Two-dimensional visualisation of space-time distortion. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity.

General relativity (GR) or general relativity theory (GRT) is a fundamental physical theory of gravitation which corrects and extends Newtonian gravitation, especially at the macroscopic level of stars or planets. Illustration of spacetime curvature. ... Illustration of spacetime curvature. ... Antonym of psychical. ... The word theory has a number distinct meanings depending on the context. ... This article covers the physics of gravitation. ... This article covers the physics of gravitation. ...

General relativity may be regarded as an extension of special relativity, this latter theory correcting Newtonian mechanics at high velocities. General relativity has a unique role amongst physical theories in the sense that it interprets the gravitational field as a geometric phenomenon. More specifically, it assumes that any object possessing mass curves the 'space' in which it exists, this curvature being equated to gravity. It deals with the motion of bodies in such 'curved spaces' and has survived every experimental test performed on it since its formulation by Albert Einstein in 1915. Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... Classical mechanics is a model of the physics of forces acting upon bodies. ... The gravitational field is a field that causes bodies with mass to attract each other. ... Portrait of Albert Einstein taken by Yousuf Karsh on February 11, 1948 Albert Einstein (March 14, 1879 – April 18, 1955) was a theoretical physicist who is widely regarded as the greatest scientist of the 20th century. ...

General relativity forms the basis for modern studies in fields such as astronomy, cosmology and astrophysics. It describes with great accuracy and precision many phenomena where classical physics fails, such as the perihelion motion of planets (classical physics cannot fully account for the perihelion shift of Mercury, for example) and the bending of starlight by the Sun (again, classical physics can only account for half the experimentally observed bending). It also predicts phenomena such as the existence of gravitational waves, black holes and the expansion of the universe. In fact, even Einstein himself initially believed that the universe cannot be expanding, but experimental observations of distant galaxies by Edwin Hubble finally forced Einstein to concede. Astronomy (Greek: αστρονομία = άστρον + νόμος, literally, law of the stars) is the science involving the observation and explanation of events occurring beyond the Earth and its atmosphere. ... Cosmology is the study of the large-scale structure and history of the universe. ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties ( luminosity, density, temperature and chemical composition) of astronomical objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... In science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual, nominal, or some other reference, value. ... The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ... The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ... This article is about the astronomical body. ... Wikipedia does not yet have an article with this exact name. ... Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was a noted American astronomer, generally credited for discovering1 the redshift of galaxies and that the universe is expanding. ... For other topics related to Einstein see Einstein (disambiguation). ...

Unlike the other revolutionary physical theory, quantum mechanics, general relativity was essentially formulated by one man - Albert Einstein. However, Einstein required the help of one of his friends, Marcel Grossmann, to help him with the mathematics of general relativity. Fig. ... Marcel Grossmann (born in Budapest on April 9th, 1878 - died in Zurich on September 7th, 1936) was a mathematician and a friend and classmate of Albert Einstein. ...

Physical Description of the Theory

In relativity theory, physical phenomena are described by observers making measurements in reference frames. In general relativity, these reference frames are arbitrarily moving relative to each other (unlike in special relativity, where the reference frames are assumed to be inertial). A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...

Consider two such reference frames, for example, one situated on Earth (the 'Earth-frame'), and another in orbit around the Earth (the 'orbit-frame'). An observer (O) in the orbit-frame will feel weightless as they 'fall' towards the Earth.

In Newtonian gravitation, O's motion is explained by the action at a distance formulation of gravity, where it is assumed that a force between the Earth and O causes O to move around the Earth. In Physics, action at a distance is the instantaneous interaction of two objects which are separated in space. ...

