Equivalence principle

A number of different forms of the equivalence principle are used in research today. Equivalence principle - 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 gravitationa ...

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Equivalence principle, Equivalence principle - History, Equivalence principle - Modern usage, Equivalence principle - The weak equivalence principle, Equivalence principle - The Einstein equivalence principle, Equivalence principle - The strong equivalence principle, Equivalence principle - Experiments

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The idea that the Coriolis field is a real physical effect and not just a mathematical artifact is justified in a Machian theory by saying that evidence of the field’s existence is not only visible to the rotating observer, its distortion is also visible and verifiable for non-rotating onlookers: the relative rotation of the roundabout and universe masses creates a real physical distortion in spacetime that is theoretically visible to all observers (see: Kerr black hole, frame-dragging, light-dragging effects), and the physical cons ...

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Coriolis field, Coriolis field - Is it real?

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edit A black hole is a concentration of mass great enough that the force of gravity prevents anything from escaping it except through quantum tunnelling behaviour (known as Hawking Radiation). The gravitational field is so strong that the escape velocity near it exceeds the speed of light. This implies that nothing, not even light, can escape its gravity, hence the word "black". The term "black hole" is widespread, even though it does not refer to a hole in the usual sense, but rather a region of space fro ...

Including:

• Black hole - History
• Black hole - Evidence
• Black hole - Formation
• Black hole - Observation
• Black hole - Have we found them?
• Black hole - Recent discoveries
• Black hole - Features and issues
• Black hole - The event horizon
• Black hole - The singularity
• Black hole - Entering a black hole
• Black hole - Rotating black holes
• Black hole - Entropy and Hawking radiation
• Black hole - Black hole unitarity
• Black hole - Mathematical theory
• Black hole - Alternative models

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edit Einstein's general theory of relativity was introduced in 1915. Physicists accepted the theory because it correctly accounted for the precession of the perihelion of Mercury, a phenomenon which had long baffled physicists and because it unified Newton's law of universal gravitation with special relativity in a conceptually simple way. (Einstein has been famously quoted as saying that if his theory was falsified, then he would have felt "sorry for the dear Lord.") Despite Einstein's proposal of three classical te ...

Including:

• Tests of general relativity - Classical tests
• Tests of general relativity - Modern tests
• Tests of general relativity - Post-Newtonian tests of gravity
• Tests of general relativity - The equivalence principle
• Tests of general relativity - Strong field tests
• Tests of general relativity - Cosmological tests

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Gravity is a force of attraction that acts between bodies that have mass. It is a physical phenomenon of fundamental importance, profoundly affecting the workings of the world around us and the universe beyond. Most familiarly, it is the gravitational attraction of the earth that endows objects with weight and causes them to fall to the ground when dropped. In fact, gravity is also the reason for the very existence of the earth, the sun and other celestial bodies; without it matter would not have coalesced into these bodies and ...

Including:

• Gravity - Overview of the history of gravitational theory
• Gravity - Newton's law of universal gravitation
• Gravity - Acceleration due to gravity
• Gravity - Bodies with spatial extent
• Gravity - Vector form
• Gravity - Gravitational field
• Gravity - The Earth's gravity
• Gravity - Comparative gravities of the Earth Sun Moon and planets
• Gravity - Mathematical equations for a falling body
• Gravity - Gravitational potential
• Gravity - Acceleration relative to the rotating Earth
• Gravity - Gravity and astronomy
• Gravity - Self-gravitating system
• Gravity - Practical uses of gravity
• Gravity - Problems with Newton's theory
• Gravity - Theoretical concerns
• Gravity - Disagreement with observation
• Gravity - Newton's reservations
• Gravity - Einstein's theory of gravitation
• Gravity - Experimental tests
• Gravity - Comparison with electromagnetic force
• Gravity - Gravity and quantum mechanics
• Gravity - Alternative theories
• Gravity - Recent alternative theories
• Gravity - Historical alternative theories
• Gravity - Notes

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Gravitation is the tendency of objects with mass to accelerate toward each other. There have been numerous theories of gravitation starting with the ideas of the Greek philosopher Aristotle in the 4th century BC. He believed that there is no effect without a cause, and therefore no motion without a force. He concluded that all things tried to move toward their proper place in the crystalline spheres of the heavens, and that bodies fell toward the center of the Earth in proportion to their weight. During the 16t ...

