General relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
is a
theory of gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
that was developed by
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.
Before the advent of general relativity, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses, even though Newton himself did not regard the theory as the final word on the nature of gravity. Within a century of Newton's formulation, careful astronomical observation revealed unexplainable differences between the theory and the observations. Under Newton's model, gravity was the result of an attractive force between massive objects. Although even Newton was bothered by the unknown nature of that force, the basic framework was extremely successful at describing motion.
However, experiments and observations show that Einstein's description accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as
gravitational wave
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
s,
gravitational lensing
A gravitational lens is a distribution of matter (such as a galaxy cluster, cluster of galaxies) between a distant light source and an observer that is capable of bending the light from the source as the light travels toward the observer. This ...
and an effect of gravity on time known as
gravitational time dilation
Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer ...
. Many of these predictions have been confirmed by experiment or observation, while others are the subject of ongoing research.
General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape. Their strong gravity is thought to be responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nuclei or
microquasar
A microquasar, the smaller version of a quasar, is a compact region surrounding a stellar black hole with a mass several times that of its companion star. The matter being pulled from the companion star forms an accretion disk around the black hole ...
s). General relativity is also part of the framework of the standard Big Bang model of cosmology.
Creation of general relativity
Early investigations
As Einstein later said, the reason for the development of general relativity was the preference of inertial motion within
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
, while a theory which from the outset prefers no particular state of motion appeared more satisfactory to him. So, while still working at the patent office in 1907, Einstein had what he would call his "happiest thought". He realized that the
principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.
For example, in the framework of special relativity the Maxwell equations have ...
could be extended to gravitational fields.
Consequently, in 1907 he wrote an article, published in 1908, on acceleration under special relativity.
In that article, he argued that
free fall
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on i ...
is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the
equivalence principle
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
. In the same article, Einstein also predicted the phenomenon of gravitational time dilation.
In 1911, Einstein published another article expanding on the 1907 article.
[ (also in ''Collected Papers'' Vol. 3, document 23)]
There, he considered the case of a uniformly accelerated box not in a gravitational field, and noted that it would be indistinguishable from a box sitting still in an unchanging gravitational field. He used special relativity to show that clocks at the top of a box accelerating upward would run faster than clocks at the bottom. He concluded that the rate at which time passes depends on the position in a gravitational field, and that the difference in rate is proportional to the gravitational potential to a first approximation.
The article also predicted the
deflection of light by massive bodies, eg. Jupiter, the Sun. Although the approximation was crude, it allowed him to calculate that the deflection is nonzero. Einstein urged astronomers to attempt direct observation of light deflection of fixed stars near the Sun during solar eclipses when they would be visible.
German astronomer
Erwin Finlay-Freundlich
Erwin Finlay-Freundlich FRSE FRAS (; 29 May 1885 – 24 July 1964) was a German astronomer, a pupil of Felix Klein. Freundlich was a working associate of Albert Einstein and introduced experiments for which the general theory of relativity cou ...
publicized Einstein's challenge to scientists around the world.
[Crelinsten, Jeffrey.]
Einstein's Jury: The Race to Test Relativity
". ''Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large.
The press was founded by Whitney Darrow, with the financial su ...
.'' 2006. Retrieved on 13 March 2007.
In October 1911, Freundlich contacted astronomer
Charles D. Perrine in Berlin to inquire as to the suitability of examining existing solar eclipse photographs to prove Einstein's prediction of light deflection. Perrine, the director of the
Argentine National Observatory at Cordoba, had participated in four solar eclipse expeditions while at the
Lick Observatory
The Lick Observatory is an astronomical observatory owned and operated by the University of California. It is on the summit of Mount Hamilton, in the Diablo Range just east of San Jose, California, United States. The observatory is managed by th ...