General relativity views the situation in a different manner, namely, by demonstrating that the Earth modifies ('warps') the geometry in its vicinity and O will naturally follow the curves (geodesics) in this geometry unless he applies accelerative force (e.g. rockets). More precisely, the presence of matter determines the geometry of spacetime, the physical arena in which all events take place. This is a profound innovation in physics, all other physical theories assuming the structure of the spacetime in advance. It is important to note that a given matter distribution will fix the spacetime once and for all. There are a few caveats here: (1) the spacetime within which the matter is distributed cannot be properly defined without the matter, so most solutions require special assumptions, such as symmetries, to allow the relativist to concoct a candidate spacetime, then see where the matter must lie, then require its properties be "reasonable" and so on. (2) Initial and boundary conditions can also be a problem, so that gravitational waves may violate the idea of the spacetime being fixed once and for all. In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. ... World line of the orbit of the Earth depicted as a circle in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, Z, making the circle appear as a helix. ... There are many kinds of events: In common language, an event is something that happens (changes). ... In physics, gravitational radiation is energy that is transmitted through waves in the gravitational field of space-time, according to Albert Einsteins theory of general relativity: The Einstein field equations imply that any accelerated mass radiates energy this way, in the same way as the Maxwell equations that any...

The motion of the observer O in orbit is rather like a ping-pong ball being forced to follow the 'dent' or depression created in a trampoline by a relatively massive object like a medicine ball. The geometry is determined by the medicine ball, the relatively light ping-pong ball causing no significant change in the local geometry. Thus, general relativity provides a simpler and more natural description of gravity than Newton's action at a distance formulation. An oft-quoted analogy used in visualising spacetime curvature is to imagine a universe of one-dimensional beings living in one dimension of space and one dimension of time. Each piece of matter is not a point on any imaginable curved surface, but a world line showing where that point moves as it goes from the past to the future. In Physics, action at a distance is the instantaneous interaction of two objects which are separated in space. ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ...

The precise means of calculating the geometry of spacetime given the matter distribution is encapsulated in Einstein's field equation. For other topics related to Einstein see Einstein (disambig) Introduction In physics, the Einstein field equation or Einstein equation is a tensor equation in the theory of gravitation. ...

The Equivalence Principle

(For more detailed information about the equivalence principle, see equivalence principle)

Inertial reference frames, in which bodies maintain a uniform state of motion unless acted upon by another body, are distinguished from non-inertial frames, in which freely moving bodies have an acceleration deriving from the reference frame itself. Einsteins principle of equivalence states that the (local) effects of a gravitational field are identical in all respects to the effect of uniform acceleration. ...

In non-inertial frames there is a perceived force which is accounted for by the acceleration of the frame, not by the direct influence of other matter. Thus we feel acceleration when cornering on the roads when we use a car as the physical base of our reference frame. Similarly there are coriolis and centrifugal forces when we define reference frames based on rotating matter (such as the Earth or a child's roundabout). In Newtonian mechanics, the coriolis and centrifugal forces are regarded as non-physical ones, arising from the use of a rotating reference frame. In General Relativity there is no way, locally, to define these "forces" as distinct from those arising through the use of any non-inertial reference frame. In physics, the Coriolis effect or Coriolis force is a manifestation of inertia first described in full by Gaspard-Gustave Coriolis, a French scientist, in 1835. ... The expression centrifugal force is used to express that if an object is being swung around on a string the object seems to be pulling on the string. ... Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ...

The principle of equivalence in general relativity states that there is no local experiment to distinguish non-rotating free fall in a gravitational field from uniform motion in the absence of a gravitational field. In relativity the equivalence principle is applied to several related concepts dealing with the uniformity of physical measurements in different frames of reference. ...

In short there is no gravity in a reference frame in free fall. From this perspective the observed gravity at the surface of the Earth is the force observed in a reference frame defined from matter at the surface which is not free, but is acted on from below by the matter within the Earth, and is analogous to the acceleration felt in a car.

In the process of discovering GR, Einstein used a fact that was known since the time of Galileo, namely, that the inertial and gravitational masses of an object happen to be the same. He used this as the basis for the principle of equivalence, which describes the effects of gravitation and acceleration as different perspectives of the same thing (at least locally), and which he stated in 1907 as: In relativity the equivalence principle is applied to several related concepts dealing with the uniformity of physical measurements in different frames of reference. ... Acceleration is the time rate of change of velocity, and at any point on a v-t graph, it is given by the gradient of the tangent to that point In physics, acceleration (symbol: a) is defined as the rate of change (or time derivative) of velocity. ... 1907 was a common year starting on Tuesday (see link for calendar). ...

We shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame.

In other words, he postulated that no experiment can locally distinguish between a uniform gravitational field and a uniform acceleration. The meaning of the Principle of Equivalence has gradually broadened, in consonance with Einstein's further writings, to include the concept that no physical measurement within a given unaccelerated reference system can determine its state of motion. This implies that it is impossible to measure, and therefore virtually meaningless to discuss, changes in fundamental physical constants, such as the rest masses or electrical charges of elementary particles in different states of relative motion. Any measured change in such a constant would represent either experimental error or a demonstration that the theory of relativity was wrong or incomplete. A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ... In particle physics, an elementary particle is a particle of which other, larger particles are composed. ...

The equivalence principle explains the experimental observation that inertial and gravitational mass are equivalent. Moreover, the principle implies that some frames of reference must obey a non-Euclidean geometry: that spacetime is curved (by matter and energy), and gravity can be seen purely as a result of this geometry. This yields many predictions such as gravitational redshifts and light bending around stars, black holes, time slowed by gravitational fields, and slightly modified laws of gravitation even in weak gravitational fields. However, it should be noted that the equivalence principle does not uniquely determine the field equations of curved spacetime, and there is a parameter known as the cosmological constant which can be adjusted. Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... World line of the orbit of the Earth depicted as a circle in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, Z, making the circle appear as a helix. ... Curvature is the amount by which a geometric object deviates from being flat. ... Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Theaetetus dealing with spatial relationships. ... This article is about the astronomical body. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...

The Covariance Principle

Following on from the spirit of special relativity, the principle of general covariance states that all coordinate systems are equivalent for the formulation of the general laws of nature. Mathematically, this suggests that the laws of physics should be tensor equations. The principle of general covariance states that the laws of physics should take the same form in all coordinate systems. ... This is the current mathematics collaboration of the week! Please help improve it to featured article standard. ...

Foundations

General relativity's mathematical foundations go back to the axioms of Euclidean geometry and the many attempts over the centuries to prove Euclid's fifth postulate, that parallel lines remain always equidistant, culminating with the realisation by Lobachevsky, Bolyai and Gauss that this postulate need not be true. It is an eternal monument to Euclid's genius that he classified this principle as a postulate and not as an axiom. The general mathematics of non-Euclidean geometries was developed by Gauss' student, Riemann, but these were thought to be mostly inapplicable to the real world until Einstein developed his theory of relativity. The existing applications were restricted to the geometry of curved surfaces in Euclidean space, as if one lived and moved in such a surface, and to the mechanics of deformable bodies. While such applications seem trivial compared to the calculations in the four dimensional spacetimes of general relativity, they provided a minimal development and test environment for some of the equations. In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. ... In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ... Euclid of Alexandria (Greek: ) (circa 365–275 BC) was a Greek mathematician, now known as the father of geometry. His most famous work is Elements, widely considered to be historys most successful textbook. ... In geometry, the parallel postulate, also called Euclids fifth postulate since it is the fifth postulate in Euclids Elements, is a distinctive axiom in what is now called Euclidean geometry. ... Nikolay Ivanovich Lobachevsky Nikolai Ivanovich Lobachevsky (Никола́й Ива́нович Лобаче́вский) (December 1, 1792 - February 24, 1856) was a Russian mathematician. ... János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician. ... Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 - February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. ... The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Bernhard Riemann. ...

