Einstein's general relativity
Eventually, astronomers noticed an eccentricity in the orbit of the planet Mercury which could not be explained by Newton's theory: the perihelion of the orbit was increasing by about 42.98 arcseconds per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body, such as a planet orbiting the Sun even closer than Mercury, but all efforts to find such a body turned out to be fruitless. In 1915, Albert Einstein developed a theory of general relativity which was able to accurately model Mercury's orbit.
Einstein's theory brought two other ideas with independent histories into the physical theories of gravity: the principle of relativity and non-Euclidean geometry.
The principle of relativity, introduced by Galileo and used as a foundational principle by Newton, led to a long and fruitless search for a luminiferous aether after Maxwell's equations demonstrated that light propagated at a fixed speed independent of reference frame. In Newton's mechanics, velocities add: a cannon ball shot from a moving ship would travel with a trajectory which included the motion of the ship. Since light speed was fixed, it was assumed to travel in a fixed, absolute medium. Many experiments sought to reveal this medium but failed and in 1905 Einstein's special relativity theory showed the aether was not needed. Special relativity proposed that mechanics be reformulated to use the Lorentz transformation already applicable to light rather than the Galilean transformation adopted by Newton. Special relativity, as in special case, specifically did not cover gravity.
While relativity was associated with mechanics and thus gravity, the idea of altering geometry only joined the story of gravity once mechanics required the Lorentz transformations. Geometry was an ancient science that gradually broke free of Euclidean limitations when Carl Gauss discovered in the 1800s that surfaces in any number of dimensions could be characterized by a metric, a distance measurement along the shortest path between two points that reduces to Euclidean distance at infinitesimal separation. Gauss' student Bernhard Riemann developed this into a complete geometry by 1854. These geometries are locally flat but have global curvature.
In 1907, Einstein took his first step by using special relativity to create a new form of the equivalence principle. The equivalence of inertial mass and gravitational mass was a known empirical law. The m in Newton's first law,
F
=
m
a
{\displaystyle F=ma}
, has the same value as the m in Newton's law of gravity on Earth,
F
=
G
M
m
/
r
2
{\displaystyle F=GMm/r^{2}}
. In what he later described as "the happiest thought of my life" Einstein realized this meant that in free-fall, an accelerated coordinate system exists with no local gravitational field. Every description of gravity in any other coordinate system must transform to give no field in the free-fall case, a powerful invariance constraint on all theories of gravity.
Einstein's description of gravity was accepted by the majority of physicists for two reasons. First, by 1910 his special relativity was accepted in German physics and was spreading to other countries. Second, his theory explained experimental results like the perihelion of Mercury and the bending of light around the Sun better than Newton's theory.
In 1919, the British astrophysicist Arthur Eddington was able to confirm the predicted deflection of light during that year's solar eclipse. Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. Although Eddington's analysis was later disputed, this experiment made Einstein famous almost overnight and caused general relativity to become widely accepted in the scientific community.
In 1959, American physicists Robert Pound and Glen Rebka performed an experiment in which they used gamma rays to confirm the prediction of gravitational time dilation. By sending the rays down a 74-foot tower and measuring their frequency at the bottom, the scientists confirmed that light is Doppler shifted as it moves towards a source of gravity. The observed shift also supports the idea that time runs more slowly in the presence of a gravitational field (many more wave crests pass in a given interval). If light moves outward from a strong source of gravity it will be observed with a redshift. The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals.
In 1971, scientists made the first-ever discovery of a black hole, in the constellation Cygnus. The black hole was detected because it was emitting bursts of x-rays as it consumed a smaller star, and it came to be known as Cygnus X-1. This discovery confirmed yet another prediction of general relativity, because Einstein's equations implied that light could not escape from a sufficiently large and compact object.
Frame dragging, the idea that a rotating massive object should twist spacetime around it, was confirmed by Gravity Probe B results in 2011. In 2015, the LIGO observatory detected faint gravitational waves, the existence of which had been predicted by general relativity. Scientists believe that the waves emanated from a black hole merger that occurred 1.5 billion light-years away.
