Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur; until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe was independent of one-dimensional time. However, in 1905, Albert Einstein based his seminal work on special relativity on two postulates: The laws of physics are invariant in all inertial systems; the logical consequence of taking these postulates together is the inseparable joining together of the four dimensions, hitherto assumed as independent, of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light has the same speed regardless of the frame of reference in which it is measured. Einstein framed his theory in terms of kinematics.

His theory was a breakthrough advance over Lorentz's 1904 theory of electromagnetic phenomena and Poincaré's electrodynamic theory. Although these theories included equations identical to those that Einstein introduced, they were ad hoc models proposed to explain the results of various experiments—including the famous Michelson–Morley interferometer experiment—that were difficult to fit into existing paradigms. In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve this flat spacetime to a Pseudo Riemannian manifold.

Non-relativistic classical mechanics treats time as a universal quantity of measurement, uniform throughout space and, separate from space. Classical mechanics assumes that time has a constant rate of passage, independent of the state of motion of an observer, or indeed of anything external. Furthermore, it assumes that space is Euclidean, to say, it assumes that space follows the geometry of common sense. In the context of special relativity, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer. General relativity, in addition, provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. In ordinary space, a position is specified by three numbers, known as dimensions. In the Cartesian coordinate system, these are called x, y, z. A position in spacetime is called an event, requires four numbers to be specified: the three-dimensional location in space, plus the position in time.

Spacetime is thus four dimensional. An event is something that happens instantaneously at a single point in spacetime, represented by a set of coordinates x, y, z and t; the word "event" used in relativity should not be confused with the use of the word "event" in normal conversation, where it might refer to an "event" as something such as a concert, sporting event, or a battle. These are not mathematical "events" in the way the word is used in relativity, because they have finite durations and extents. Unlike the analogies used to explain events, such as firecrackers or lightning bolts, mathematical events have zero duration and represent a single point in spacetime; the path of a particle through spacetime can be considered to be a succession of events. The series of events can be linked together to form a line which represents a particle's progress through spacetime; that line is called the particle's world line. Mathematically, spacetime is a manifold, to say, it appears locally "flat" near each point in the same way that, at small enough scales, a globe appears flat.

An large scale factor, c relates distances measured in space with distances measured in time. The magnitude of this scale factor, along with the fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe, noticeably different from what they might observe if the world were Euclidean, it was only with the advent of sensitive scientific measurements in the mid-1800s, such as the Fizeau experiment and the Michelson–Morley experiment, that puzzling discrepancies began to be noted between observation versus predictions based on the implicit assumption of Euclidean space. In special relativity, an observer will, in most

ADM formalism

The ADM formalism is a Hamiltonian formulation of general relativity that plays an important role in canonical quantum gravity and numerical relativity. It was first published in 1959; the comprehensive review of the formalism that the authors published in 1962 has been reprinted in the journal General Relativity and Gravitation, while the original papers can be found in the archives of Physical Review. The formalism supposes that spacetime is foliated into a family of spacelike surfaces Σ t, labeled by their time coordinate t, with coordinates on each slice given by x i; the dynamic variables of this theory are taken to be the metric tensor of three dimensional spatial slices γ i j and their conjugate momenta π i j. Using these variables it is possible to define a Hamiltonian, thereby write the equations of motion for general relativity in the form of Hamilton's equations. In addition to the twelve variables γ i j and π i j, there are four Lagrange multipliers: the lapse function, N, components of shift vector field, N i.

These describe. The equations of motion for these variables can be specified. Most references adopt notation in which four dimensional tensors are written in abstract index notation, that Greek indices are spacetime indices taking values and Latin indices are spatial indices taking values. In the derivation here, a superscript is prepended to quantities that have both a three-dimensional and a four-dimensional version, such as the metric tensor for three-dimensional slices g i j and the metric tensor for the full four-dimensional spacetime g μ ν; the text here uses Einstein notation. Two types of derivatives are used: Partial derivatives are denoted either by the operator ∂ i or by subscripts preceded by a comma. Covariant derivatives are denoted either by the operator ∇ i or by subscripts preceded by a semicolon; the absolute value of the determinant of the matrix of metric tensor coefficients is represented by g. Other tensor symbols written without indices represent the trace of the corresponding tensor such as π = g i j π i j.

