General Relativity

General relativity

Introduction to... Mathematical formulation of... Image File history File links Download high resolution version (1024x768, 7 KB) Description: Gravitational light deflection at a neutron star Source: Gallery of Tempolimit Lichtgeschwindigkeit Date: 09. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... Newton’s conception and quantification of gravitation held until the beginning of the 20th century, when Albert Einstein extended the special relativity to form the general relativity (GR) theory. ... Notational point: General relativity articles using tensors will use the abstract index notation . ...

Fundamental concepts

Special relativity · Equivalence principle World line · Riemannian geometry The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. ... In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ...

Phenomena

Black hole · Event horizon · Lenses Waves · Singularity Frame-dragging · Geodetic effect Simulated view of a black hole in front of the Milky Way. ... For the science fiction film, see Event Horizon (film). ... This article or section is in need of attention from an expert on the subject. ... In physics, a gravitational wave is a fluctuation in the curvature of spacetime which propagates as a wave, traveling outward from a moving object or system of objects. ... A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. ... According to Albert Einsteins theory of general relativity, space and time get pulled out of shape near a rotating body in a phenomenon referred to as frame-dragging. ... The geodetic effect represents the effect of the curvature of spacetime, predicted by general relativity, on a spinning, moving body. ...

Equations

Linearized Gravity Einstein field equations It has been suggested that Weak-field approximation be merged into this article or section. ... This article or section is in need of attention from an expert on the subject. ...

Advanced theories

Kaluza-Klein Quantum gravity Kaluza-Klein theory (or KK theory, for short) is a model which sought to unify classical gravity and electromagnetism. ... This article or section does not adequately cite its references or sources. ...

Solutions

Schwarzschild · Kasner · Kerr Milne · Reissner-Nordström Robertson-Walker It has been suggested that Deriving the Schwarzschild solution be merged into this article or section. ... The Kasner metric is an exact solution to Einsteins theory of general relativity. ... In general relativity, the Kerr metric (or Kerr vacuum) describes the geometry of spacetime around a rotating massive body, such as a rotating black hole. ... Milnes model follows the description from special relativity of an observable universes spacetime diagram containing past and future light cones along with elsewhere in spacetime. ... In physics and astronomy, a Reissner-Nordström black hole, discovered by Gunnar Nordström and Hans Reissner, is a black hole that carries mass , electric charge , and no angular momentum. ... // The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations of general relativity and which describes a homogeneous, isotropic expanding/contracting universe. ...

Scientists

Einstein · Minkowski · Eddington Lemaître · Schwarzschild Robertson · Kerr · Friedman Chandrasekhar · Hawking · others Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is best known for his theory of relativity and specifically mass-energy equivalence, . He was awarded the 1921 Nobel Prize in Physics for his services to Theoretical Physics, and especially for his discovery of the... Hermann Minkowski. ... One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the English-speaking world. ... Father Georges-Henri Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer. ... Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a noted German Jewish physicist and astronomer, father of astrophysicist Martin Schwarzschild. ... Howard Percy Robertson (January 27, 1903 - August 26, 1961) was a scientist known for contributions related to cosmology and the uncertainty principle. ... Roy Patrick Kerr (1934- ) is a New Zealand born mathematician who is best known for discovering the famous Kerr vacuum, an exact solution to the Einstein field equation of general relativity, which models the gravitational field outside an uncharged rotating massive object, or even a rotating black hole. ... Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман) (June 16, 1888 – September 16, 1925) was a Russian cosmologist and mathematician. ... Chandrasekhar redirects here. ... Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ... This is a partial list of persons who have made major contributions to the development of standard mainstream general relativity. ...

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In the physics of relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. They are related to the Copernican idea that the laws of physics should be the same everywhere in the universe, to the equivalence of gravitational and inertial mass, and also to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference. Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and characterization of universal laws which govern matter, energy, space, and time. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... This article or section is in need of attention from an expert on the subject. ... The Copernican principle is the philosophical statement that no special observers should be proposed. ... Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is best known for his theory of relativity and specifically mass-energy equivalence, . He was awarded the 1921 Nobel Prize in Physics for his services to Theoretical Physics, and especially for his discovery of the... An inertial reference frame is one in which Newtons first and second laws of motion are valid. ...

