History of gravitational theory
Encyclopedia
In physics
, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation
since ancient times.
philosopher Aristotle
believed that there is no effect
or motion
without a cause
. The cause of the downward motion of heavy bodies, such as the element earth
, was related to their nature
, which caused them to move downward toward the center of the universe, which was their natural place. Conversely, light bodies such as the element fire
, move by their nature upward toward the inner surface of the sphere
of the Moon. Thus in Aristotle's system heavy bodies are not attracted to the earth by an external force of gravity, but tend toward the center of the universe because of an inner gravitas or heaviness.
In Book VII of his De Architectura
, the Roman engineer and architect Vitruvius
contends that gravity is not dependent on a substance's "weight" but rather on its "nature".
In the 7th Century the Indian mathematician Brahmagupta
stated "Bodies fall towards the earth as it is in the nature of the earth to attract bodies, just as it is in the nature of water to flow."
"Aakrishti sakthischa mahee thayaa yathkhastham guru swa abhimukham swa sakthyaa . aakrushyathe thath pathathi iti bhaathi same samanthaath kwa pathathi ayam khe" is the verse which describes that the earth attracts the solid objects in the sky by its own force towards itself. Bhaskaracharya further discusses the forces between the celestial bodies using a question: Where can the celestial bodies fall since they attract each other?
Before 1543 in De revolutionibus orbium coelestium
Copernicus
wrote :"...inter centrum gravitatis terrae, & centrum magnitudis..."
During the 17th century, Galileo
found that, counter to Aristotle's teachings, all objects accelerated equally when falling.
In the late 17th century, as a result of Robert Hooke's suggestion that there is a gravitational force which depends on the inverse square
of the distance
, Isaac Newton
was able to mathematically
derive Kepler's three kinematic
laws of planetary motion
, including the elliptical
orbits for the seven known planet
s:
So Newton's original formula was:
where the symbol
means "is proportional to".
To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them. This gravitational constant
was first measured in 1797 by Henry Cavendish
.
In 1907 Albert Einstein
, in what was described by him as "the happiest thought of my life", realized that an observer who is falling from the roof of a house experiences no gravitational field. In other words, gravitation was exactly equivalent to acceleration
. Between 1911 and 1915 this idea, initially stated as the Equivalence principle
, was formally developed into Einstein's theory of general relativity
.
of universal gravitation. In his own words, “I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”
Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune
based on motions of Uranus
that could not be accounted by the actions of the other planets. Calculations by John Couch Adams
and Urbain Le Verrier both predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle
to the discovery of Neptune.
Years later, it was another discrepancy in a planet's orbit that showed Newton's theory to be inaccurate. By the end of the 19th century, it was known that the orbit of Mercury
could not be accounted for entirely under Newtonian gravity, and all searches for another perturbing body (such as a planet orbiting the Sun
even closer than Mercury) have been fruitless. This issue was resolved in 1915 by Albert Einstein
's new general theory of relativity, which accounted for the discrepancy in Mercury's orbit.
Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations still use it because it is much easier to work with and is sufficiently accurate for most applications.
. These theories were developed from the 16th until the 19th century in connection with the aether theories
.
René Descartes
(1644) and Christiaan Huygens (1690) used vortices to explain gravitation.
Robert Hooke
(1671) and James Challis
(1869) assumed, that every body emits waves which lead to an attraction of other bodies.
Nicolas Fatio de Duillier
(1690) and Georges-Louis Le Sage
(1748) proposed a corpuscular model
, using some sort of screening or shadowing mechanism. Later a similar model was created by Hendrik Lorentz
, who used electromagnetic radiation
instead of the corpuscles.
Isaac Newton
(1675) and Bernhard Riemann
(1853) argued that aether streams carry all bodies to each other.
Newton (1717) and Leonhard Euler
(1760) proposed a model, in which the aether loses density near the masses, leading to a net force directing to the bodies.
Lord Kelvin (1871) proposed that every body pulsates, which might be an explanations of gravitation and the electric charges.
However, those models were overthrown because most of them lead to an unacceptable amount of drag
, which is not observed. Other models are violating the energy conservation law and are incompatible with modern thermodynamics
.
, the effects of gravitation are ascribed to spacetime
curvature
instead of to a force. The starting point for general relativity is the equivalence principle
, which equates free fall with inertial motion. The issue that this creates is that free-falling objects can accelerate with respect to each other. In Newtonian physics, no such acceleration can occur unless at least one of the objects is being operated on by a force (and therefore is not moving inertially).