The starting point for the ADM formulation is the Lagrangian L = R g, a product of the square root of the determinant of the four-dimensional metric tensor for the full spacetime and its Ricci scalar. This is the Lagrangian from the Einstein–Hilbert action; the desired outcome of the derivation is to define an embedding of three-dimensional spatial slices in the four-dimensional spacetime. The metric of the three-dimensional slices g i j = g i j will be the generalized coordinates for a Hamiltonian formulation; the conjugate momenta can be computed as π i j = g g i p g j q, using standard techniques and definitions. The symbols Γ i j 0 are Christoffel symbols associated with the metric of the full four-dimensional spacetime; the lapse N = − 1 / 2 and the shift vector

Spin (physics)

In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum; the orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies. The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. In some ways, spin is like a vector quantity. All elementary particles of a given kind have the same magnitude of spin angular momentum, indicated by assigning the particle a spin quantum number; the SI unit of spin is the or, just as with classical angular momentum. In practice, spin is given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant ħ, which has the same units of angular momentum, although this is not the full computation of this value.

The "spin quantum number" is called "spin", leaving its meaning as the unitless "spin quantum number" to be inferred from context. When combined with the spin-statistics theorem, the spin of electrons results in the Pauli exclusion principle, which in turn underlies the periodic table of chemical elements. Wolfgang Pauli in 1924 was the first to propose a doubling of electron states due to a two-valued non-classical "hidden rotation". In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested the simple physical interpretation of a particle spinning around its own axis, in the spirit of the old quantum theory of Bohr and Sommerfeld. Ralph Kronig anticipated the Uhlenbeck-Goudsmit model in discussion with Hendrik Kramers several months earlier in Copenhagen, but did not publish; the mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it; as the name suggests, spin was conceived as the rotation of a particle around some axis.

This picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta: Spin quantum numbers may take half-integer values. Although the direction of its spin can be changed, an elementary particle cannot be made to spin faster or slower; the spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur classically if the internal charge of the particle were distributed differently from its mass; the conventional definition of the spin quantum number, s, is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 1/2, 1, 3/2, 2, etc.. The value of s for an elementary particle depends only on the type of particle, cannot be altered in any known way; the spin angular momentum, S, of any physical system is quantized. The allowed values of S are S = ℏ s = h 4 π n, where h is the Planck constant and ℏ = h/2π is the reduced Planck constant.

In contrast, orbital angular momentum can only take on integer values of s. Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons; the two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is. In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may "bunch together" if in identical states. Composite particles can have spins different from their component particles. For example, a helium atom in the ground state has spin 0 and behaves like a boson though the quarks and electrons which make it up are all fermions; this has some profound consequences: Quarks and leptons, which make up what is classically known as matter, are all fermions with spin 1/2. The common idea that "matter takes up space" comes from the Pauli exclusion principle acting on these particles to prevent the fermions that make up matter from being in the same quantum state.

Further compaction would require electrons to occupy the same energy states, therefore a kind of pressure acts to resist the fermions being overly close. Elementary fermions with other spins are not known to exist. Elementary particles which are thought of as carrying forces are all bosons with spin 1, they include the photon which carries the electromagnetic force, the gluon, the W and Z bosons. The ability of bosons to occupy the same quantu

Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars and light—are brought toward one another. On Earth, gravity gives weight to physical objects, the Moon's gravity causes the ocean tides; the gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming stars – and for the stars to group together into galaxies – so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become weaker on farther objects. Gravity is most described by the general theory of relativity which describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass; the most extreme example of this curvature of spacetime is a black hole, from which nothing—not light—can escape once past the black hole's event horizon. However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravity is the weakest of the four fundamental forces of physics 1038 times weaker than the strong force, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant force at the macroscopic scale, is the cause of the formation and trajectory of astronomical bodies. For example, gravity causes the Earth and the other planets to orbit the Sun, it causes the Moon to orbit the Earth, causes the formation of tides, the formation and evolution of the Solar System and galaxies; the earliest instance of gravity in the Universe in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a unknown manner. Attempts to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework with the other three forces of physics, are a current area of research.