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General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. It unifies special relativity and Isaac Newton's law of universal gravitation with the insight that gravitation is not viewed as being due to a force (in the traditional sense) but rather a manifestation of curved space and time, this curvature being produced by the mass-energy content of the spacetime. Overview of GR History Mathematics Resources Tests Including:

• General relativity - Overview
• General relativity - Justification
• General relativity - Fundamental principles
• General relativity - Spacetime as a curved Lorentzian manifold
• General relativity - The mathematics of general relativity
• General relativity - The Einstein field equations
• General relativity - Coordinate vs. physical acceleration
• General relativity - Predictions of General Relativity
• General relativity - Gravitational effects
• General relativity - Cosmological effects
• General relativity - Other predictions
• General relativity - Relationship to other physical theories
• General relativity - Classical mechanics and special relativity
• General relativity - Quantum mechanics
• General relativity - Alternative theories
• General relativity - History
• General relativity - Status
• General relativity - Quotes
• General relativity - Notes

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History of general relativity - Early investigations. 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 phenomenon of gravitational time dilation in the 1907 article. In 1911, Einstein published another article expanding on the 1907 article, in which additional effects such ...

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History of general relativity, History of general relativity - Development, History of general relativity - Early investigations, History of general relativity - General covariance and the hole argument, History of general relativity - The development of the Einstein Field Equations, History of general relativity - Einstein and Hilbert, History of general relativity - Subsequent events, History of general relativity - The Schwarzschild solution, History of general relativity - The expanding universe and the cosmological constant, History of general relativity - More exact solutions, History of general relativity - Testing the theory, History of general relativity - Alternative theories

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In a gravitational lens, the gravity from the massive object bends light like a lens. As a result, the path of the light from the source is curved, distorting its image, and the apparent location of the source may be different from its actual position. In addition, the observer may see multiple images of a single source. If the source, massive object, and the observer lie on a straight line, the source will appear as a ring behind the massive object. This phenomenon was first mentioned by Chwolson in 1924, and quantified by Einstein in 1936. ...

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Gravitational lens, Gravitational lens - Description, Gravitational lens - History, Gravitational lens - Cosmological applications, Gravitational lens - Astronomical applications, Gravitational lens - Historical papers and references

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One can ask what happens, when a stationary observer is in orbit just outside the event horizon and (against all advice) sticks his hand through the horizon? The answer is: he won't succeed in doing so. Free orbits are only possible at a certain distance (for a non-rotating black hole, this figure is at least three times the Schwarzschild radius). Near the event horizon, an observer can only remain at a constant radius when he uses a force (e.g. from a rocket) to keep him there. The force needed grows to infinity when the observer wants to m ...

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Event horizon, Event horizon - Sticking your hand through an event horizon, Event horizon - Event horizon in the absence of gravity, Event horizon - Other examples of an event horizon, Event horizon - External link

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The first mathematical formulation of gravity was Isaac Newton's law of universal gravitation, published in his 1687 work Principia Mathematica. Professor William Whewell of Cambridge University, author of History of the Inductive Sciences (1837) stated: "The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth." [In A Treasury o ...

See also:

Gravity, Gravity - Overview of the history of gravitational theory, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Philosophy of space and time - Leibniz and Newton. The debate between whether space and time are real objects themselves, i.e absolute, or merely orderings upon real objects, i.e. relational, began with a debate between Isaac Newton, through his spokesman Samuel Clarke, and Gottfried Leibniz in the famous Leibniz-Clarke Correspondence. Arguing against the absolutist position, Leibniz offers a number of thought experiments aiming to show that assuming the existence of facts such as absolute location and vel ...