Gauss had realised that there is no a priori reason for the geometry of space to be Euclidean. This means that if a physicist holds up a stick, and a cartographer stands some distance away and measures its length by a triangulation technique based on Euclidean geometry, then he is not guaranteed to get the same answer as if the physicist brings the stick to him and he measures its length directly. Of course, for a stick he could not in practice measure the difference between the two measurements, but there are equivalent measurements which do detect the non-Euclidean geometry of space-time directly; for example the Pound-Rebka experiment (1959) detected the change in wavelength of light from a cobalt source rising 22.5 meters against gravity in a shaft in the Jefferson Physical Laboratory at Harvard, and the rate of atomic clocks in GPS satellites orbiting the Earth has to be corrected for the effect of gravity. A priori is a Latin phrase meaning from the former or less literally before experience. In much of the modern Western tradition, the term a priori is considered to mean propositional knowledge that can be had without, or prior to, experience. ... 1959 was a common year starting on Thursday (link will take you to calendar). ... General Name, Symbol, Number cobalt, Co, 27 Chemical series transition metals Group, Period, Block 9 , 4, d Density, Hardness 8. ... Harvard University is a private university in Cambridge, Massachusetts, USA and a member of the Ivy League. ... An atomic clock is a type of clock that uses an atomic resonance frequency standard as its counter. ... Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ... A satellite is an object that orbits another object (known as its primary). ...

Newton's theory of gravity had assumed that objects had absolute velocities: that some things really were at rest while others really were in motion. He realized, and made clear, that there was no way these absolutes could be measured. All the measurements one can make provide only velocities relative to one's own velocity (positions relative to one's own position, and so forth), and all the laws of mechanics would appear to operate identically no matter how one was moving. Newton believed, however, that the theory could not be made sense of without presupposing that there are absolute values, even if they cannot be experimental error or a demonstration that the theory of relativity was wrong or incomplete. This article is about the SI unit of force. ...

The equivalence principle explains the experimental observation that inertial and gravitational mass are equivalent. Moreover, the principle implies that some frames of reference must obey a non-Euclidean geometry: that spacetime is curved (by matter and energy), and gravity can be seen purely as a result of this geometry. This yields many predictions such as gravitational redshifts and light bending around stars, black holes, time slowed by gravitational fields, and slightly modified laws of gravitation even in weak gravitational fields. However, it should be noted that the equivalence principle does not uniquely determine the field equations of curved spacetime, and there is a parameter known as the cosmological constant which can be adjusted. Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... World line of the orbit of the Earth depicted as a circle in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, Z, making the circle appear as a helix. ... Curvature is the amount by which a geometric object deviates from being flat. ... Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Theaetetus dealing with spatial relationships. ... This article is about the astronomical body. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...

Predictions of GR

(For more detailed information about tests and predictions of general relativity, see Tests of general relativity)

Like any good scientific theory, general relativity makes predictions which can be tested. Some of the predictions of general relativity include the perihelion shifts of planet orbits ( particularly that of Mercury ), bending of light by massive objects, and the existence of gravitational waves. The first two of these tests have been verified to a high degree of accuracy and precision. Most researchers believe in the existence of gravitational waves, but more accurate experiments are needed to raise this prediction to the status of the other two, if one demands direct detection of the waves. Nevertheless, indirect effects of gravitational wave emission have been observed for a binary system of orbiting neutron stars, as described in Tests of general relativity. The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ... In mathematics, theory is used informally to refer to a body of knowledge about mathematics. ... The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ...

Other predictions include the expansion of the universe, the existence of black holes and possibly the existence of wormholes. The existence of black holes is generally accepted, but the existence of wormholes is still very controversial, many researchers believing that wormholes may exist only in the presence of exotic matter. The existence of white holes is very speculative, as they appear to contradict the second law of thermodynamics. Wikipedia does not yet have an article with this exact name. ... This article is about the astronomical body. ... 2D analogy to a wormhole. ... Exotic matter is a hypothetical concept of particle physics. ... In astrophysics, a white hole is a postulated celestial body that spews out matter, in essence an anti-black hole, or the time reversal of a black hole. ...

Many other quantitative predictions of general relativity have since been confirmed by astronomical observations. One of the most recent, the discovery in 2003 of PSR J0737-3039, a binary neutron star in which one component is a pulsar and where the perihelion precesses 16.88° per year (or about 140,000 times faster than the precession of Mercury's perihelion), enabled the most precise experimental verification yet of the effects predicted by general relativity. [1] (http://skyandtelescope.com/news/article_1124_1.asp) [2] (http://skyandtelescope.com/news/article_1473_1.asp). 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January January 1 - Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ... Artists impression. ... A neutron star is a compact star in which the weight of the star is carried by the pressure of free neutrons. ... Composite Optical/X-ray image of the Crab Nebula pulsar, showing surrounding nebular gases stirred by the pulsars magnetic field and radiation. ...