History

Aristotle asserted that heavier objects fall faster than lighter ones. The equivalence principle emerged in the late 16th and early 17th centuries, when Galileo showed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated, thereby refuting Aristotle. These findings led to gravitational theory, which concludes that inertial and gravitational masses are identical. Aristotle (Greek: Aristotélēs) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... Galileo Galilei (15 February 1564 – 8 January 1642) was an Italian physicist, mathematician, astronomer, and philosopher who is closely associated with the scientific revolution. ... In the scientific method, an experiment (Latin: ex-+-periri, of (or from) trying), is a set of actions concerning phenomena. ... Acceleration is the time rate of change of velocity, and at any point on a velocity-time graph, it is given by the slope of the tangent to that point basicly. ... This article or section is in need of attention from an expert on the subject. ... “Gravity” redirects here. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ...

Christiaan Huygens used two frames of reference studying an elastic collision: one observer is on shore while the other is in a boat.

The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s² being the acceleration of gravity at the Earth's surface) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus: Image File history File links Collision_huygens. ... Image File history File links Collision_huygens. ... Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629 – July 8, 1695), was a Dutch mathematician, astronomer and physicist; born in The Hague as the son of Constantijn Huygens. ... 1907 (MCMVII) was a common year starting on Tuesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 13-day-slower Julian calendar). ... Adjectives: Terrestrial, Terran, Telluric, Tellurian, Earthly Atmosphere Surface pressure: 101. ... The term g force or gee force refers to the symbol g, the force of acceleration due to gravity at the earths surface. ...

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." (Einstein 1907)

That is, remaining at rest in a uniform gravitational field is physically equivalent to experiencing an acceleration (e.g. being at rest with respect to the Earth while under the influence of its gravitational field, is an accelerated state of motion). From this principle, Einstein deduced that free-fall is actually inertial motion. By contrast, in Newtonian mechanics, gravity is assumed to be a force. This force draws objects having mass towards the center of any massive body. At the Earth's surface, the force of gravity is counteracted by the mechanical resistance of the Earth's surface. So in Newtonian physics, a person at rest on the surface of a (non-rotating) massive object is in an inertial frame of reference. While this picture works very well for most calculations, the inertial mass in Newton's second law, F = ma, mysteriously equals the gravitational mass in Newton's law of universal gravitation. Under the equivalence principle, this mystery is solved because gravity is an acceleration from inertial motion caused by the mechanical resistance of the Earth's surface. These considerations suggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911: Free Fall opens with one of the most stunning first paragraphs I have ever, or am ever likely to, read. ... 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. ... It has been suggested that this article or section be merged with Classical mechanics. ... Gravity is a force of attraction that acts between bodies that have mass. ... In physics, force is an influence that may cause a body to accelerate. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... It has been suggested that this article or section be merged into Gravity. ...

"Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of each object, that observer is in an accelerated frame of reference."

Einstein also referred to two reference frames, K and K'. K is a uniform gravitational field, whereas K' has no gravitational field but is uniformly accelerated such that objects in the two frames experience identical forces:

"We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course." (Einstein 1911)

This observation was the start of a process that culminated in general relativity. Einstein suggested that it should be elevated to the status of a general principle when constructing his theory of relativity: General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ...

"As long as we restrict ourselves to purely mechanical processes in the realm where Newton's mechanics holds sway, we are certain of the equivalence of the systems K and K'. But this view of ours will not have any deeper significance unless the systems K and K' are equivalent with respect to all physical processes, that is, unless the laws of nature with respect to K are in entire agreement with those with respect to K'. By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. For by theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes in a homogeneous gravitational field." (Einstein 1911)

Einstein combined the equivalence principle with special relativity to predict that clocks run at different rates in a gravitational potential, and light rays bend in a gravitational field, even before he developed the concept of curved spacetime. It is important to note that any accelerated frame of reference has a gravitational potential associated with it. Therefore clocks displaced in the direction of acceleration with respect to an accelerating rocket will be found to be going faster or slower by the observer in the accelerating rocket in accord with gravitational time dilation. The same applies to other gravitaitional effects such as gravitational red shifting and the bending of light. The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... In physics, gravitational potential is the measure of potential energy an object possesses due to its position in a gravitational field. ... 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. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. ... For other topics related to Einstein see Einstein (disambig) In the general theory of relativity by Albert Einstein, the gravitational redshift or Einstein shift is the effect that clocks in a gravitational field tick slower when observed by a distant observer. ...