, in 1900, 1901, 1905, and 1908. "...he had become, in the opinion of the director of the Lick Observatory,
W. W. Campbell
William Wallace Campbell (April 11, 1862 – June 14, 1938) was an American astronomer, and director of Lick Observatory from 1901 to 1930. He specialized in spectroscopy. He was the tenth president of the University of California from 1923 to ...
, an observer without peer in the field of solar eclipses." He did not believe existing eclipse photos would be useful in proving Einstein's claim. In 1912 Freundlich asked if Perrine would include observation of light deflection as part of his program for the solar eclipse of October 10, 1912, in Brazil. W. W. Campbell, director of the Lick Observatory, loaned Perrine its intramercurial camera lenses. Perrine and the Cordoba team were the only eclipse expedition to construct specialized equipment dedicated to observing light deflection. Unfortunately all the expeditions experienced heavy rain which prevented any observations. Nevertheless Perrine was the first astronomer to make a dedicated attempt to observe light deflection to test Einstein's prediction.
Two years later, the three observatory directors, Perrine, Freundlich, and Campbell included light deflection in their expeditions to the Russian Empire for the solar eclipse of August 21, 1914. Unfortunately due to clouds and the outbreak of
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
, no results were possible.
However, Perrine was able to take the first photographs in an attempt to verify Einstein's prediction of light deflection. A light cloud cover prevented determining accurate star positions.
In hindsight, the occluding weather and lack of results in 1912 and 1914 favored Einstein. If clear photographs and measurable results had been possible, Einstein's 1911 prediction might have been proven wrong. The amount of deflection that he calculated in 1911 was too small (0.83 seconds of arc) by a factor of two because the approximation he used does not work well for things moving at near the speed of light. When Einstein completed the full theory of general relativity in 1915, he rectified this error and predicted the correct amount of light deflection caused by the Sun (1.75 seconds of arc). Eddington and Dyson in 1919 and W. W. Campbell in 1922 were able to compare their results to Einstein's corrected prediction.
Another of Einstein's notable thought experiments about the nature of the gravitational field is that of a rotating disk (a variant of the
Ehrenfest paradox
The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity.
In its original 1909 formulation as presented by Paul Ehrenfest in relation to the concept of Born rigidity within special relativity, it discusses an idea ...
). He imagined an observer performing experiments on a rotating turntable. He noted that such an observer would find a different value for the mathematical constant π than the one predicted by Euclidean geometry. The reason is that the radius of a circle would be measured with an uncontracted ruler, but, according to special relativity, the circumference would seem to be longer because the ruler would be contracted. Since Einstein believed that the laws of physics were local, described by local fields, he concluded from this that spacetime could be locally curved. This led him to study
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to poin ...
, and to formulate general relativity in this language.
Developing general relativity
In 1912, Einstein returned to Switzerland to accept a professorship at his
alma mater,
ETH Zurich
(colloquially)
, former_name = eidgenössische polytechnische Schule
, image = ETHZ.JPG
, image_size =
, established =
, type = Public
, budget = CHF 1.896 billion (2021)
, rector = Günther Dissertori
, president = Joël Mesot
, ac ...
. Once back in Zurich, he immediately visited his old ETH classmate
Marcel Grossmann
Marcel Grossmann (April 9, 1878 – September 7, 1936) was a Swiss mathematician and a friend and classmate of Albert Einstein. Grossmann was a member of an old Swiss family from Zurich. His father managed a textile factory. He became a Profe ...
, now a professor of mathematics, who introduced him to Riemannian geometry and, more generally, to
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
. On the recommendation of Italian mathematician
Tullio Levi-Civita
Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significa ...
, Einstein began exploring the usefulness of
general covariance
In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the ''form'' of physical laws under arbitrary differentiable coordinate transformations. The essential idea is ...
(essentially the use of
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
s) for his gravitational theory. For a while, Einstein thought that there were problems with the approach, but he later returned to it and, by late 1915, had published his
general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
in the form in which it is used today. This theory explains gravitation as the distortion of the structure of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
by matter, affecting the
inertia
Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...
l motion of other matter.