Mathematics of GR

(For more detailed information about the mathematics of general relativity, see mathematics of general relativity)

The idea of curvature can be clarified by the following considerations. While it can be helpful for visualization to imagine a curved surface sitting in a space of higher dimension, this model is not very useful for the real universe; although a two dimensional surface can be embedded in three, and thus visualized well, a curved four dimensional spacetime such as our universe cannot be imbedded in a flat space of even five dimensions, but many more are required. Curvature can be measured entirely within a surface, and similarly within a higher-dimensional manifold such as space or spacetime. On Earth, if you start at the North Pole, walk south for about 10,000 km (to the Equator), turn left by 90 degrees, walk for 10,000 more km, and then do the same again (walk for 10,000 more km, turn left by 90 degrees, walk for 10,000 more km), you will be back where you started. Such a triangle with three right angles is only possible because the surface of the earth is curved. The curvature of spacetime can be evaluated, and indeed given meaning, in a similar way. Curvature may be quantified by the Riemann tensor, essentially a matrix of numbers which describes how a vector that is moved along a curve parallel to itself changes when a round trip is made. In flat space, the vector returns to the same orientation, but in a curved space it generally does not. In spaces of two dimensions, the Riemann tensor is a matrix (i.e., just a number) called the Gaussian or scalar curvature. To formulate the description of gravity as a geometric phenomena, the idea of a spacetime is used, as it incorporates a very useful mathematical structure known as a manifold. ... In mathematics, a manifold M is a type of space, characterized in one of two equivalent ways: near every point of the space, we have a coordinate system; or near every point, the environment is like that in Euclidean space of a given dimension. ... Curvature is the amount by which a geometric object deviates from being flat. ... In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest way of describing the curvature of a Riemannian manifold. ...

Relationship to other physical theories

Special and general relativity

In relativity theory, all events are referred to a reference frame. A reference frame is defined by choosing particular matter as the basis for its definition. Thus, all motion is defined and quantified relative to other matter. In the special theory of relativity it is assumed that reference frames can be extended indefinitely in all directions in space and time. The theory of special relativity concerns itself with reference frames that move at a constant velocity with respect to each other (i.e. inertial reference frames), whereas general relativity deals with all frames of reference. In the general theory it is recognised that we can only define local frames to given accuracy for finite time periods and finite regions of space (similarly we can draw flat maps of regions of the surface of the earth but we cannot extend them to cover the whole surface without distortion). In general relativity Newton's laws are assumed to hold in locally inertial reference frames. Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... There are many kinds of events: In common language, an event is something that happens (changes). ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... Sir Isaac Newton in Knellers 1689 portrait Sir Isaac Newton (25 December 1642 – 20 March 1727 by the Julian calendar in use in England at the time; or 4 January 1643 – 31 March 1727 by the Gregorian calendar) was an English physicist, mathematician, astronomer, philosopher, and alchemist who wrote...

The special theory of relativity (1905) modified the equations used in comparing the measurements made by differently moving bodies, in view of the constant value of the speed of light, i.e. its observed invariance in reference frames moving uniformly relative to each other. This had the consequence that physics could no longer treat space and time separately, but only as a single four-dimensional system, "space-time," which was divided into "time-like" and "space-like" directions differently depending on the observer's motion. The general theory added to this that the presence of matter "warped" the local space-time environment, so that apparently "straight" lines through space and time have the properties we think of "curved" lines as having. Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... 1905 was a common year starting on Sunday (see link for calendar). ... Cherenkov effect in a swimming pool nuclear reactor. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... The word space has many meanings, including: Physics The definition of space in physics is contentious. ... 8:17 am, August 6, 1945, Japanese time. ...

Thus Newton's first law is replaced by the law of geodesic motion.