To deal with this difficulty, Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. (This type of path is called a geodesic
). More specifically, Einstein and Hilbert discovered the field equation
s of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations
are a set of 10 simultaneous, non-linear
, differential equation
s. The solutions of the field equations are the components of the metric tensor
of spacetime. A metric tensor describes the geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.
Notable solutions of the Einstein field equations include:
General relativity has enjoyed much success because of how its predictions of phenomena which are not called for by the theory of gravity have been regularly confirmed. For example:
. Later it was understood that it is possible to describe gravity in the framework of quantum field theory
like the other fundamental forces. In this framework the attractive force of gravity arises due to exchange of virtual
gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons. This reproduces general relativity in the classical limit
. However, this approach fails at short distances of the order of the Planck length.
It is notable that in general relativity, gravitational radiation, which under the rules of quantum mechanics must be composed of gravitons, is created only in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. The amount of gravitational radiation emitted by the solar system
is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as PSR 1913+16
. It is believed that neutron star
mergers and black hole
formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO
have been created to study the problem. No confirmed detections have been made of this hypothetical radiation, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
since ancient times.
Antiquity
In the 4th century BC, the GreekAncient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...
philosopher Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
believed that there is no effect
Effect
Effect may refer to:* A result or change of something** List of effects** Cause and effect, an idiom describing causalityIn pharmacy and pharmacology:* Drug effect, a change resulting from the administration of a drug...
or motion
Motion (physics)
In physics, motion is a change in position of an object with respect to time. Change in action is the result of an unbalanced force. Motion is typically described in terms of velocity, acceleration, displacement and time . An object's velocity cannot change unless it is acted upon by a force, as...
without a cause
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
. The cause of the downward motion of heavy bodies, such as the element earth
Earth (classical element)
Earth, home and origin of humanity, has often been worshipped in its own right with its own unique spiritual tradition.-European tradition:Earth is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with qualities of heaviness, matter and the...
, was related to their nature
Nature (philosophy)
Nature is a concept with two major sets of inter-related meanings, referring on the one hand to the things which are natural, or subject to the normal working of "laws of nature", or on the other hand to the essential properties and causes of those things to be what they naturally are, or in other...
, which caused them to move downward toward the center of the universe, which was their natural place. Conversely, light bodies such as the element fire
Fire (classical element)
Fire has been an important part of all cultures and religions from pre-history to modern day and was vital to the development of civilization. It has been regarded in many different contexts throughout history, but especially as a metaphysical constant of the world.-Greek and Roman tradition:Fire...
, move by their nature upward toward the inner surface of the sphere
Celestial spheres
The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others...
of the Moon. Thus in Aristotle's system heavy bodies are not attracted to the earth by an external force of gravity, but tend toward the center of the universe because of an inner gravitas or heaviness.
In Book VII of his De Architectura
De architectura
' is a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus, as a guide for building projects...
, the Roman engineer and architect Vitruvius
Vitruvius
Marcus Vitruvius Pollio was a Roman writer, architect and engineer, active in the 1st century BC. He is best known as the author of the multi-volume work De Architectura ....
contends that gravity is not dependent on a substance's "weight" but rather on its "nature".
If the quicksilverMercury (element)Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
is poured into a vessel, and a stone weighing one hundred pounds is laid upon it, the stone swims on the surface, and cannot depress the liquid, nor break through, nor separate it. If we remove the hundred pound weight, and put on a scruple of gold, it will not swim, but will sink to the bottom of its own accord. Hence, it is undeniable that the gravity of a substance depends not on the amount of its weight, but on its nature.
In the 7th Century the Indian mathematician Brahmagupta
Brahmagupta
Brahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...
stated "Bodies fall towards the earth as it is in the nature of the earth to attract bodies, just as it is in the nature of water to flow."
Modern era
Gravity was described by the 11th century Indian Mathematician Bhaskaracharya in his book called Siddhantha Siromani."Aakrishti sakthischa mahee thayaa yathkhastham guru swa abhimukham swa sakthyaa . aakrushyathe thath pathathi iti bhaathi same samanthaath kwa pathathi ayam khe" is the verse which describes that the earth attracts the solid objects in the sky by its own force towards itself. Bhaskaracharya further discusses the forces between the celestial bodies using a question: Where can the celestial bodies fall since they attract each other?
Before 1543 in De revolutionibus orbium coelestium
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus...