During World War I, the work of
Central Powers
The Central Powers, also known as the Central Empires,german: Mittelmächte; hu, Központi hatalmak; tr, İttifak Devletleri / ; bg, Централни сили, translit=Tsentralni sili was one of the two main coalitions that fought in ...
scientists was available only to Central Powers academics, for national security reasons. Some of Einstein's work did reach the United Kingdom and the United States through the efforts of the Austrian
Paul Ehrenfest
Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition a ...
and physicists in the Netherlands, especially 1902 Nobel Prize-winner
Hendrik Lorentz
Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) 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. He also derived the Lorentz t ...
and
Willem de Sitter of
Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...
. After the war, Einstein maintained his relationship with Leiden University, accepting a contract as an
Extraordinary Professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia.
Overview
Appointment grades
* (Pay grade: ''W3'' or ''W2'')
* (''W3'')
* (''W2'')
* (''W2'', ...
; for ten years, from 1920 to 1930, he travelled to the Netherlands regularly to lecture.
In 1917, several astronomers accepted Einstein's 1911 challenge from Prague. The
Mount Wilson Observatory
The Mount Wilson Observatory (MWO) is an astronomical observatory in Los Angeles County, California, United States. The MWO is located on Mount Wilson, a peak in the San Gabriel Mountains near Pasadena, northeast of Los Angeles.
The observat ...
in California, United States, published a solar
spectroscopic
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
analysis that showed no gravitational redshift. In 1918, the
Lick Observatory
The Lick Observatory is an astronomical observatory owned and operated by the University of California. It is on the summit of Mount Hamilton, in the Diablo Range just east of San Jose, California, United States. The observatory is managed by th ...
, also in California, announced that it too had disproved Einstein's prediction, although its findings were not published.
However, in May 1919, a team led by the British astronomer
Arthur Stanley Eddington
Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lumi ...
claimed to have confirmed Einstein's prediction of gravitational deflection of starlight by the sun while photographing a solar eclipse with dual expeditions in
Sobral, northern Brazil, and
Príncipe
Príncipe is the smaller, northern major island of the country of São Tomé and Príncipe lying off the west coast of Africa in the Gulf of Guinea. It has an area of (including offshore islets) and a population of 7,324 at the 2012 Census; , a west African island.
Nobel laureate
Max Born
Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a n ...
praised general relativity as the "greatest feat of human thinking about nature"; fellow laureate
Paul Dirac
Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...
was quoted saying it was "probably the greatest scientific discovery ever made".
Jürgen Schmidhuber
Jürgen Schmidhuber (born 17 January 1963) is a German computer scientist most noted for his work in the field of artificial intelligence, deep learning and artificial neural networks. He is a co-director of the Dalle Molle Institute for Artif ...
.
Albert Einstein (1879–1955) and the 'Greatest Scientific Discovery Ever'
. 2006. Retrieved on 4 October 2006.
There have been claims that scrutiny of the specific photographs taken on the Eddington expedition showed the experimental uncertainty to be comparable to the magnitude of the effect Eddington claimed to have demonstrated, and that a 1962 British expedition concluded that the method was inherently unreliable.
The deflection of light during a solar eclipse was confirmed by later, more accurate observations. Some resented the newcomer's fame, notably some nationalistic German physicists, who later started the ''
Deutsche Physik
''Deutsche Physik'' (, "German Physics") or Aryan Physics (german: Arische Physik) was a nationalist movement in the German physics community in the early 1930s which had the support of many eminent physicists in Germany. The term was taken ...
'' (German Physics) movement.
General covariance and the hole argument
By 1912, Einstein was actively seeking a theory in which
gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
was explained as a
geometric phenomenon. At the urging of Tullio Levi-Civita, Einstein began by exploring the use of general covariance (which is essentially the use of curvature
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
s) to create a gravitational theory. However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "
hole argument In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while developing his famous field equations.