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Philosophy of space and time, Philosophy of space and time - Idealism and anti-realism, Philosophy of space and time - Absolutism vs. Relationalism, Philosophy of space and time - Leibniz and Newton, Philosophy of space and time - Mach, Philosophy of space and time - Einstein, Philosophy of space and time - Conventionalism, Philosophy of space and time - The structure of spacetime, Philosophy of space and time - Invariance vs. Covariance, Philosophy of space and time - Historical Frameworks, Philosophy of space and time - Holes, Philosophy of space and time - The direction of time, Philosophy of space and time - The Causation solution, Philosophy of space and time - The Thermodynamics solution, Philosophy of space and time - The Laws Solution, Philosophy of space and time - The flow of time, Philosophy of space and time - Dualities, Philosophy of space and time - Quantum gravity, Philosophy of space and time - Presentism and Eternalism, Philosophy of space and time - Endurantism and perdurantism

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The Schwarzschild solution appears to have singularities at r = 0 and r = rs; some of the metric components blow up at these radii. Since the Schwarzschild metric is only expected to be valid for radii larger than the radius R of the gravitating body, there is no problem as long as R > rs. For ordinary stars and planets this is always the case. For example, the radius of the Sun is ...

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Schwarzschild metric, Schwarzschild metric - The Schwarzschild metric, Schwarzschild metric - Singularities and black holes, Schwarzschild metric - Embedding Schwarzschild space in Euclidean space, Schwarzschild metric - Orbital motion, Schwarzschild metric - Quotes

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The first mathematical formulation of gravity was Isaac Newton's law of universal gravitation, published in his 1687 work Principia Mathematica. Professor William Whewell of Cambridge University, author of History of the Inductive Sciences (1837) stated: "The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth." [In A Treasury o ...

See also:

Gravity, Gravity - Overview of the history of gravitational theory, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Transition from Newtonian mechanics to General relativity - Newtonian mechanics for circular orbits. Consider the situation in which there are two particles in nearby circular polar orbits of the earth at radius r and speed v. Since the orbits are circular, the gravitational force on the particles must equal the centripetal force, < ...

See also:

Transition from Newtonian mechanics to General relativity, Transition from Newtonian mechanics to General relativity - The equivalence of gravitational and inertial mass, Transition from Newtonian mechanics to General relativity - Test for flatness in spacetime, Transition from Newtonian mechanics to General relativity - Two nearby particles in a radial gravitational field, Transition from Newtonian mechanics to General relativity - Newtonian mechanics for circular orbits, Transition from Newtonian mechanics to General relativity - General motion in the earth's gravitational field, Transition from Newtonian mechanics to General relativity - Tensor description, Transition from Newtonian mechanics to General relativity - Simple diagonal frame, Transition from Newtonian mechanics to General relativity - Arbitrary orientation of the local frame, Transition from Newtonian mechanics to General relativity - Time dependent rotation of the local frame: Christoffel symbols, Transition from Newtonian mechanics to General relativity - Arbitrariness in the curvature, Transition from Newtonian mechanics to General relativity - General geodesic and field equations in a Newtonian setting, Transition from Newtonian mechanics to General relativity - Geodesic equation, Transition from Newtonian mechanics to General relativity - Field equation, Transition from Newtonian mechanics to General relativity - Overview of the Newtonian picture, Transition from Newtonian mechanics to General relativity - Relativistic generalization

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The Einstein field equation (EFE) is usually written in the form Here Rab is the Ricci tensor, R is the Ricci scalar, gab is the metric tensor, Tab is the stress-energy tensor, and the constant is given in terms of π (pi), cSee also:

Einstein's field equation, Einstein's field equation - Mathematical form of Einstein's field equation, Einstein's field equation - Properties of Einstein's equation, Einstein's field equation - Conservation of energy and momentum, Einstein's field equation - Nonlinearity of the field equations, Einstein's field equation - The correspondence principle, Einstein's field equation - The cosmological constant, Einstein's field equation - Solutions of the field equations, Einstein's field equation - Vacuum field equations, Einstein's field equation - The linearised EFE

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For details on tensors, see the articles: Tensor, Tensor (intrinsic definition), Classical treatment of tensors, Intermediate treatment of tensors. The description of phenomena in nature should not depend upon who does the measuring - one coordinate system is as good as any other. One of the profound consequences of relativity theory was the abolishment of preferred reference frames. Special relativity banished the singling out of inertial frames for the description of physical phenomena, whereas general relativity elimin ...