So the original equivalence principle, as described by Einstein, concluded that free fall and inertial motion were physically equivalent. This form of the equivalence principle can be stated as follows. An observer in a windowless room cannot distinguish between being on the surface of the Earth, and being in a spaceship in deep space accelerating at 1g. This is not strictly true, because massive bodies give rise to tidal effects (caused by variations in the strength and direction of the gravitational field) which are absent from an accelerating spaceship in deep space. Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...

Although the equivalence principle guided the development of general relativity, it is not a founding principle of relativity but rather a simple consequence of the geometrical nature of the theory. In general relativity, objects in free fall follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doing so. General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... Gravity is a force of attraction that acts between bodies that have mass. ...

Contemporary extensions of the equivalence principle began in 1937 when Paul Dirac formulated his large numbers hypothesis, asserting that large, dimensionless numbers should not arise as fundamental quantities in physics: there should only be one fundamental energy scale in physics. He claimed that the following coincidence supported the hypothesis. In a hydrogen atom, the electron and proton are bound by gravitational as well as electrostatic forces. The dimensionless ratio of the strengths of those forces,about 10⁴⁰, is of the same order of magnitude as the age of the universe, measured in units of time required for light to cross a hydrogen atom. Dirac proposed to explain this surprising coincidence by postulating that Newton's constant varied inversely with the age of the universe; hence the feebleness of gravity followed from the age of the universe. While Dirac turned out to be wrong, he gave the first coherent argument for why the laws of physics may vary over space and time, and for why the values of the physical constants could be set dynamically rather than be fundamental. These ideas, together with Mach's principle – roughly, the idea that the inertia of a mass is a function of the amount and distribution of all mass in the universe – led physicists to scalar-tensor theories, such as Brans-Dicke theory, in which the value of the gravitational constant is determined dynamically. Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... The Dirac large numbers hypothesis refers to an observation made by Paul Dirac in 1937 relating ratios of size scales in the universe to that of force scales. ... In physics, energy scale is a particular value of energy determined with the precision of one order (or a few orders) of magnitude. ... Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius. ... e- redirects here. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. ... In theoretical physics, particularly in discussions of gravitation theories, Machs principle is the name given by Einstein to a vague hypothesis first supported by the physicist and philosopher Ernst Mach. ... This article or section is in need of attention from an expert on the subject. ...

Modern usage

Three forms of the equivalence principle are in current use: weak, Einsteinian, and strong.

The weak equivalence principle

The weak equivalence principle, also known as the universality of free fall:

The trajectory of a falling test body depends only on its initial position and velocity, and is independent of its composition.

or

All bodies at the same spacetime point in a given gravitational field will undergo the same acceleration.

The principle does not apply to large bodies, which might experience tidal forces, or heavy bodies, whose presence will substantially change the gravitational field around them. This form of the equivalence principle is closest to Einstein's original statement: in fact, his statements imply this one.

Since Einstein developed general relativity, there was a need to develop a framework to test the theory against other possible theories of gravity compatible with special relativity. This was developed by Robert Dicke as part of his program to test general relativity. Two new principles were suggested, the so-called Einstein equivalence principle and the strong equivalence principle, each of which assumes the weak equivalence principle as a starting point. They only differ in whether or not they apply to gravitational experiments. The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... Robert Henry Dicke (May 6, 1916 – March 4, 1997) was an American experimental physicist, who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity. ...