Some philosophers of physics take the argument to raise a problem for '' manifold substantialism'', a ...
". In 1914 and much of 1915, Einstein was trying to create
field equations
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum ...
based on another approach. When that approach was proven to be inconsistent, Einstein revisited the concept of general covariance and discovered that the hole argument was flawed.
The development of the Einstein field equations
When Einstein realized that general covariance was tenable, he quickly completed the development of the field equations that are named after him. However, he made a now-famous mistake. The field equations he published in October 1915 were
:
,
where
is the
Ricci tensor
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measur ...
, and
the
energy–momentum tensor Energy–momentum may refer to:
* Four-momentum
* Stress–energy tensor
* Energy–momentum relation
{{dab ...
. This predicted the non-
Newtonian perihelion precession
In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points closest (periapsi ...
of
Mercury
Mercury commonly refers to:
* Mercury (planet), the nearest planet to the Sun
* Mercury (element), a metallic chemical element with the symbol Hg
* Mercury (mythology), a Roman god
Mercury or The Mercury may also refer to:
Companies
* Merc ...
, and so had Einstein very excited. However, it was soon realized that they were inconsistent with the local
conservation of energy–momentum unless the universe had a constant density of mass–energy–momentum. In other words, air, rock and even a vacuum should all have the same density. This inconsistency with observation sent Einstein back to the drawing board and, on 25 November 1915, Einstein presented the updated Einstein field equations to the
Prussian Academy of Sciences
The Royal Prussian Academy of Sciences (german: Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin ...
:
:
,
where
is the
Ricci scalar
In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometr ...
and
the
metric tensor
In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
. With the publication of the field equations, the issue became one of solving them for various cases and interpreting the solutions. This and experimental verification have dominated general relativity research ever since.
Einstein and Hilbert
Although Einstein is credited with finding the field equations, the German mathematician
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
published them in an article before Einstein's article. This has resulted in accusations of
plagiarism
Plagiarism is the fraudulent representation of another person's language, thoughts, ideas, or expressions as one's own original work.From the 1995 '' Random House Compact Unabridged Dictionary'': use or close imitation of the language and thought ...
against Einstein, although not from Hilbert, and assertions that the field equations should be called the "Einstein–Hilbert field equations". However, Hilbert did not press his claim for priority and some have asserted that Einstein submitted the correct equations before Hilbert amended his own work to include them. This suggests that Einstein developed the correct field equations first, though Hilbert may have reached them later independently (or even learned of them afterwards through his correspondence with Einstein). However, others have criticized those assertions.
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
stated, "Remarkably, Einstein was not the first to discover the correct form of the law of warpage
. . .Recognition for the first discovery must go to Hilbert."
Sir Arthur Eddington
In the early years after Einstein's theory was published,
Sir Arthur Eddington
Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lumi ...
lent his considerable prestige in the British scientific establishment in an effort to champion the work of this German scientist. Because the theory was so complex and abstruse (even today it is popularly considered the pinnacle of scientific thinking; in the early years it was even more so), it was rumored that only three people in the world understood it. There was an illuminating, though probably apocryphal, anecdote about this. As related by
Ludwik Silberstein
Ludwik Silberstein (1872 – 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework. His textbook '' The Theory of Relativity'' was published by Macmillan in 1914 with a se ...
, during one of Eddington's lectures he asked "Professor Eddington, you must be one of three persons in the world who understands general relativity." Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is."
Solutions
The Schwarzschild solution
Since the field equations are
non-linear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
, Einstein assumed that they were unsolvable. However,
Karl Schwarzschild
Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.
Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-r ...
discovered in 1915 and published in 1916 an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in
spherical coordinates
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measu ...
. This is now known as the
Schwarzschild solution
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assump ...
. Since then, many other exact solutions have been found.