There are no known experimental results that suggest that a theory of gravity radically different from general relativity is necessary. For example, the Allais effect was initially speculated to demonstrate "gravitational shielding," but was subsequently explained by conventional phenomena. Photo taken by John Walker during the Zambia 2001 eclipse Allaiss paraconical pendulum The Allais effect is a claimed anomalous precession of the plane of oscillation of a pendulum during a solar eclipse. ...

Quantum mechanics and general relativity

There are good theoretical reasons for considering general relativity to be incomplete. General relativity does not include quantum mechanics, and this causes the theory to break down at sufficiently high energies. A continuing unsolved challenge of modern physics is the question of how to correctly combine general relativity with quantum mechanics, thus applying it also to the smallest scales of time and space. Fig. ... Fig. ...

Other theories

The Brans-Dicke theory and the Rosen bi-metric theory are modifications of general relativity and cannot be ruled out by current experiments. Brans-Dicke theory is an extension to Einsteins theory of general relativity. ...

There have been attempts to formulate consistent theories which combine gravity and electromagnetism, some of the first being the Kaluza-Klein theory and Weyl's gauge theory. Kaluza-Klein theory (or KK theory, for short) is a model which sought to unify classical gravity and electromagnetism. ...

Nonlinearity of the field equations

The field equations of general relativity are a set of nonlinear partial differential equations for the metric. As such, this distinguishes the field equations of general relativity from some of the other important field equations in physics, such as Maxwell's equations (which are linear in the electric and magnetic fields) and Schrodinger's equation (which is linear in the wavefunction). A field equation is an equation in a physical theory that describes how a fundamental force (or a combination of such forces) interacts with matter. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...

History

Full article: The development of general relativity
See also: Tests of general relativity The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ...

The development of general relativity began in 1907 with the publication of an article by Einstein on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the Equivalence principle. Einstein also predicted the existance of gravitational time dilation in the 1907 article. In 1911, Einstein published another article expanding on the 1907 article, in which additional effects such as the deflection of light by massive bodies were predicted. 1907 was a common year starting on Tuesday (see link for calendar). ... Freefall or free fall in the strict sense is the condition of acceleration which is due only to gravity. ... Einsteins principle of equivalence states that the (local) effects of a gravitational field are identical in all respects to the effect of uniform acceleration. ... Gravitational time dilation is a phenomenon of the time running at the vicinity of a mass slower than at infinite distance from that mass (in space without any other masses). ... A database query syntax error has occurred. ...

By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. At the urging of Levi-Civita, Einstein started by exploring the use of general covariance (which is essentially the use of curvature tensors) to create a gravitational theory. However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "hole argument". In 1914 and much of 1915, Einstein was trying to create field equations based on another approach. When that approach was proven to be inconsistent, Einstein revisited the concept of general covariance and discovered that the hole argument was flawed. Realizing that general covariance was tenable, Einstein quickly completed the development of the field equations that are named after him. Tullio Levi-Cività (March 29, 1873 - December 29, 1941) was an Italian mathematician, most famous for his work on tensor calculus but who also made significant contributions in other areas, some related to this work and some not. ... For more technical Wiki articles on tensors, see the section later in this article. ... 1913 is a common year starting on Wednesday. ...

In this final phase, Einstein made one famous goof. In October of 1914, Einstein published field equations that were

R_μν = T_μν.

These field equations predicted the non-Newtonian perihelion precession of Mercury, and so had Einstein very excited. However, it was soon realized that they were inconsistent with the local conservation of energy-momentum unless the universe had of a constant density of mass-energy-momentum. In other words, air, rock, and even vacuum should all have the same density! This inconsistency with observation sent Einstein back to the drawing board. However, the solution was all but obvious, and in November of 1915 Einstein published the actual Einstein field equations:

R_μν − (1 / 2)Rg_μν = T_μν.

With the publication of the field equations, the issue became one of solving them for various cases and interpreting the solutions. This and experimental verification have dominated general relativity research ever since.