The Einstein equivalence principle states that the result of a local non-gravitational experiment in an inertial frame of reference is independent of the velocity or location in the universe of the experiment. This is a kind of Copernican extension of Einstein's original formulation, which requires that suitable frames of reference all over the universe behave identically. It is an extension of the postulates of special relativity in that it requires that dimensionless physical values such as the fine-structure constant and electron-to-proton mass ratio be constant. Many physicists believe that any Lorentz invariant theory that satisfies the weak equivalence principle also satisfies the Einstein equivalence principle. In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... e- redirects here. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ...

The strong equivalence principle states that the results of any local experiment, gravitational or not, in an inertial frame of reference are independent of where and when in the universe it is conducted. This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which have substantial internal gravitational interactions. It requires that the gravitational constant be the same everywhere in the universe and is incompatible with a fifth force. It is much more restrictive than the Einstein equivalence principle. General relativity is the only known theory of gravity compatible with this form of the equivalence principle. According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ...

Tests of the weak equivalence principle

Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. These experiments demonstrate that all objects fall at the same rate when the effect of air resistance is either eliminated or negligible. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum, and see if they hit the ground at the same time. More sophisticated tests use a torsion balance of a type invented by Loránd Eötvös. They verify the weak principle. Image:Lorand Eotvos. ...

Experiments are still being performed at the University of Washington which have placed limits on the differential acceleration of objects towards the Earth, the sun and towards dark matter in the galactic center. Future satellite experiments – STEP (Satellite Test of the Equivalence Principle), Galileo Galilei, and MICROSCOPE (MICROSatellite pour l'Observation de Principe d'Equivalence) – will test the weak equivalence principle in space, to much higher accuracy. It has been suggested that this article or section be merged with Joannes Philoponus. ... Simon Stevin Simon Stevin (1548/49 – 1620) was a Flemish mathematician and engineer. ... Nieuwe Kerk, Delft Nieuwe Kerk is a landmark church in Delft, the Netherlands. ... Galileo Galilei (15 February 1564 – 8 January 1642) was an Italian physicist, mathematician, astronomer, and philosopher who is closely associated with the scientific revolution. ... Sir Isaac Newton, (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist, regarded by many as the greatest figure in the history of science. ... Periodicity is the quality of occurring at regular intervals (e. ... Friedrich Wilhelm Bessel (July 22, 1784 – March 17, 1846) was a German mathematician, astronomer, and systematizer of the Bessel functions (which, despite their name, were discovered by Daniel Bernoulli). ... Image:Lorand Eotvos. ... // Mathmatics In mathematics, the term torsion has several meanings, mostly unrelated to each other. ... Gravity is a force of attraction that acts between bodies that have mass. ... A sphere rotating around its axis. ... Adjectives: Terrestrial, Terran, Telluric, Tellurian, Earthly Atmosphere Surface pressure: 101. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... Aluminum is a soft and lightweight metal with a dull silvery appearance, due to a thin layer of oxidation that forms quickly when it is exposed to air. ... GOLD refers to one of the following: GOLD (IEEE) is an IEEE program designed to garner more student members at the university level (Graduates of the Last Decade). ... David Scotts Apollo 15 training space suit on display in the Air and Space Museum, Washington, DC. Colonel David Randolph Scott (born June 6, 1932), a former NASA astronaut, was one of the third group of astronauts named by NASA in October 1963 and is one of only twelve... General Name, Symbol, Number platinum, Pt, 77 Chemical series transition metals Group, Period, Block 10, 6, d Appearance grayish white Standard atomic weight 195. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ... The University of Washington, founded in 1861, is a public research university in Seattle, Washington. ... Adjectives: Terrestrial, Terran, Telluric, Tellurian, Earthly Atmosphere Surface pressure: 101. ... The Sun (Latin: Sol) is the star at the center of the Solar System. ... In astrophysics and cosmology, dark matter refers to hypothetical matter of unknown composition that does not emit or reflect enough electromagnetic radiation to be observed directly, but whose presence can be inferred from gravitational effects on visible matter. ... The Galactic Center is the rotational center of the Milky Way galaxy. ... In physics, the Satellite Test of the Equivalence Principle as a planned (as of 2005) space science experiment to test the equivalence principle of general relativity. ...