The expanding universe and the cosmological constant
In 1922,
Alexander Friedmann
Alexander Alexandrovich Friedmann (also spelled Friedman or Fridman ; russian: Алекса́ндр Алекса́ндрович Фри́дман) (June 16 .S. 4 1888 – September 16, 1925) was a Russian and Soviet physicist and mathematician ...
found a solution in which the universe may expand or contract, and later
Georges Lemaître
Georges Henri Joseph Édouard Lemaître ( ; ; 17 July 1894 – 20 June 1966) was a Belgian Catholic priest, theoretical physicist, mathematician, astronomer, and professor of physics at the Catholic University of Louvain. He was the first to th ...
derived a solution for an expanding universe. However, Einstein believed that the universe was static, and since a static cosmology was not supported by the general relativistic field equations, he added a
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
Λ to the field equations, which became
:
.
This permitted the creation of
steady-state solutions, but they were unstable: the slightest perturbation of a static state would result in the universe expanding or contracting. In 1929,
Edwin Hubble
Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology.
Hubble proved that many objects ...
found evidence for the universe expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career". At the time, it was an
ad hoc
Ad hoc is a Latin phrase meaning literally 'to this'. In English, it typically signifies a solution for a specific purpose, problem, or task rather than a generalized solution adaptable to collateral instances. (Compare with ''a priori''.)
Com ...
hypothesis to add in the cosmological constant, as it was only intended to justify one result (a static universe).
More exact solutions
Progress in solving the field equations and understanding the solutions has been ongoing. The solution for a spherically symmetric charged object was discovered by Reissner and later rediscovered by Nordström, and is called the
Reissner–Nordström solution. The black hole aspect of the Schwarzschild solution was very controversial, and Einstein did not believe that singularities could be real. However, in 1957 (two years after Einstein's death),
Martin Kruskal
Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and ...
published a proof that black holes are called for by the Schwarzschild solution. Additionally, the solution for a rotating massive object was obtained by
Roy Kerr
Roy Patrick Kerr (; born 16 May 1934) is a New Zealand mathematician who discovered the Kerr metric, Kerr geometry, an exact solutions in general relativity, exact solution to the Einstein field equation of general relativity. His solution mo ...
in the 1960s and is called the
Kerr solution
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...
. The
Kerr–Newman solution for a rotating, charged massive object was published a few years later.
Testing the theory
The first piece of evidence in support of general relativity came from its correct prediction of the anomalous rate of precession of Mercury's orbit. Subsequently, Arthur Stanley Eddington's 1919 expedition confirmed Einstein's prediction of the deflection of light by the Sun during the total
solar eclipse of 29 May 1919, which helped to cement the status of general relativity as a viable theory. Since then, many observations have shown agreement with the predictions of general relativity. These include studies of
binary pulsar
A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. (In at least one case, the double pulsar PSR J0737-3039, the companion neutron star is another pulsar as well.) Binary pulsars are one of the few objects ...
s, observations of radio signals passing the limb of the Sun, and even the
global positioning system
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
.
![Black hole - Messier 87 crop max res](https://upload.wikimedia.org/wikipedia/commons/4/4f/Black_hole_-_Messier_87_crop_max_res.jpg)
The theory predicts
gravitational waves
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that Wave propagation, propagate as waves outward from their source at the speed of light. They were first proposed by Oliv ...
, which are ripples in the
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
of spacetime that propagate as
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
s, travelling outward from the source. The
first observation of gravitational waves
The first direct observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016. Previously, gravitational waves had been inferred only indirectly, via their effect on t ...
, which came from the merger of two
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s, was made on 14 September 2015 by the
Advanced LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large ...
team, corroborating another prediction of the theory 100 years after it was published.
The first image of a black hole, the supermassive one at the center of galaxy
Messier 87
Messier 87 (also known as Virgo A or NGC 4486, generally abbreviated to M87) is a supergiant elliptical galaxy with several trillion stars in the constellation Virgo. One of the largest and most massive galaxies in the local uni ...