Copernicus
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
wrote :"...inter centrum gravitatis terrae, & centrum magnitudis..."
During the 17th century, Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
found that, counter to Aristotle's teachings, all objects accelerated equally when falling.
In the late 17th century, as a result of Robert Hooke's suggestion that there is a gravitational force which depends on the inverse square
Inverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....
of the distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
, Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
was able to mathematically
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
derive Kepler's three kinematic
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
, including the elliptical
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
orbits for the seven known planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
s:
So Newton's original formula was:
where the symbol
means "is proportional to".To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them. This gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
was first measured in 1797 by Henry Cavendish
Henry Cavendish
Henry Cavendish FRS was a British scientist noted for his discovery of hydrogen or what he called "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper "On Factitious Airs". Antoine Lavoisier later reproduced Cavendish's experiment and...
.
In 1907 Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
, in what was described by him as "the happiest thought of my life", realized that an observer who is falling from the roof of a house experiences no gravitational field. In other words, gravitation was exactly equivalent to acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
. Between 1911 and 1915 this idea, initially stated as the Equivalence principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
, was formally developed into Einstein's theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
.
Newton's theory of gravitation
In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square lawInverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....
of universal gravitation. In his own words, “I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”
Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune
Neptune
Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...
based on motions of Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...
that could not be accounted by the actions of the other planets. Calculations by John Couch Adams
John Couch Adams
John Couch Adams was a British mathematician and astronomer. Adams was born in Laneast, near Launceston, Cornwall, and died in Cambridge. The Cornish name Couch is pronounced "cooch"....
and Urbain Le Verrier both predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle
Johann Gottfried Galle
Johann Gottfried Galle was a German astronomer at the Berlin Observatory who, on 23 September 1846, with the assistance of student Heinrich Louis d'Arrest, was the first person to view the planet Neptune, and know what he was looking at...
to the discovery of Neptune.
Years later, it was another discrepancy in a planet's orbit that showed Newton's theory to be inaccurate. By the end of the 19th century, it was known that the orbit of Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
could not be accounted for entirely under Newtonian gravity, and all searches for another perturbing body (such as a planet orbiting the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
even closer than Mercury) have been fruitless. This issue was resolved in 1915 by Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
's new general theory of relativity, which accounted for the discrepancy in Mercury's orbit.
Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations still use it because it is much easier to work with and is sufficiently accurate for most applications.
Mechanical explanations of gravitation
The mechanical theories or explanations of the gravitation are attempts to explain the law of gravity by aid of basic mechanical processes, such as pushes, and without the use of any action at a distanceAction at a distance (physics)
In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant...
. These theories were developed from the 16th until the 19th century in connection with the aether theories
Aether theories
Aether theories in early modern physics proposed the existence of a medium, the aether , a space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic waves...
.
René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...
(1644) and Christiaan Huygens (1690) used vortices to explain gravitation.
Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
(1671) and James Challis
James Challis
James Challis FRS was an English clergyman, physicist and astronomer. Plumian Professor and director of the Cambridge Observatory, he investigated a wide range of physical phenomena though made few lasting contributions outside astronomy...
(1869) assumed, that every body emits waves which lead to an attraction of other bodies.
Nicolas Fatio de Duillier
Nicolas Fatio de Duillier
Nicolas Fatio de Duillier was a Swiss mathematician known for his work on the zodiacal light problem, for his very close relationship with Isaac Newton, for his role in the Newton v. Leibniz calculus controversy, and for originating the "push" or "shadow" theory of gravitation...
(1690) and Georges-Louis Le Sage
Georges-Louis Le Sage
Georges-Louis Le Sage was a physicist and is most known for his theory of gravitation, for his invention of an electric telegraph and his anticipation of the kinetic theory of gases....
(1748) proposed a corpuscular model
Le Sage's theory of gravitation
Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles impacting...
, using some sort of screening or shadowing mechanism. Later a similar model was created by Hendrik Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
, who used electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
instead of the corpuscles.
Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
(1675) and Bernhard Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
(1853) argued that aether streams carry all bodies to each other.
Newton (1717) and Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
(1760) proposed a model, in which the aether loses density near the masses, leading to a net force directing to the bodies.
Lord Kelvin (1871) proposed that every body pulsates, which might be an explanations of gravitation and the electric charges.
However, those models were overthrown because most of them lead to an unacceptable amount of drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
, which is not observed. Other models are violating the energy conservation law and are incompatible with modern thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
.
