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. Though initially it was intended as an extension of special relativity to non-inertial frames, nowadays only the theory of gravitation is considered GR, and non-inertial frames are considered just an introduction. The newton (symbol: N) is the SI unit of force. ... In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. ... Albert Einstein, photographed by Yousuf Karsh in 1948. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... For a non-technical introduction to the topic, please see Introduction to General relativity. ... In theoretical physics, an accelerated reference frame is usually a coordinate system or frame of reference, that undergoes a constant and continual change in velocity over time as judged from an inertial frame. ...

Einstein's treatment of gravitation

The equivalence principle

Einstein was uncomfortable with the equations he had for gravitation as a force. Then he noticed something. A person free falling in an elevator will notice that he is floating, something very similar to an inertial system in the space.

He postulated that a free falling system is a privileged system, similar to the inertial systems of special relativity, but while an inertial system follows a straight line in space-time (see special relativity), these free-falling systems follow bent lines. For a non-technical introduction to the topic, please see Introduction to Special relativity. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

He postulated that the presence of the earth bends the space-time inertial paths in some way, making the straight lines of the inertial systems a curve. With this in mind, we can explain usual things in a different way:

• A satellite circling the earth is following an inertial path, with that the path being curved by the presence of the earth.
• If we throw a stone it will make something close to a parabola, but in fact is like an ellipse. The stone is following an inertial path like the one of the satellite.
• And when we are sitting on a chair, we are trying to follow an inertial path or orbit, but the chair does not allow us to do it. Therefore we are accelerated with respect to the inertial path of freefall. This explains the sensation of acceleration or gravity when living on earth.

Therefore, the gravitational field we feel at the surface of the earth is really a fictitious force like those of other non-inertial frames of reference. From this moment, we will use in this article the word "gravitational" to refer to any fictious field. Freefall or free fall in the strict sense is the condition of acceleration which is due only to gravity. ... A fictitious force is a force used to explain acceleration in a non-inertial frame of reference, such as a rotating frame. ... In theoretical physics, a common coordinate system or frame of reference, that refers to a non-inertial state of motion can be referred to as a noninertial frame (as opposed to an inertial frame). ...

Extension of special relativity to non-inertial frames of reference

Accelerated frames of reference can be examined in special relativity by considering the instantaneous inertial frame of reference that an accelerated observer is in at a given event. This consideration will lead to two related effects: gravitational time dilation and gravitational red shift. In theoretical physics, a common coordinate system or frame of reference, that refers to a non-inertial state of motion can be referred to as a noninertial frame (as opposed to an inertial frame). ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... An inertial frame is a coordinate system in which Newtons First Law of Motion is valid. ... An event is something that takes place; an occurrence and arbitrary point in time. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories under which a clock at a different gravitational potential is found to tick at a different rate than ones own clock. ... 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. ...

For example consider two people in an accelerating rocket ship with one being above the other (in the direction of acceleration) in the rocket ship. If the "lower" person emits a beam of light towards the "upper" person, during the time the light is traveling the upper will accelerate from the inertial frame in which the light was emitted to one which is moving away from the source of the light. As a result, the light will be red-shifted for the upper person. The is the gravitational red shift effect. Similarly, the light emitted by the upper person will be blue shifted for the lower person (since the lower person is being accelerated towards the source of the light). This article is about the light phenomenon. ... 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. ...

The red-shifting being continuous reveals another effect for accelerated observers: gravitational time dilation. Since the red-shift means that the light is not vibrating as fast, it must follow that time for the lower person runs slow in the perception of the upper person. Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories under which a clock at a different gravitational potential is found to tick at a different rate than ones own clock. ...

Another effect is the bending of light. For an accelerated observer, a beam of light which is initially traveling horizontally will be bent "downwards" over time as the observers accelerate into "upwards" moving frames of reference.

By virtue of the equivalence principle as described above, all of these effects should be observable in the gravitational fields of the Earth and the stars. For example:

• The gravitational red-shift of light was confirmed by Pound and Rebka in 1959 [1].
• The Hafele-Keating experiment validated gravitational time dilation. An even more rigorous confirmation was done by the GPS system.
• In 1919, Eddington verified the bending of light by the Sun's gravitational field.

The Pound-Rebka experiment is a well known experiment in general relativity. ... The Hafele-Keating experiment was a test of the theory of relativity. ... Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ... Eddington is the name of several places United States of America Eddington, Maine Eddington, Pennsylvania United Kingdom Eddington, Berkshire Eddington, Kent Edington, Somerset Edington, Wiltshire Also see: Arthur Eddington, an important astrophysicist This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same...