Since the field equations are non-linear, Einstein assumed that they were insolvable. He was disabused of this notion in 1916, when Karl Schwarzschild sent him an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in spherical coordinates. This is now known as the Schwarzschild solution. Since then many other exact solutions have been found. 1916 is a leap year starting on Saturday (link will take you to calendar) Events January-February January 1 -The first successful blood transfusion using blood that had been stored and cooled. ... Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a noted German Jewish physicist and astronomer, father of astrophysicist Martin Schwarzschild. ...

The expansion of the universe created an interesting episode for general relativity. In 1922, Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe. Einstein did not believe in an expanding universe, and so he once again edited the field equations, adding in a cosmological constant Λ. The revised field equations were 1922 was a common year starting on Sunday (see link for calendar). ... Alexander Alexandrovich Friedman (June 16, 1888 – September 16, Russian cosmologist and mathematician. ... Georges-Henri Lemaître ( July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest and astronomer. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...

R_μν − (1 / 2)Rg_μν + Λg_μν = T_μν.

This permitted the creation of steady-state solutions, but they were notorious for being unstable: The slightest deviation from an ideal state would still result in the universe expanding or contracting. In 1929 Edwin Hubble showed that the universe actually is expanding. This resulted in Einstein dropping the Cosmological constant, referring to it as "the biggest blunder in my career". 1929 was a common year starting on Tuesday (link will take you to calendar). ... Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was a noted American astronomer, generally credited for discovering1 the redshift of galaxies and that the universe is expanding. ...

Progress in solving the field equations and understanding the solutions has been ongoing. The solution for a spherically symmetric charged object was discovered by Reissner and later rediscovered by Nordström, and is called the Reissner-Nordström solution. The black hole aspect of the Schwarzschild solution was very controversial, and Einstein did not beleive it. However, in 1957 (two years after Einstein's death in 1955), Kruskal published a proof that black holes are called for by the Schwarzschild Solution. Additionally, the solution for a rotataing massive object was obtained by Kerr in the 1960's as is called the Kerr solution. The Kerr-Newman solution for a rotatating, charged massive object was published a few years later. 1957 was a common year starting on Tuesday (link will take you to calendar). ... 1955 is a common year starting on Saturday. ... People named Kerr: Archibald John Kerr Clark Kerr, 1st Baron Inverchapel, British diplomat Baine Kerr, Huston lawyer Ben Kerr, Canadian author Bill Kerr, actor Bobby Kerr, Irish-Canadian sprinter Brian Kerr, Irish soccer manager Brooke Kerr; American actress Clark Kerr, first Chancellor of the University of California, Berkeley David Kerr...

Observationally, general relativity has a history too. The perihelion precession of Mercury was the first evidence that general relativity is correct. Eddington's 1919 expedition in which he confirmed Einstein's prediction for the deflection of light by the Sun helped to cement the status of general relativity as a likely true theory. Since then many observations have confirmed the correctness of general relativity. These include studies of binary pulsars, observations of radio signals passing the limb of the Sun, and even the GPS system. For more information, see the Tests of general relativity article. Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ... The three principal experimental tests of general relativity are the perihelion shift of the planet Mercurys orbit, the bending of starlight by a massive object and the existence of gravitational waves. ...

Finally, there have been various attempts through the years to find modifications to general relativity. The most famous of these are the Brans-Dicke theory (also known as scalar-tensor theory), and Rosen's bimetric theory. Both of these proposed changes to the field equations, and both have been found to be in conflict with observation. In fact, the viability of any approach that changes the field equations is doubful due to a proof published in the 1990s that only the Einstein Field Equations can provide both self-consistency and local consistency with special relativity. However, general relativity is known to be inconsistent with quantum mechanics, a theory which has been better verified than general relativity. So speculation continues that some modification of general relativity is needed. Brans-Dicke theory is an extension to Einsteins theory of general relativity. ... Fig. ...

Quotes

The theory appeared to me then, and still does, the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill. But its connections with experience were slender. It appealed to me like a great work of art, to be enjoyed and admired from a distance. —Max Born

Max Born (December 11, 1882 – January 5, 1970) was a Jewish German mathematician and physicist and was the only child of Gustav Born and Margarete Kauffmann. ...