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Mathematics of general relativity, Mathematics of general relativity - Why tensors?, Mathematics of general relativity - Spacetime as a manifold, Mathematics of general relativity - Local versus global structure, Mathematics of general relativity - Tensors in GR, Mathematics of general relativity - Symmetric and antisymmetric tensors, Mathematics of general relativity - The metric tensor, Mathematics of general relativity - Invariants, Mathematics of general relativity - Tensor classifications, Mathematics of general relativity - Tensor fields in GR, Mathematics of general relativity - Tensorial derivatives, Mathematics of general relativity - Affine connections, Mathematics of general relativity - The covariant derivative, Mathematics of general relativity - The Lie derivative, Mathematics of general relativity - The Riemann curvature tensor, Mathematics of general relativity - The energy-momentum tensor, Mathematics of general relativity - Energy conservation, Mathematics of general relativity - The Einstein field equations, Mathematics of general relativity - The geodesic equations, Mathematics of general relativity - Lagrangian formulation, Mathematics of general relativity - Mathematical techniques for analysing spacetimes, Mathematics of general relativity - Frame fields, Mathematics of general relativity - Symmetry vector fields, Mathematics of general relativity - The Cauchy problem, Mathematics of general relativity - Spinor formalism, Mathematics of general relativity - Regge calculus, Mathematics of general relativity - Singularity theorems, Mathematics of general relativity - Numerical relativity, Mathematics of general relativity - Perturbation methods, Mathematics of general relativity - Notes

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The modern era of testing general relativity was ushered in largely at the impetus of Dicke (1959, 1962) and Schiff (1960) who laid out a framework for testing general relativity. They emphasized the importance not only of the classical tests, but of null experiments, testing for effects which in principle could occur in a theory of gravitation, but do not occur in general relativity. Another important theoretical development were the new alternatives to general relativity theory – such as Brans-Dicke theory and other scalar-tensor theorie ...

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Tests of general relativity, Tests of general relativity - Classical tests, Tests of general relativity - Modern tests, Tests of general relativity - Post-Newtonian tests of gravity, Tests of general relativity - The equivalence principle, Tests of general relativity - Strong field tests, Tests of general relativity - Cosmological tests

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In this theory, spacetime is treated as a 4-dimensional Lorentzian manifold which is curved by the presence of mass, energy, and momentum (or stress-energy) within it. The relationship between stress-energy and the curvature of spacetime is governed by the Einstein field equations. The motion of objects being influenced solely by the geometry of spacetime (inertial motion) occurs along special paths called timelike and null geodesics of spacetime. See also:

General relativity, General relativity - Overview, General relativity - Justification, General relativity - Fundamental principles, General relativity - Spacetime as a curved Lorentzian manifold, General relativity - The mathematics of general relativity, General relativity - The Einstein field equations, General relativity - Coordinate vs. physical acceleration, General relativity - Predictions of General Relativity, General relativity - Gravitational effects, General relativity - Cosmological effects, General relativity - Other predictions, General relativity - Relationship to other physical theories, General relativity - Classical mechanics and special relativity, General relativity - Quantum mechanics, General relativity - Alternative theories, General relativity - History, General relativity - Status, General relativity - Quotes, General relativity - Notes

Read more here: » General relativity: Encyclopedia II - General relativity - Overview

Black hole - Formation. General relativity (as well as most other metric theories of gravity) not only says that black holes can exist, but in fact predicts that they will be formed in nature whenever a sufficient amount of mass gets packed in a given region of space, through a process called gravitational collapse. For example, if you compressed the Sun to a radius of three kilometers, about four millionths of its present size, it would become a black hole. As the mass inside the given region of space inc ...

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Black hole, Black hole - History, Black hole - Evidence, Black hole - Formation, Black hole - Observation, Black hole - Have we found them?, Black hole - Recent discoveries, Black hole - Features and issues, Black hole - The event horizon, Black hole - The singularity, Black hole - Entering a black hole, Black hole - Rotating black holes, Black hole - Entropy and Hawking radiation, Black hole - Black hole unitarity, Black hole - Mathematical theory, Black hole - Alternative models

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