The geometry of gravitation

In general relativity, spacetime is non-Euclidean, or curved. The need for curvature arises from the equivalence principle and a child's simple question: "What keeps the people on the other side of the world from falling off?". In other words, should not the inertial paths on the other side of the Earth take objects away from the planet? Instead, all free-fall trajectories in the vicinity of a massive object will draw objects towards it. The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Curvature refers to a number of loosely related concepts in different areas of geometry. ...

The issue can be better illustrated by considering two balls on opposite sides of the Earth that start at rest with respect to the center of the Earth (and therefore with respect to each other). In the at-rest state, they are taking parallel world lines through spacetime. Now if both balls are allowed to free fall starting as a specified time, they will accelerate towards each other. The resultant movement towards each other means that their world lines are no longer parallel. Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ... World line of the orbit of the Earth depicted in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, usually put as the vertical axis. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

Einstein needed a way in which parallel inertial world lines could become non-parallel, something that special relativity does not allow. Einstein found the answer in curvature. An example of curvature is the surface of the Earth. For example, the lines of longitude are locally straight on the surface of the Earth. At the equator, they are parallel, but at the poles they cross. The lines of longitude also describe geodesic paths on the surface of the Earth, and in fact any great circle is a geodesic on the Earth. The equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. Definition of geodesic depends on the type of curved space. If the space carries a natural metric then geodesics are defined to be (locally) the shortest path between points on the space. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the...

With this in mind, Einstein proposed that inertially moving objects follow timelike geodesic world lines through spacetime. Given an appropriate curvature of the spacetime, free fall and orbital motion can now be inertial motion, as described above. In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... In physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force. ...

The Einstein field equations

As orbital motion and free-fall are dependent on the presence of a massive object, it follows in general relativity and related metric theories of gravitation that the presence of mass somehow curves spacetime. Furthermore, mass is a form of energy in relativity (due to E=mc²), and energy and momentum are intertwined in relativity (just as space and time are intertwined). So it follows that presence of mass, energy, and momentum (or "matter") causes spacetime to be curved. This article or section is in need of attention from an expert on the subject. ... Mass is a property of a physical object that quantifies the amount of matter and energy it contains. ... A display of the famous equation on Taipei 101 during the event of the World Year of Physics 2005. ... In classical mechanics momentum (pl. ...

In general relativity, this relationship between matter and curvature is described by the Einstein field equations. These equations were discovered by Einstein in late 1915. The Einstein field equations are expressed using tensor calculus, and are a collection of up to 10 independent simultaneous differential equations. These field equations are solved to create metrics of spacetime. (A metric of spacetime describes the invariant intervals squared between neighboring positions in spacetime whose coordinates differ by an infinitesimal amount. The simplest metric of spacetime is the Minkowski metric.) These metrics described the shape of the spacetime, and the curvature of spacetime and equations of motion for inertially moving objects can be obtained from it. For other topics related to Einstein see Einstein (disambig) In physics, the Einstein field equation or the Einstein equation is a tensor equation in the theory of gravitation. ... For more technical Wiki articles on tensors, see the section later in this article. ... In mathematics, simultaneous equations are a set of equations where variables are shared. ... Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In general relativity, the metric tensor (or simply the metric) is the fundamental object of study. ... In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ... In physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force. ...

The actual shapes of spacetime are described by solutions of the Einstein field equations. In particular, the Schwarzschild solution (1916) describes the gravitational field around a spherically symmetric massive object. The geodesics of the Schwarzschild solution describe the observed behavior of objects being acted on gravitationally, including the anomalous perihelion precession of Mercury and the bending of light as it passes the Sun. Strictly speaking, any Lorentz metric is a solution of the Einstein field equation, as this amounts to nothing more than a mathematical definition of the energy-momentum tensor (by the field equations). ... Introduction In Einsteins theory of general relativity, the Schwarzschild metric is the most general static, spherically symmetric solution of the vacuum field equations. ... 1916 (MCMXVI) was a leap year starting on Saturday (link will take you to calendar). ...