References

Textbooks

• Bernard F. Schutz, A First Course in General Relativity, Cambridge University Press (2003). This book focuses on the key mathematical building block of relativity: Tensor analysis. Schutz assumes a solid knowledge on vectors and calculus.
• Carroll, Sean M., Spacetime and Geometry: An introduction to general relativity (http://pancake.uchicago.edu/~carroll/grbook/), Addison Wesley, San Francisco (2004). ISBN 0-8053-8732-3. A modern graduate level textbook.
• Robert M. Wald, General Relativity, University Of Chicago Press (1984). A valuable reference for GR. The book contains a very good treatment of energy in GR, Killing vector fields, and ADM energy-momentum.
• D'Inverno, Ray, Introducing Einstein's Relativity, Oxford University Ass Press (1993). A modern undergraduate level text.
• Misner, Charles, Kip Thorne, and John Wheeler, Gravitation, Freeman (1973). ISBN 0716703440. A classic graduate level text book, which, if somewhat long winded, pays more attention to the geometrical basis and the development of ideas in general relativity than some other approaches.

For more technical Wiki articles on tensors, see the section later in this article. ... 2004 is a leap year starting on Thursday of the Gregorian calendar. ... 1993 is a common year starting on Friday of the Gregorian calendar and marked the Beginning of the International Decade to Combat Racism and Racial Discrimination (1993-2003) Events Media:January January 1 - Czechoslovakia divides. ... Kip S. Thorne Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in the field of gravitation physics and astrophysics. ... John Archibald Wheeler (born 1911) is an American theoretical physicist. ... 1973 was a common year starting on Monday. ...

Online notes and courses

• Baez, Bunn, 2001, The Meaning of Einstein's Equation (http://arxiv.org/abs/gr-qc/0103044), intuitive explanation of Einstein-Hilbert equations - requires familiarity with special relativity.
• Carroll, Sean M., A No-Nonsense Introduction to General Relativity (http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf). Also see the notes from an earlier version of his above textbook: arXiv:gr-qc/9712019 (http://arxiv.org/abs/gr-qc/9712019).
• MIT 8.962 Course Notes (http://arcturus.mit.edu/8.962/notes.html) Notes and handouts from the MIT 8.962 course on General Relativity
• MIT OCW Site (http://ocw.mit.edu/OcwWeb/Physics/8-033Fall2003/CourseHome/index.htm) Notes and resources from the MIT open Courseware website
• Reflections on Relativity (http://www.mathpages.com/rr/rrtoc.htm) A complete online course on Relativity

Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ...

Other

• Bondi, Herman, Relativity and Common Sense, Heinemann (1964). A school level introduction to the principle of relativity by a renowned scientist.
• Einstein, Albert, Relativity: The special and general theory. ISBN 0517884410. The special and general relativity theories in their original form.
• Epstein, Lewis Caroll, Relativity Visualized. ISBN 093521805X. Requires no mathematical background. Actually explains general relativity, rather than merely hinting at it with a few metaphors.
• Perret, W. and G.B. Jeffrey, trans.: The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity, New York Dover (1923).
• Thorne, Kip, and Stephen Hawking, Black Holes and Time Warps, Papermac (1995). A recent popular account by leading experts.
• J. J. O'Connor and E. F. Robertson, History of General Relativity (http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.html) at the MacTutor History of Mathematics archive.
• The original 1915 article by David Hilbert containing the gravitational field equation.
• Malcolm MacCallum's GR News (http://www.maths.qmw.ac.uk/hyperspace/) service for current research in relativity.
• Thomas A. Ryckman's Early Philosophical Interpretations of GR (http://plato.stanford.edu/entries/genrel-early/) Stanford Encyclopedia of Philosophy

1964 was a leap year starting on Wednesday (link will take you to calendar). ... 1923 was a common year starting on Monday (link will take you to calendar). ... Kip S. Thorne Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in the field of gravitation physics and astrophysics. ... Stephen Hawking in his classroom. ... 1995 was a common year starting on Sunday of the Gregorian calendar. ... David Hilbert David Hilbert ( January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ...