of extended objects ( D-brane , orientifold ). In the 1990s it was first argued by Edward Witten that type I string theory with
6912-439: The camera obscura (his thousand-year-old version of the pinhole camera ) and delved further into the way the eye itself works. Using the knowledge of previous scholars, he began to explain how light enters the eye. He asserted that the light ray is focused, but the actual explanation of how light projected to the back of the eye had to wait until 1604. His Treatise on Light explained the camera obscura , hundreds of years before
7040-579: The empirical world. This is usually combined with the claim that the laws of logic express universal regularities found in the structural features of the world, which may explain the peculiar relation between these fields. Physics uses mathematics to organise and formulate experimental results. From those results, precise or estimated solutions are obtained, or quantitative results, from which new predictions can be made and experimentally confirmed or negated. The results from physics experiments are numerical data, with their units of measure and estimates of
7168-407: The first superstring revolution in 1984, many 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. Another feature of string theory that many physicists were drawn to in the 1980s and 1990s
7296-402: The point-like particles of particle physics are replaced by one-dimensional objects called strings . String theory describes how strings propagate through space and interact with each other. In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can vibrate in different ways. On distance scales larger than
7424-411: The quarks and gluons that make up atomic nuclei . The strength with which the particles of this theory interact is measured by a number called the coupling constant . The result of Montonen and Olive, now known as Montonen–Olive duality , states that N = 4 supersymmetric Yang–Mills theory with coupling constant g is equivalent to the same theory with coupling constant 1/ g . In other words,
7552-543: The standard consensus that the laws of physics are universal and do not change with time, physics can be used to study things that would ordinarily be mired in uncertainty . For example, in the study of the origin of the Earth, a physicist can reasonably model Earth's mass, temperature, and rate of rotation, as a function of time allowing the extrapolation forward or backward in time and so predict future or prior events. It also allows for simulations in engineering that speed up
7680-435: The 16th and 17th centuries, and Isaac Newton 's discovery and unification of the laws of motion and universal gravitation (that would come to bear his name). Newton also developed calculus , the mathematical study of continuous change, which provided new mathematical methods for solving physical problems. The discovery of laws in thermodynamics , chemistry , and electromagnetics resulted from research efforts during
7808-446: The AdS/CFT correspondence states that M-theory on the product space AdS 7 × S is equivalent to the so-called (2,0)-theory on the six-dimensional boundary. Here "(2,0)" refers to the particular type of supersymmetry that appears in the theory. In this example, the spacetime of the gravitational theory is effectively seven-dimensional (hence the notation AdS 7 ), and there are four additional " compact " dimensions (encoded by
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#17327649258567936-451: The AdS/CFT correspondence, the geometry of spacetime is described in terms of a certain vacuum solution of Einstein's equation called anti-de Sitter space . In very elementary terms, anti-de Sitter space is a mathematical model of spacetime in which the notion of distance between points (the metric ) is different from the notion of distance in ordinary Euclidean geometry . It is closely related to hyperbolic space , which can be viewed as
8064-511: The attacks from invaders and continued to advance various fields of learning, including physics. In the sixth century, Isidore of Miletus created an important compilation of Archimedes ' works that are copied in the Archimedes Palimpsest . In sixth-century Europe John Philoponus , a Byzantine scholar, questioned Aristotle 's teaching of physics and noted its flaws. He introduced the theory of impetus . Aristotle's physics
8192-461: 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. These calculations led them to propose that the BFSS matrix model is exactly equivalent to M-theory. The BFSS matrix model can therefore be used as a prototype for a correct formulation of M-theory and
8320-474: The branes. Starting in 1991, a team of researchers including Michael Duff, Ramzi Khuri, Jianxin Lu, and Ruben Minasian considered a special compactification of string theory in which four of the ten dimensions curl up. If one considers a five-dimensional brane wrapped around these extra dimensions, then the brane looks just like a one-dimensional string. In this way, the conjectured relationship between strings and branes
8448-500: The commutative law (that is, objects for which xy is not necessarily equal to yx ). One imagines that these noncommuting objects are coordinates on some more general notion of "space" and proves theorems about these generalized spaces by exploiting the analogy with ordinary geometry. In a paper from 1998, Alain Connes , Michael R. Douglas , and Albert Schwarz showed that some aspects of matrix models and M-theory are described by
8576-434: The concepts of space, time, and matter from that presented by classical physics. Classical mechanics approximates nature as continuous, while quantum theory is concerned with the discrete nature of many phenomena at the atomic and subatomic level and with the complementary aspects of particles and waves in the description of such phenomena. The theory of relativity is concerned with the description of phenomena that take place in
8704-409: The constant speed predicted by Maxwell's equations of electromagnetism. This discrepancy was corrected by Einstein's theory of special relativity , which replaced classical mechanics for fast-moving bodies and allowed for a constant speed of light. Black-body radiation provided another problem for classical physics, which was corrected when Planck proposed that the excitation of material oscillators
8832-466: The development of a new technology. There is also considerable interdisciplinarity , so many other important fields are influenced by physics (e.g., the fields of econophysics and sociophysics ). Physicists use the scientific method to test the validity of a physical theory . By using a methodical approach to compare the implications of a theory with the conclusions drawn from its related experiments and observations, physicists are better able to test
8960-429: The development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory and Albert Einstein 's theory of relativity. Both of these theories came about due to inaccuracies in classical mechanics in certain situations. Classical mechanics predicted that the speed of light depends on the motion of the observer, which could not be resolved with
9088-407: The development of new experiments (and often related equipment). Physicists who work at the interplay of theory and experiment are called phenomenologists , who study complex phenomena observed in experiment and work to relate them to a fundamental theory . Theoretical physics has historically taken inspiration from philosophy; electromagnetism was unified this way. Beyond the known universe,
9216-430: The dimensions curled up into a circle. In this setting, one can imagine the membrane wrapping around the circular dimension. If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime. In fact, Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory. In 1990, Andrew Strominger published
9344-481: The dual description. For example, type IIA string theory is equivalent to type IIB string theory via T-duality, and the two versions of heterotic string theory are also related by T-duality. In general, the term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. 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
9472-462: The electromagnetic field, which are extended in space and time, is known as quantum field theory . In particle physics, quantum field theories form the basis for our understanding of elementary particles, which are modeled as excitations in the fundamental fields. Quantum field theories are also used throughout condensed matter physics to model particle-like objects called quasiparticles . One approach to formulating M-theory and studying its properties
9600-682: The errors in the measurements. Technologies based on mathematics, like computation have made computational physics an active area of research. Ontology is a prerequisite for physics, but not for mathematics. It means physics is ultimately concerned with descriptions of the real world, while mathematics is concerned with abstract patterns, even beyond the real world. Thus physics statements are synthetic, while mathematical statements are analytic. Mathematics contains hypotheses, while physics contains theories. Mathematics statements have to be only logically true, while predictions of physics statements must match observed and experimental data. The distinction
9728-931: The field of theoretical physics also deals with hypothetical issues, such as parallel universes , a multiverse , and higher dimensions . Theorists invoke these ideas in hopes of solving particular problems with existing theories; they then explore the consequences of these ideas and work toward making testable predictions. Experimental physics expands, and is expanded by, engineering and technology. Experimental physicists who are involved in basic research design and perform experiments with equipment such as particle accelerators and lasers , whereas those involved in applied research often work in industry, developing technologies such as magnetic resonance imaging (MRI) and transistors . Feynman has noted that experimentalists may seek areas that have not been explored well by theorists. Type I string The classic 1976 work of Ferdinando Gliozzi , Joël Scherk and David Olive paved
9856-415: The field. His approach is entirely superseded today. He explained ideas such as motion (and gravity ) with the theory of four elements . Aristotle believed that each of the four classical elements (air, fire, water, earth) had its own natural place. Because of their differing densities, each element will revert to its own specific place in the atmosphere. So, because of their weights, fire would be at
9984-450: The four-dimensional world, although so far none have been verified to give rise to physics as observed in high-energy physics experiments. One of the deepest problems in modern physics is the problem of quantum gravity . The current understanding of gravity is based on Albert Einstein 's general theory of relativity , which is formulated within the framework of classical physics . However, nongravitational forces are described within
10112-488: The framework of quantum mechanics , a radically different formalism for describing physical phenomena based on probability . A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity. String theory is a theoretical framework that attempts to reconcile gravity and quantum mechanics. In string theory,
10240-476: The fundamental objects that give rise to elementary particles are the one-dimensional strings. Although the physical phenomena described by M-theory are still poorly understood, physicists know that the theory describes two- and five-dimensional branes. Much of the current research in M-theory attempts to better understand the properties of these branes. In the early 20th century, physicists and mathematicians including Albert Einstein and Hermann Minkowski pioneered
10368-446: The idea of new dimensions to be taken seriously again. New concepts and mathematical tools provided fresh insights into general relativity, giving rise to a period in the 1960s–1970s now known as the golden age of general relativity . In the mid-1970s, physicists began studying higher-dimensional theories combining general relativity with supersymmetry, the so-called supergravity theories. General relativity does not place any limits on
10496-445: 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
10624-429: The late 1980s, it was natural for theorists to attempt to formulate other extensions in which particles are replaced by two-dimensional supermembranes or by higher-dimensional objects called branes. Such objects had been considered as early as 1962 by Paul Dirac , and they were reconsidered by a small but enthusiastic group of physicists in the 1980s. Supersymmetry severely restricts the possible number of dimensions of
10752-400: The latter include such branches as hydrostatics , hydrodynamics and pneumatics . Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics , the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics , the physics of animal calls and hearing, and electroacoustics ,
10880-490: The laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match predictions provided by classical mechanics. Einstein contributed the framework of special relativity, which replaced notions of absolute time and space with spacetime and allowed an accurate description of systems whose components have speeds approaching
11008-412: The manipulation of audible sound waves using electronics. Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation , which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light. Heat is a form of energy, the internal energy possessed by
11136-704: The modern development of photography. The seven-volume Book of Optics ( Kitab al-Manathir ) influenced thinking across disciplines from the theory of visual perception to the nature of perspective in medieval art, in both the East and the West, for more than 600 years. This included later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to Johannes Kepler . The translation of The Book of Optics had an impact on Europe. From it, later European scholars were able to build devices that replicated those Ibn al-Haytham had built and understand
11264-410: The other Philoponus' criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries later, during the Scientific Revolution . Galileo cited Philoponus substantially in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan , a teacher in the faculty of arts at the University of Paris , developed the concept of impetus. It
11392-459: 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, then the corresponding collections in the boundary theory would also have a 40 percent chance of colliding. One particular realization of
11520-410: The other theory. The two theories are then said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena. Another important theoretical idea that plays a role in M-theory is supersymmetry . This is a mathematical relation that exists in certain physical theories between a class of particles called bosons and
11648-459: The other, you will see that the ratio of the times required for the motion does not depend on the ratio of the weights, but that the difference in time is a very small one. And so, if the difference in the weights is not considerable, that is, of one is, let us say, double the other, there will be no difference, or else an imperceptible difference, in time, though the difference in weight is by no means negligible, with one body weighing twice as much as
11776-572: The particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy. Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field , and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest. Classical physics
11904-414: The particles that arise at low energies exhibit different symmetries . 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 and IIB include only closed strings. Each of these five string theories arises as a special limiting case of M-theory. This theory, like its string theory predecessors, is an example of
12032-602: The positions of the planets . According to Asger Aaboe , the origins of Western astronomy can be found in Mesopotamia , and all Western efforts in the exact sciences are descended from late Babylonian astronomy . Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer wrote of various celestial objects in his Iliad and Odyssey ; later Greek astronomers provided names, which are still used today, for most constellations visible from
12160-428: The possible dimensions of spacetime. Although the theory is typically formulated in four dimensions, one can write down the same equations for the gravitational field in any number of dimensions. Supergravity is more restrictive because it places an upper limit on the number of dimensions. In 1978, work by Werner Nahm showed that the maximum spacetime dimension in which one can formulate a consistent supersymmetric theory
12288-478: The previous results on S- and T-duality and the appearance of two- and five-dimensional branes in string theory. In the months following Witten's announcement, hundreds of new papers appeared on the Internet confirming that the new theory involved membranes in an important way. Today this flurry of work is known as the second superstring revolution . One of the important developments following Witten's announcement
12416-538: The product of two coordinates does not depend on the order of multiplication. That is, xy = yx . This property of multiplication is known as the commutative law , and this relationship between geometry and the commutative algebra of coordinates is the starting point for much of modern geometry. Noncommutative geometry is a branch of mathematics that attempts to generalize this situation. Rather than working with ordinary numbers, one considers some similar objects, such as matrices, whose multiplication does not satisfy
12544-443: The quantum properties of five-dimensional branes. The first of these problems was solved in 1993 when Ashoke Sen established that certain physical theories require the existence of objects with both electric and magnetic charge which were predicted by the work of Montonen and Olive. In spite of this progress, the relationship between strings and five-dimensional branes remained conjectural because theorists were unable to quantize
12672-399: The related entities of energy and force . Physics is one of the most fundamental scientific disciplines. A scientist who specializes in the field of physics is called a physicist . Physics is one of the oldest academic disciplines . Over much of the past two millennia, physics, chemistry , biology , and certain branches of mathematics were a part of natural philosophy , but during
12800-537: The relationships that can exist between these different physical theories is called S-duality . This is a relationship which says that a collection of strongly interacting particles in one theory can, in some cases, be viewed as a collection of weakly interacting particles in a completely different theory. Roughly speaking, a collection of particles is said to be strongly interacting if they combine and decay often and weakly interacting if they do so infrequently. Type I string theory turns out to be equivalent by S-duality to
12928-416: The rules of quantum mechanics. They can have mass and other attributes such as charge. A p -brane sweeps out a ( p + 1) -dimensional volume in spacetime called its worldvolume . Physicists often study fields analogous to the electromagnetic field which live on the worldvolume of a brane. The word brane comes from the word "membrane" which refers to a two-dimensional brane. In string theory,
13056-461: The sense that all observable quantities in one description are identified with quantities in the dual description. For example, a string has momentum as it propagates around a circle, and it can also wind around the circle one or more times. The number of times the string winds around a circle is called the winding number . If a string has momentum p and winding number n in one description, it will have momentum n and winding number p in
13184-440: The speed being proportional to the weight and the speed of the object that is falling depends inversely on the density object it is falling through (e.g. density of air). He also stated that, when it comes to violent motion (motion of an object when a force is applied to it by a second object) that the speed that object moves, will only be as fast or strong as the measure of force applied to it. The problem of motion and its causes
13312-412: The speed of light. Planck, Schrödinger, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales. Later, quantum field theory unified quantum mechanics and special relativity. General relativity allowed for a dynamical, curved spacetime, with which highly massive systems and the large-scale structure of
13440-623: 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. In this way, all of the different elementary particles may be viewed as vibrating strings. One of the vibrational states of a string gives rise to the graviton , a quantum mechanical particle that carries gravitational force. There are several versions of string theory: type I , type IIA , type IIB , and two flavors of heterotic string theory ( SO (32) and E 8 × E 8 ). The different theories allow different types of strings, and
13568-412: The study of probabilities and groups . Physics deals with a wide variety of systems, although certain theories are used by all physicists. Each of these theories was experimentally tested numerous times and found to be an adequate approximation of nature. For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at
13696-432: The theories were related in intricate and nontrivial ways. Physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality . Witten's conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity . Although a complete formulation of M-theory
13824-484: The title should be decided when a more fundamental formulation of the theory is known. Investigations of the mathematical structure of M-theory have spawned important theoretical results in physics and mathematics. More speculatively, M-theory may provide a framework for developing a unified theory of all of the fundamental forces of nature. Attempts to connect M-theory to experiment typically focus on compactifying its extra dimensions to construct candidate models of
13952-444: The top, air underneath fire, then water, then lastly earth. He also stated that when a small amount of one element enters the natural place of another, the less abundant element will automatically go towards its own natural place. For example, if there is a fire on the ground, the flames go up into the air in an attempt to go back into its natural place where it belongs. His laws of motion included: that heavier objects will fall faster,
14080-423: The understanding of electromagnetism , solid-state physics , and nuclear physics led directly to the development of technologies that have transformed modern society, such as television, computers, domestic appliances , and nuclear weapons ; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus . The word physics comes from
14208-423: The universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed. Physics, as with the rest of science, relies on the philosophy of science and its " scientific method " to advance knowledge of the physical world. The scientific method employs a priori and a posteriori reasoning as well as
14336-573: The use of Bayesian inference to measure the validity of a given theory. Study of the philosophical issues surrounding physics, the philosophy of physics , involves issues such as the nature of space and time , determinism , and metaphysical outlooks such as empiricism , naturalism , and realism . Many physicists have written about the philosophical implications of their work, for instance Laplace , who championed causal determinism , and Erwin Schrödinger , who wrote on quantum mechanics. The mathematical physicist Roger Penrose has been called
14464-479: The use of four-dimensional geometry for describing the physical world. These efforts culminated in the formulation of Einstein's general theory of relativity, which relates gravity to the geometry of four-dimensional spacetime. The success of general relativity led to efforts to apply higher dimensional geometry to explain other forces. In 1919, work by Theodor Kaluza showed that by passing to five-dimensional spacetime, one can unify gravity and electromagnetism into
14592-472: The vacuum to cancel various anomalies giving it a gauge group of SO(32) via Chan–Paton factors . At low energies, type I string theory is described by the type I supergravity in ten dimensions coupled to the SO(32) supersymmetric Yang–Mills theory . The discovery in 1984 by Michael Green and John H. Schwarz that anomalies in type I string theory cancel sparked the first superstring revolution . However,
14720-988: The validity of a theory in a logical, unbiased, and repeatable way. To that end, experiments are performed and observations are made in order to determine the validity or invalidity of a theory. A scientific law is a concise verbal or mathematical statement of a relation that expresses a fundamental principle of some theory, such as Newton's law of universal gravitation. Theorists seek to develop mathematical models that both agree with existing experiments and successfully predict future experimental results, while experimentalists devise and perform experiments to test theoretical predictions and explore new phenomena. Although theory and experiment are developed separately, they strongly affect and depend upon each other. Progress in physics frequently comes about when experimental results defy explanation by existing theories, prompting intense focus on applicable modelling, and when new theories generate experimentally testable predictions , which inspire
14848-474: The way to a systematic understanding of the rules behind string spectra in cases where only closed strings are present via modular invariance . It did not lead to similar progress for models with open strings, despite the fact that the original discussion was based on the type I string theory. As first proposed by Augusto Sagnotti in 1988, the type I string theory can be obtained as an orientifold of type IIB string theory, with 32 half- D9-branes added in
14976-579: The way vision works. Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics . Major developments in this period include the replacement of the geocentric model of the Solar System with the heliocentric Copernican model , the laws governing the motion of planetary bodies (determined by Kepler between 1609 and 1619), Galileo's pioneering work on telescopes and observational astronomy in
15104-399: The works of many scientists like Ibn Sahl , Al-Kindi , Ibn al-Haytham , Al-Farisi and Avicenna . The most notable work was The Book of Optics (also known as Kitāb al-Manāẓir), written by Ibn al-Haytham, in which he presented the alternative to the ancient Greek idea about vision. In his Treatise on Light as well as in his Kitāb al-Manāẓir , he presented a study of the phenomenon of
15232-421: Was Witten's work in 1996 with string theorist Petr Hořava . Witten and Hořava studied M-theory on a special spacetime geometry with two ten-dimensional boundary components. Their work shed light on the mathematical structure of M-theory and suggested possible ways of connecting M-theory to real world physics. Initially, some physicists suggested that the new theory was a fundamental theory of membranes, but Witten
15360-550: Was a step toward the modern ideas of inertia and momentum. Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further, especially placing emphasis on observation and a priori reasoning, developing early forms of the scientific method . The most notable innovations under Islamic scholarship were in the field of optics and vision, which came from
15488-513: Was found to be correct approximately 2000 years after it was proposed by Leucippus and his pupil Democritus . During the classical period in Greece (6th, 5th and 4th centuries BCE) and in Hellenistic times , natural philosophy developed along many lines of inquiry. Aristotle ( Greek : Ἀριστοτέλης , Aristotélēs ) (384–322 BCE), a student of Plato , wrote on many subjects, including
15616-449: Was its high degree of uniqueness. 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 1990s, 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
15744-417: Was not scrutinized until Philoponus appeared; unlike Aristotle, who based his physics on verbal argument, Philoponus relied on observation. On Aristotle's physics Philoponus wrote: But this is completely erroneous, and our view may be corroborated by actual observation more effectively than by any sort of verbal argument. For if you let fall from the same height two weights of which one is many times as heavy as
15872-545: Was reduced to a relationship between strings and strings, and the latter could be tested using already established theoretical techniques. Speaking at the string theory conference at the University of Southern California in 1995, Edward Witten of the Institute for Advanced Study 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
16000-452: Was skeptical of the role of membranes in the theory. In a paper from 1996, Hořava and Witten wrote As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the M-theory, leaving to the future the relation of M to membranes. In the absence of an understanding of the true meaning and structure of M-theory, Witten has suggested that
16128-548: Was studied carefully, leading to the philosophical notion of a " prime mover " as the ultimate source of all motion in the world (Book 8 of his treatise Physics ). The Western Roman Empire fell to invaders and internal decay in the fifth century, resulting in a decline in intellectual pursuits in western Europe. By contrast, the Eastern Roman Empire (usually known as the Byzantine Empire ) resisted
16256-551: 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. Interest in eleven-dimensional supergravity soon waned as various flaws in this scheme were discovered. One of the problems was that the laws of physics appear to distinguish between clockwise and counterclockwise, a phenomenon known as chirality . Edward Witten and others observed this chirality property cannot be readily derived by compactifying from eleven dimensions. In
16384-435: Was unable to correctly predict the ratio of an electron's mass to its charge. In addition, these theories were being developed just as other physicists were beginning to discover quantum mechanics, which would ultimately prove successful in describing known forces such as electromagnetism, as well as new nuclear forces that were being discovered throughout the middle part of the century. Thus it would take almost fifty years for
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