Experimental tests

General Relativity is consistent with all currently available measurements of large-scale phenomena. Arthur Eddington found observational evidence for the bending of light passing the Sun as predicted by general relativity in 1919. Subsequent observations have confirmed Eddington's results, and observations of a pulsar which is occulted by the Sun every year have permitted this confirmation to be done to a high degree of accuracy. There have also in the years since 1919 been numerous other tests of general relativity, all of which have confirmed Einstein's theory. Crucial experiments that justified the adoption of General Relativity over Newtonian gravity were the classical tests: the gravitational redshift, the deflection of light rays by the Sun, and the precession of the orbit of Mercury. One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the English-speaking world. ... 1919 (MCMXIX) was a common year starting on Wednesday (see link for calendar). ... Composite Optical/X-ray image of the Crab Nebula pulsar, showing surrounding nebular gases stirred by the pulsars magnetic field and radiation. ... In this July, 1997 still frame captured from video, the bright star Aldebaran has just reappeared on the dark limb of the waning crescent moon in this predawn occultation. ... Einsteins general theory of relativity was introduced in 1915. ... Einsteins general theory of relativity was introduced in 1915. ... This article is in need of attention from an expert on the subject. ... This article is in need of attention from an expert on the subject. ... Precession refers to a change in the direction of the axis of a rotating object. ...

More recent experimental confirmations of General Relativity were the (indirect) deduction of gravitational waves being emitted from orbiting binary stars, the existence of neutron stars and black holes, gravitational lensing, and the convergence of measurements in observational cosmology to an approximately flat model of the observable Universe, with a matter density parameter of approximately 30% of the critical density and a cosmological constant of approximately 70% of the critical density. Artists impression of a binary star system consisting of a black hole, with an accretion disc around it, and a main sequence star. ... A neutron star is one of the few possible endpoints of stellar evolution. ... A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is bent around a massive object (such as a massive galaxy) between the source object and the observer. ... // Cosmology, from the Greek: κοσμολογία (cosmologia, κόσμος (cosmos) world + λογια (logia) discourse) is the study of the Universe in its totality, and by extension, humanitys place in it. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... In cosmology, the Big Crunch is a hypothesis that states the universe will stop expanding and start to collapse upon itself; a counterpart to the Big Bang. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...

The equivalence principle, the postulate of general relativity that presumes that inertial mass and gravitational mass are the same, is also under test. Past, present, and future tests are discussed in the equivalence principle article. THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...

Even to this day, scientists try to challenge General Relativity with more and more precise direct experiments. The goal of these tests is to shed light on the yet unknown relationship between gravity and quantum mechanics. Space probes are used to either make very sensitive measurements over large distances, or to bring the instruments into an environment that is much more controlled than it could be on Earth. For example, in 2004 a dedicated satellite for gravity experiments, called Gravity Probe B, was launched to test general relativity's predicted frame-dragging effect, among others. Also, land-based experiments like LIGO and a host of "bar detectors" are trying to detect gravitational waves directly. A space-based hunt for gravitational waves, LISA, is in its early stages. It should be sensitive to low frequency gravitational waves from many sources, perhaps including the Big Bang. A space probe is an unmanned space mission in which a spacecraft leaves Earths orbit. ... 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... A satellite is any object that orbits another object (which is known as its primary). ... Gravity Probe B (GP-B) is a satellite-based mission to measure the stress-energy tensor (the distribution, and especially the motion, of matter) in and near Earth, and thus to test related models; in application of Einsteins general theory of relativity. ... 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 LIGO Hanford Control Room LIGO stands for Laser Interferometer Gravitational-Wave Observatory. ... The LISA is the Laser Interferometer Space Antenna experiment. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ...

Einstein's theory of relativity predicts that the speed of gravity (defined as the speed at which changes in location of a mass are propagated to other masses) should be the speed of light. In 2002, the Fomalont-Kopeikin experiment produced measurements of the speed of gravity which matched this prediction. However, this experiment has not yet been widely peer-reviewed, and is facing criticism from those who claim that Fomalont-Kopeikin did nothing more than measure the speed of light in a convoluted manner. The speed of gravity is the speed at which changes in the location of an object propagate their gravitational effects to all other objects in the Universe. ... Sergei Kopeikin (born April 10, 1956) is a USSR-born physicist presently living and working in the United States, where he holds the position of Associate Professor of Physics at the University of Missouri-Columbia (UMC). ...

The Pioneer anomaly is an empirical observation that the positions of the Pioneer 10 and Pioneer 11 space probes differ very slightly from what would be expected according to known effects (gravitational or otherwise). The possibility of new physics has not been ruled out, despite very thorough investigation in search of a more prosaic explanation. 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. ... Pioneer 10 in the final stage of construction Pioneer 10 was the first spacecraft to travel through the asteroid belt, and was the first spacecraft to make direct observations of Jupiter. ... Pioneer 11 at Saturn (artists impression) Pioneer 11 was the second mission to investigate Jupiter and the outer solar system and the first to explore the planet Saturn and its main rings. ... A space probe is an unmanned space mission in which a spacecraft leaves Earths orbit. ...

See also

• Gravitation
• General relativity
• Nordström's theory of gravitation