, was published by the
Event Horizon Telescope Collaboration on 10 April 2019.
Alternative theories
There have been various attempts to find modifications to general relativity. The most famous of these are the
Brans–Dicke theory (also known as
scalar–tensor theory
In theoretical physics, a scalar–tensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction. For example, the Brans–Dicke theory of gravitation uses both a scalar field and a ...
), and
Rosen's bimetric theory. Both of these theories proposed changes to the field equations of general relativity, and both suffer from these changes permitting the presence of bipolar gravitational radiation. As a result, Rosen's original theory has been refuted by observations of binary pulsars. As for Brans–Dicke (which has a tunable parameter ''ω'' such that ω = ∞ is the same as general relativity), the amount by which it can differ from general relativity has been severely constrained by these observations. Many other alternatives to general relativity have also been ruled out by analyses of the neutron-star merger
GW170817
GW 170817 was a gravitational wave (GW) signal observed by the LIGO and Virgo detectors on 17 August 2017, originating from the shell elliptical galaxy . The signal was produced by the last minutes of a binary pair of neutron stars' insp ...
.
In addition, general relativity is inconsistent with
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, the physical theory that describes the wave–particle duality of matter, and quantum mechanics does not currently describe gravitational attraction at relevant (microscopic) scales. There is a great deal of speculation in the physics community as to the modifications that might be needed to both general relativity and quantum mechanics in order to unite them consistently. The speculative theory that unites general relativity and quantum mechanics is usually called
quantum gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
, prominent examples of which include
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
and
loop quantum gravity.
Golden age
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
identifies the "golden age of general relativity" as the period roughly from 1960 to 1975, during which the study of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, which had previously been regarded as something of a curiosity, entered the mainstream of
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
. During this period, many of the concepts and terms which continue to inspire the imaginations of gravitation researchers and the general public were introduced, including black holes and
gravitational singularities
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer part of the regular sp ...
. At the same time, in a closely related development, the study of
physical cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of f ...
entered the mainstream and the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
became well established.
Fulvio Melia
Fulvio Melia (born 2 August 1956) is an Italian- American astrophysicist, cosmologist and author. He is professor of physics, astronomy and the applied math program at the University of Arizona and was a scientific editor of ''The Astrophysical ...
refers frequently to the "golden age of relativity" in his book ''Cracking the Einstein Code''.
Andrzej Trautman hosted a relativity conference in
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...
in 1962 to which Melia refers:
:General relativity moved very successfully from that meeting in Warsaw, hot on the heels of the
Pound–Rebka experiment
The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
, and entered its golden age of discovery that lasted into the mid-1970s.
Roy Kerr, protagonist of the book, contributed an Afterword, saying of the book: "It is a remarkable piece of writing capturing beautifully the period we now refer to as the golden age of relativity."
[Roy Kerr (2009) Afterword, ''Cracking the Einstein Code'', page 127]
See also
*
List of contributors to general relativity
*
Golden age of cosmology The ''golden age of cosmology'' is a term often used to describe the period from 1992 to the present in which important advances in observational cosmology have been made.
The golden age of cosmology is a term used to describe a period of time that ...
*
Golden age of physics
*
Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothe ...
*
Timeline of gravitational physics and relativity
The following is a timeline of gravitational physics and general relativity.
Before 1500
* 3rd century BC - Aristarchus of Samos proposes heliocentric model, measures the distance to the Moon and its size
1500s
* 1543 – Nicolaus Copernicus pla ...
*
W. K. Clifford#Premonition of relativity
References
Bibliography
*
*
*''Einstein and the Changing Worldviews of Physics'' (editors—Lehner C., Renn J., Schemmel M.) 2012 (
Birkhäuser
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields:
* Springer continues to publish science (particu ...
).
Genesis of general relativity series
*
*
External links
*
{{History of physics
General relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
Albert Einstein