The need to continue testing Einstein's theory of gravity may seem superfluous, as it is by far the most elegant theory of gravity known, and is compatible with almost all observations to date (except for instance the Pioneer anomaly). However, no quantum theory of gravity is known, and most suggestions violate one of the equivalence principles at some level. String theory, supergravity and even quintessence, for example, seem to violate the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths. These fields should generate fifth forces and variation of the fundamental constants. There are a number of mechanisms that have been suggested by physicists to reduce these violations of the equivalence principle to below observable levels. Elegance is the attribute of being tastefully designed or decorated, with focus on basic features. ... The Pioneer anomaly or Pioneer effect refers to the observed deviation from expectations of the trajectories of various unmanned spacecraft visiting the outer solar system, notably Pioneer 10 and 11. ... This article or section does not adequately cite its references or sources. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... In theoretical physics, supergravity (supergravity theory) refers to a field theory which combines the two theories of supersymmetry and general relativity. ... In physics, quintessence is a hypothetical form of dark energy postulated as an explanation of observations of an accelerating universe. ... In mathematics and physics, a scalar field associates a scalar to every point in space. ... The Compton wavelength of a particle is given by , where is the Planck constant, is the particles mass and is the speed of light. ... Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. ...

Laboratory equivalence principle composition and spin tests are supported by observation of binary pulsar PSR J0737-3039 (arXiv, Matters of Gravity). A neutron star core might be strange matter, pion condensate, lambda hyperon, delta isobar, or free quark matter. Extreme bound (gravitational binding energy ~30% of disassembled rest mass), spinning (~20% of lightspeed at equator), magnetic (~10⁸ tesla), dense (4-9x10¹⁴ g/cm³), superconducting neutronium obeys general relativity orbital predictions within 0.05% or better. A binary pulsar is a pulsar with a binary companion, often another pulsar, white dwarf or neutron star. ... Artists impression. ... A neutron star is one of the few possible endpoints of stellar evolution. ... Strange matter is a particular form of quark matter, namely a liquid of up, down, and strange quarks. ... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ... The gravitational binding energy of an object is the amount of energy required to accelerate every component of that object to the escape velocity of every other component. ...

The equivalence principle is untested against opposite geometric parity (chirality in all directions) mass distributions. A parity Eötvös experiment contrasting solid single crystal spheres of identical composition α-quartz in enantiomorphic space groups P3₁21 (right-handed screw axis) versus P3₂21 (left-handed screw axis) is appropriate. Equivalence principle parity violation validates a chiral vacuum background forbidden within general relativity but allowed within Einstein-Cartan theory; affine, teleparallel, and noncomutative gravitation theories. Look up Parity in Wiktionary, the free dictionary Parity is a concept of equality of status or functional equivalence. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... In crystallography, a screw axis is a symmetry operation describing how a combination of rotation about an axis and a translation parallel to that axis leaves a crystal unchanged. ... This article is in need of attention from an expert on the subject. ...

The Einstein equivalence principle

The Einstein equivalence principle states that the weak equivalence principle holds, and that

The outcome of any local non-gravitational experiment in a laboratory moving in an inertial frame of reference is independent of the velocity of the laboratory, or its location in spacetime.

Here local has a very special meaning: not only must the experiment not look outside the laboratory, but it must also be small compared to variations in the gravitational field, tidal forces, so that the entire laboratory is moving inertially. The tidal force is a secondary effect of the force of gravity and is responsible for the tides. ...

The principle of relativity implies that the outcome of local experiments must be independent of the velocity of the apparatus, so the most important consequence of this principle is the Copernican idea that any of the fundamental physical parameters – other than masses and Newton's gravitational constant – must not depend on where in space or time we measure them. In practice, these are dimensionless numbers, such as the ratio of two masses, or coupling constants such as the fine-structure constant. Wikisource has original text related to this article: Relativity: The Special and General Theory A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in certain similar situations. ...

Schiff's conjecture suggests that the weak equivalence principle actually implies the Einstein equivalence principle, but it has not been proven. Nonetheless, the two principles are tested with very different kinds of experiments. The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley [1] and Durand [2]).

