General Relativity (1915): Einstein's New Theory of Gravity

General relativity is Albert Einstein’s theory of gravity, completed when he presented its final field equations to the Prussian Academy of Sciences in Berlin on 25 November 1915. It describes gravity not as a force but as the curving of space and time by mass and energy. The theory explained a puzzle in the orbit of Mercury, predicted the bending of light, black holes and gravitational waves, and remains the foundation of modern cosmology.

Background: Newton and the limits of relativity

For more than two centuries, Isaac Newton’s law of universal gravitation, published in 1687, had explained the motions of planets, moons and comets with great accuracy. In Newton’s theory, gravity is a force that acts instantly between masses across any distance.

In 1905 Einstein published his special theory of relativity, part of his miracle year. It showed that space and time are linked, and that nothing, including any influence, can travel faster than light. Newton’s instantaneous gravity did not fit this picture. Special relativity also dealt only with observers moving at steady speeds, not with acceleration. Einstein wanted a theory in which the laws of physics took the same form for every observer, whether moving steadily, accelerating or falling.

The road to 1915

In 1907, while working at the patent office in Bern, Einstein had what he later called the happiest thought of his life: a person falling freely would not feel their own weight. From this came the principle of equivalence, the idea that the effects of gravity and acceleration cannot be told apart locally.

Turning that insight into a full theory took eight years. Einstein realised he needed the mathematics of curved geometry developed in the 19th century by Bernhard Riemann and others. His old friend, the mathematician Marcel Grossmann, introduced him to these tools, and in 1913 they published a first version, the so-called Entwurf (“outline”) theory. It had serious flaws, which Einstein struggled with after moving to Berlin in 1914. In April 1914 he had taken up a research post at the Prussian Academy of Sciences, which freed him from teaching. His personal life was turbulent: his marriage to Mileva Marić broke down that year, and she returned to Zurich with their two sons.

November 1915

In the autumn of 1915, with the First World War raging, Einstein worked intensely on the theory. He was also aware that the leading mathematician David Hilbert in Göttingen, to whom he had lectured on the problem that summer, was working on the same question.

Einstein presented four papers to the Prussian Academy on successive Thursdays in November 1915: on the 4th, 11th, 18th and 25th. Each paper corrected or extended the one before, as he abandoned parts of the 1913 theory and returned to ideas he had earlier set aside. On 18 November he showed that his theory accounted exactly for an anomaly in the orbit of Mercury: its closest point to the Sun shifts by about 43 arcseconds per century more than Newtonian theory predicts. He was so excited that he later said he had heart palpitations.

On 25 November he presented the final, correct field equations. In simple terms, they state that the distribution of matter and energy determines the curvature of spacetime, and the curvature of spacetime determines how matter moves. A common image is a heavy ball placed on a stretched rubber sheet, which makes a dip that causes smaller balls to roll towards it. The analogy is imperfect, because it is time as well as space that is curved, but it captures the idea that gravity is geometry rather than a pull. Hilbert submitted a paper with closely related equations on 20 November; historians still discuss the details of who reached which step first, but the two men remained on good terms, and the physical theory is generally credited to Einstein.

What the theory predicted

Einstein set out the theory in full in the journal Annalen der Physik in 1916. Its predictions included:

• The bending of light. Starlight passing close to the Sun should be deflected by about 1.75 arcseconds, twice the value suggested by Newtonian reasoning.
• Gravitational time dilation. Clocks run more slowly in stronger gravity, and light climbing out of a gravitational field is shifted towards the red.
• Gravitational waves. In 1916 Einstein predicted ripples in spacetime travelling at the speed of light.
• Extreme objects. In 1916 the German astronomer Karl Schwarzschild, then serving in the army on the Eastern Front, found an exact solution to the equations that later became the basis for describing black holes.

Testing the theory

The first dramatic test came in 1919, when British expeditions organised by Frank Dyson and Arthur Eddington photographed stars near the Sun during a total eclipse. Their results, announced in November 1919, supported Einstein, and he became world famous almost overnight. The story is told in Eddington’s eclipse expedition.

Other confirmations took longer. Gravitational redshift was measured precisely in a laboratory experiment by Robert Pound and Glen Rebka at Harvard in 1959. Radar signals bounced off planets in the 1960s showed the predicted time delays. On 14 September 2015 the LIGO detectors in the United States recorded gravitational waves from two merging black holes, a result announced in February 2016. In 2019 the Event Horizon Telescope released the first image of the shadow of a black hole.

Key people

• Albert Einstein formulated the theory over eight years of work.
• Marcel Grossmann introduced Einstein to the mathematics of curved geometry and co-authored the 1913 Entwurf theory.
• David Hilbert worked on the field equations at the same time and derived them independently from a different approach.
• Karl Schwarzschild found the first exact solution, shortly before his death in 1916.
• Arthur Eddington championed the theory in Britain and led the 1919 eclipse expedition to Príncipe.

Legacy

General relativity transformed cosmology. Applying it to the whole universe, Alexander Friedmann in 1922 and Georges Lemaître in 1927 showed that the universe could be expanding, an idea supported by Edwin Hubble’s observations of an expanding universe in 1929. The theory underlies modern ideas about the Big Bang, black holes and the large-scale structure of the cosmos.

It also has practical uses. Satellite navigation systems must correct for relativistic effects on their clocks, and astronomers use the bending of light by galaxies, known as gravitational lensing, to study distant objects and dark matter. In Potsdam, the Einstein Tower, a solar observatory designed by Erich Mendelsohn, was built in the early 1920s to search for the gravitational redshift of sunlight.

General relativity has passed every experimental test so far, but it remains incompatible with quantum mechanics, the theory that describes the smallest scales. Reconciling the two is one of the biggest unsolved problems in physics. Physicists have proposed approaches such as string theory and loop quantum gravity, but none has yet been confirmed by experiment.

Timeline

• 1905: Einstein publishes special relativity.
• 1907: Einstein formulates the equivalence principle.
• 1913: Einstein and Grossmann publish the Entwurf theory.
• 1915, 18 November: Einstein explains the anomalous orbit of Mercury.
• 1915, 25 November: Einstein presents the final field equations in Berlin.
• 1916: The full theory appears in Annalen der Physik; Schwarzschild’s solution is published.
• 1919, 6 November: Eclipse results confirming light bending are announced in London.
• 2015, 14 September: LIGO detects gravitational waves for the first time.

Why it matters

General relativity changed our basic picture of space, time and gravity. More than a century later, it still guides how scientists understand the universe, from satellite clocks to colliding black holes.