Archimedes discovered the center of gravity of a triangle. He postulated that if the centers of gravity of two equal weights wasn't the same, it would be located in the middle of the line that joins them; the Roman architect and engineer Vitruvius in De Architectura postulated that gravity of an object didn't depend on weight but its "nature". Aryabhata first identified the force to explain why objects are not thrown out when the earth rotates. Brahmagupta described gravity as an attractive force and used the term "gruhtvaakarshan" for gravity. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous experiment dropping balls from the Tower of Pisa, with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects; this was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass fall more in an atmosphere.

Galileo's work set the stage for the formulation of Newton's theory of gravity. In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; the equation is the following: F = G m 1 m 2 r 2 Where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.

A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for under Newton's theory, but all searches for another perturbing body had been fruitless; the issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century. Although Newton's theory has been superseded by Einstein's general relativity, most modern non-relativistic gravitational calculations are still made using Newton

Loop quantum gravity

Loop quantum gravity is a theory of quantum gravity, merging quantum mechanics and general relativity, making it a possible candidate for a theory of everything. Its goal is to unify gravity in a common theoretical framework with the other three fundamental forces of nature, beginning with relativity and adding quantum features, it competes with string theory that adds gravity. From the point of view of Einstein's theory, all attempts to treat gravity as another quantum force equal in importance to electromagnetism and the nuclear forces have failed. According to Einstein, gravity is not a force – it is a property of spacetime itself. Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation. To do this, in LQG theory space and time are quantized, analogously to the way quantities like energy and momentum are quantized in quantum mechanics; the theory gives a physical picture of spacetime where space and time are granular and discrete directly because of quantization just like photons in the quantum theory of electromagnetism and the discrete energy levels of atoms.

Distance exists with a minimum. Space's structure prefers an fine fabric or network woven of finite loops; these networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length 10−35 metres, smaller scales do not exist. Not just matter, but space itself, prefers an atomic structure; the vast areas of research developed in several directions that involve about 30 research groups worldwide. They all share the basic physical assumptions and the mathematical description of quantum space. Research follows two directions: the more traditional canonical loop quantum gravity, the newer covariant loop quantum gravity, called spin foam theory. Physical consequences of the theory proceed in several directions; the most well-developed applies to cosmology, called loop quantum cosmology, the study of the early universe and the physics of the Big Bang. Its greatest consequence sees the evolution of the universe continuing beyond the Big Bang called the Big Bounce.

In 1986, Abhay Ashtekar reformulated Einstein's general relativity in a language closer to that of the rest of fundamental physics. Shortly after, Ted Jacobson and Lee Smolin realized that the formal equation of quantum gravity, called the Wheeler–DeWitt equation, admitted solutions labelled by loops when rewritten in the new Ashtekar variables. Carlo Rovelli and Lee Smolin defined a nonperturbative and background-independent quantum theory of gravity in terms of these loop solutions. Jorge Pullin and Jerzy Lewandowski understood that the intersections of the loops are essential for the consistency of the theory, the theory should be formulated in terms of intersecting loops, or graphs. In 1994, Rovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum; that is, geometry is quantized. This result defines an explicit basis of states of quantum geometry, which turned out to be labelled by Roger Penrose's spin networks, which are graphs labelled by spins.

The canonical version of the dynamics was put on firm ground by Thomas Thiemann, who defined an anomaly-free Hamiltonian operator, showing the existence of a mathematically consistent background-independent theory. The covariant or spin foam version of the dynamics developed during several decades, crystallized in 2008, from the joint work of research groups in France, Canada, UK, Germany, leading to the definition of a family of transition amplitudes, which in the classical limit can be shown to be related to a family of truncations of general relativity; the finiteness of these amplitudes was proven in 2011. It requires the existence of a positive cosmological constant, this is consistent with observed acceleration in the expansion of the Universe. In theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations; the essential idea is that coordinates are only artifices used in describing nature, hence should play no role in the formulation of fundamental physical laws.