General relativity
In general relativityGeneral relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the effects of gravitation are ascribed to spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
instead of to a force. The starting point for general relativity is the equivalence principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
, which equates free fall with inertial motion. The issue that this creates is that free-falling objects can accelerate with respect to each other. In Newtonian physics, no such acceleration can occur unless at least one of the objects is being operated on by a force (and therefore is not moving inertially).
To deal with this difficulty, Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. (This type of path is called a geodesic
Geodesic (general relativity)
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational, force is a particular type of geodesic...
). More specifically, Einstein and Hilbert discovered the field equation
Field equation
A field equation is an equation in a physical theory that describes how a fundamental force interacts with matter...
s of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations
Einstein field equations
The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
are a set of 10 simultaneous, non-linear
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...
, differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s. The solutions of the field equations are the components of the metric tensor
Metric tensor (general relativity)
In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...
of spacetime. A metric tensor describes the geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.
Notable solutions of the Einstein field equations include:
- The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotatingRotationA rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
uncharged massive object. For compact enough objects, this solution generated a black holeBlack holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
with a central singularityGravitational singularityA gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...
. For radial distances from the center which are much greater than the Schwarzschild radiusSchwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity. - The Reissner-Nordström solution, in which the central object has an electrical charge. For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with an event horizonEvent horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
surrounding a Cauchy horizonCauchy horizonIn physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem...
. - The Kerr solution for rotating massive objects. This solution also produces black holes with multiple horizons.
- The cosmologicalPhysical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
Robertson-Walker solution, which predicts the expansion of the universeUniverseThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
.
General relativity has enjoyed much success because of how its predictions of phenomena which are not called for by the theory of gravity have been regularly confirmed. For example:
- General relativity accounts for the anomalous perihelionApsisAn apsis , plural apsides , is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system...
precessionPrecessionPrecession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
of the planet MercuryMercury (planet)Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
. - The prediction that time runs slower at lower potentials has been confirmed by the Pound-Rebka experimentPound-Rebka experimentThe Pound–Rebka experiment is a well known experiment to test Albert Einstein's theory of general relativity. It was proposed by Robert Pound and his graduate student Glen A. Rebka Jr. in 1959, and was the last of the classical tests of general relativity to be verified...
, the Hafele-Keating experimentHafele-Keating experimentThe Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared...
, and the GPS. - The prediction of the deflection of light was first confirmed by Arthur Eddington in 1919, and has more recently been strongly confirmed through the use of a quasarQuasarA quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...
which passes behind the SunSunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
as seen from the EarthEarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. See also gravitational lensing. - The time delay of light passing close to a massive object was first identified by Irwin Shapiro in 1964 in interplanetary spacecraft signals.
- Gravitational radiation has been indirectly confirmed through studies of binary pulsarPulsarA pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...
s. - The expansion of the universe (predicted by the Robertson-Walker metric) was confirmed by Edwin HubbleEdwin HubbleEdwin Powell Hubble was an American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way - our own galaxy...
in 1929.
Gravity and quantum mechanics
Several decades after the discovery of general relativity it was realized that it cannot be the complete theory of gravity because it is incompatible with quantum mechanicsQuantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. Later it was understood that it is possible to describe gravity in the framework of quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
like the other fundamental forces. In this framework the attractive force of gravity arises due to exchange of virtual
Virtual particle
In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...
gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons. This reproduces general relativity in the classical limit
Classical limit
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior...
. However, this approach fails at short distances of the order of the Planck length.
It is notable that in general relativity, gravitational radiation, which under the rules of quantum mechanics must be composed of gravitons, is created only in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. The amount of gravitational radiation emitted by the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as PSR 1913+16
PSR 1913+16
PSR B1913+16 is a pulsar which together with another neutron star is in orbit around a common center of mass, thus forming a binary star system. In 1974 it was discovered by Russell Alan Hulse and Joseph Hooton Taylor, Jr., of Princeton University...
. It is believed that neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
mergers and black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO
LIGO
LIGO, which stands for the Laser Interferometer Gravitational-Wave Observatory, is a large-scale physics experiment aiming to directly detect gravitational waves. Cofounded in 1992 by Kip Thorne and Ronald Drever of Caltech and Rainer Weiss of MIT, LIGO is a joint project between scientists at MIT,...
have been created to study the problem. No confirmed detections have been made of this hypothetical radiation, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change.