Tests of the Einstein equivalence principle

In addition to the tests of the weak equivalence principle, the Einstein equivalence principle can be tested by searching for variation of dimensionless constants and mass ratios. The present best limits on the variation of the fundamental constants have mainly been set by studying the naturally occurring Oklo natural nuclear fission reactor, where nuclear reactions similar to ones we observe today have been shown to have occurred underground approximately two billion years ago. These reactions are extremely sensitive to the values of the fundamental constants. In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... In physics, fundamental physical constants are physical constants that are independent of systems of units and are in general dimensionless numbers. ... Oklo is a place in the West African state of Gabon. ... Natural Reactors refer to a handful of Uranium deposits that have been discovered, mostly in Oklo, Gabon. ...

There have been a number of controversial attempts to constrain the variation of the strong interaction constant. There have been several suggestions that "constants" do vary on cosmological scales. The best known is the reported detection of variation (at the 10^-5 level) of the fine-structure constant from measurements of distant quasars (see Webb et al [3]. Other researchers dispute these findings. Other tests of the Einstein equivalence principle are gravitational redshift experiments, such as the Pound-Rebka experiment which test the position independence of experiments. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... e- redirects here. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... In physics, the gyromagnetic ratio or Landé g-factor is a dimensionless unit which expresses the ratio of the magnetic dipole moment to the angular momentum of an elementary particle or atomic nucleus. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... This article or section is in need of attention from an expert on the subject. ... The Pound-Rebka experiment is a well known experiment in general relativity. ...

The strong equivalence principle

The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. In particular,

The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution.

and

The outcome of any local experiment, whether gravitational or not, in a laboratory moving in an inertial frame of reference is independent of the velocity of the laboratory, or its location in spacetime.

The first part is a version of the weak equivalence principle that applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or Cavendish experiments. The second part is the Einstein equivalence principle, restated to allow gravitational experiments and self-gravitating bodies. The freely-falling object or laboratory, however, must still be small, so that tidal forces may be neglected. This idealized requirement has been misunderstood. This form of the equivalence principle does not imply that the effects of a gravitational field cannot be measured by observers in free-fall. For example, an observer in free-fall into a black hole will experience strong tidal forces: he will notice a more powerful force on the parts closer to the black hole. In physics, the Cavendish experiment was the first experiment to accurately measure the gravitational constant by measuring the force of gravity between two masses in the laboratory. ... Simulated view of a black hole in front of the Milky Way. ...

The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe. Einstein's theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans-Dicke theory, satisfy only the Einstein equivalence principle. In general relativity, the metric tensor (or simply the metric) is the fundamental object of study. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ...

Tests of the strong equivalence principle

The strong equivalence principle can be tested by searching for a variation of Newton's gravitational constant G over the life of the universe, or equivalently, variation in the masses of the fundamental particles. A number of independent constraints, from orbits in the solar system and studies of big bang nucleosynthesis have shown that G cannot have varied by more than 10%. In cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than H-1, the normal, light hydrogen, during the early phases of the universe, shortly after the Big Bang. ...

Thus, the strong equivalence principle can be tested by searching for fifth forces (deviations from the gravitational force-law predicted by general relativity). These experiments typically look for failures of the inverse-square law (specifically Yukawa forces or failures of Birkhoff's theorem) behavior of gravity in the laboratory. The most accurate tests over short distances have been performed by the Eöt-Wash group. A future satellite experiment, SEE (Satellite Energy Exchange), will search for fifth forces in space and should be able to further constrain violations of the strong equivalence principle. Other limits, looking for much longer-range forces, have been placed by searching for the Nordtvedt effect, a "polarization" of solar system orbits that would be caused by gravitational self-energy accelerating at a different rate from normal matter. This effect has been sensitively tested by the Lunar Laser Ranging Experiment. Other tests include studying the deflection of radiation from distant radio sources by the sun, which can be accurately measured by very long baseline interferometry. Another sensitive test comes from measurements of the frequency shift of signals to and from the Cassini spacecraft. Together, these measurements have put tight limits on Brans-Dicke theory and other alternative theories of gravity. Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. ... This diagram shows how the law works. ... A Yukawa potential (also called a screened Coulomb potential) is a potential of the form Hideki Yukawa showed in the 1930s that such a potential arises from the exchange of a massive scalar field such as the field of the pion whose mass is . ... In general relativity, Birkhoffs theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. ... In theoretical astrophysics, the Nordtvedt Effect refers to the relative motion between the Earth and the Moon which would be observed if the graviational self-energy of a body contributes to its gravitational mass but not its inertial mass. ... The Lunar Laser Ranging Experiment from the Apollo 11 mission The ongoing Lunar Laser Ranging Experiment was first made possible by a lunar laser ranging retroreflector array planted on the Moon on July 21, 1969, by the crew of the Apollo 11. ... Radio sources are objects in outer space that emit strong radio waves. ... Very Long Baseline Interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy, in which the data received at each antenna in the array is paired with timing information, usually from a local atomic clock, and then stored for later analysis on magnetic tape or hard disk. ... Cassini-Huygens is a joint NASA/ESA/ASI unmanned space mission intended to study Saturn and its moons. ...

References

• R. H. Dicke, "New Research on Old Gravitation," Science 129, 3349 (1959). This paper is the first to make the distinction between the strong and weak equivalence principles.
• R. H. Dicke, "Mach's Principle and Equivalence," in Evidence for gravitational theories: proceedings of course 20 of the International School of Physics "Enrico Fermi", ed C. Møller (Academic Press, New York, 1962). This article outlines the approach to precisely testing general relativity advocated by Dicke and pursued from 1959 onwards.
• Albert Einstein, "Über das Relativitätsprinzip und die aus demselben gezogene Folgerungen," Jahrbuch der Radioaktivitaet und Elektronik 4 (1907); translated "On the relativity principle and the conclusions drawn from it," in The collected papers of Albert Einstein. Vol. 2 : The Swiss years: writings, 1900–1909 (Princeton University Press, Princeton, NJ, 1989), Anna Beck translator. This is Einstein's first statement of the equivalence principle.
• Albert Einstein, "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes," Annalen der Physik 35 (1911); translated "On the Influence of Gravitation on the Propagation of Light" in The collected papers of Albert Einstein. Vol. 3 : The Swiss years: writings, 1909–1911 (Princeton University Press, Princeton, NJ, 1994), Anna Beck translator, and in The Principle of Relativity, (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, ISBN 0-486-60081-5. The two Einstein papers are discussed online at The Genesis of General Relativity.
• C. Brans, "The roots of scalar-tensor theory: an approximate history", arXiv:gr-qc/0506063. Discusses the history of attempts to construct gravity theories with a scalar field and the relation to the equivalence principle and Mach's principle.
• C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Company, New York (1973), Chapter 16 discusses the equivalence principle.
• Hans Ohanian and Remo Ruffini Gravitation and Spacetime 2nd edition, Norton, New York (1994). ISBN 0-393-96501-5 Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong.
• J. P. Uzan, "The fundamental constants and their variation: Observational status and theoretical motivations," Rev. Mod. Phys. 75, 403 (2003). [4] This technical article reviews the best constraints on the variation of the fundamental constants.
• C. M. Will, Theory and experiment in gravitational physics, Cambridge University Press, Cambridge (1993). This is the standard technical reference for tests of general relativity.
• C. M. Will, Was Einstein Right?: Putting General Relativity to the Test, Basic Books (1993). This is a popular account of tests of general relativity.
• C. M. Will, The Confrontation between General Relativity and Experiment, Living Reviews in Relativity (2001). An online, technical review, covering much of the material in Theory and experiment in gravitational physics. The Einstein and strong variants of the equivalence principles are discussed in sections 2.1 and 3.1, respectively.

Experiments

• University of Washington Eöt-Wash group
• Lunar Laser Ranging [5]
• Galileo-Galilei satellite experiment [6]
• Satellite Test of the Equivalence Principle (STEP) [7]
• MICROSCOPE [8]
• Satellite Energy Exchange (SEE) [9]
• 16 November 2004, physicsweb: Equivalence principle passes atomic test Quote: "...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."