A more significant requirement is the principle of general relativity that states that the laws of physics take the same form in all reference systems. This is a generalization of the principle of special relativity which states that the laws of physics take the same form in all inertial frames. In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds, it is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. These are the defining symmetry transformations of General Relativity since the theory is formulated only in terms of a differentiable manifold. In general relativity, general covariance is intimately related to "diffeomorphism invariance"; this symmetry is one of the defining features of the theory. However, it is a common misunderstanding that "diffeomorphism invariance" refers to the invariance of the physical predictions of a theory under arbitrary coordinate transformations. Diffeomorphisms, as mathematicians define them, correspond to something much more radical.

Diffeomorphisms are the true symmetry transformations of general relativity, come about from the assertion that the formulation of the theory is based on a bare different

General relativity

General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present; the relation is specified by the Einstein field equations, a system of partial differential equations. Some predictions of general relativity differ from those of classical physics concerning the passage of time, the geometry of space, the motion of bodies in free fall, the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the gravitational time delay; the predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date.

Although general relativity is not the only relativistic theory of gravity, it is the simplest theory, consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes; the bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO.

In addition, general relativity is the basis of current cosmological models of a expanding universe. Acknowledged as a theory of extraordinary beauty, general relativity has been described as the most beautiful of all existing physical theories. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations; these equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, form the core of Einstein's general theory of relativity. The Einstein field equations are nonlinear and difficult to solve.

Einstein used approximation methods in working out initial predictions of the theory. But as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric; this solution laid the groundwork for the description of the final stages of gravitational collapse, the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, which resulted in the Reissner–Nordström solution, now associated with electrically charged black holes. In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption. By 1929, the work of Hubble and others had shown that our universe is expanding; this is described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant.

Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an hot and dense earlier state. Einstein declared the cosmological constant the biggest blunder of his life. During that period, general relativity remained something of a curiosity among physical theories, it was superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters. A 1919 expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, 1919, making Einstein famous, yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between 1960 and 1975, now known as the golden age of general relativity. Physicists began to understand the concept of a black hole, to identify quasars as one of these objects' astrophysical manifestations.

More precise solar system tests confirmed the theory's predictive power, relativistic cosmology, became amenable to direct observational tests. Over the years, general relativity has acqui

String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force, thus string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, condensed matter physics, it has stimulated a number of major developments in pure mathematics; because string theory provides a unified description of gravity and particle physics, it is a candidate for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter.

Despite much work on these problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of its details. String theory was first studied in the late 1960s as a theory of the strong nuclear force, before being abandoned in favor of quantum chromodynamics. Subsequently, it was realized that the properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity; the earliest version of string theory, bosonic string theory, incorporated only the class of particles known as bosons. It developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990s that they were all different limiting cases of a single theory in eleven dimensions known as M-theory. In late 1997, theorists discovered an important relationship called the AdS/CFT correspondence, which relates string theory to another type of physical theory called a quantum field theory.

One of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. Another issue is that the theory is thought to describe an enormous landscape of possible universes, this has complicated efforts to develop theories of particle physics based on string theory; these issues have led some in the community to criticize these approaches to physics and question the value of continued research on string theory unification. In the twentieth century, two theoretical frameworks emerged for formulating the laws of physics; the first is Albert Einstein's general theory of relativity, a theory that explains the force of gravity and the structure of space and time. The other is quantum mechanics, a different formulation to describe physical phenomena using the known probability principles. 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.

In spite of these successes, there are still many problems. One of the deepest problems in modern physics is the problem of quantum gravity; 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. 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. 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, the early universe. String theory is a theoretical framework that attempts to address many others; the starting point for string theory is the idea that the point-like particles of particle physics can be modeled as one-dimensional objects called strings. String theory describes how strings propagate through 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, it can vibrate in different ways. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its mass 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. In string theory, one of the vibrational states of the string gives rise to the graviton, a quantum mechanical particle that carries gravitational force, thus string theory is a theory of quantum gravity. One of the main developments of the past several decades in string theory was the discovery of certain "dualities", mathematical transformations that identify one physical theory with another. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as M-theory.

Studies of string theory have yielded a number of results on the nature of black holes and the gravitational interaction. There are certain paradoxes that arise when one attempts to understand the quantum aspects of black holes, work on string theory