General Relativity — Einstein Curves Spacetime

On 25 November 1915, after eight years of work, Albert Einstein presented the field equations of general relativity to the Prussian Academy of Sciences: gravity is no longer a force, but the curvature of spacetime produced by mass and energy. Four years later, the eclipse observed by Eddington confirmed the deflection of light by the Sun; a century later, LIGO detected the gravitational waves the theory had predicted. One hundred and ten years on, no deviation has been measured — and GPS would not work without it.

Source: physicstoday.aip.org

In plain terms

Picture a stretched sheet with a heavy ball placed on it: the fabric sags, and a marble rolled past it follows the slope instead of travelling straight. That is Einstein's idea: the Earth does not "fall" toward the Sun, it follows the dip that the Sun's mass presses into spacetime. The consequence is very concrete: time does not flow at the same rate everywhere, and GPS satellites must correct 38 µs per day or drift by roughly 10 km per day. In 110 years the theory has passed every test with no deviation observed. It does not explain everything, though: no one yet knows how to reconcile it with quantum mechanics, which governs the very small.

Discovery — The field equations (1915)

After 8 years of relentless work generalising special relativity (1905), Einstein formulated the field equations that describe how matter and energy curve spacetime, and how that curvature dictates the motion of objects. He published four papers in November 1915, culminating on 25 November with the final equation.

Technical explanation — Gravity as geometry

Before Einstein, Newtonian gravity was an instantaneous force at a distance: two masses attract each other in proportion to $F = Gm_1m_2/r^2$F=Gm1​m2​/r2. The problem: this force acts instantaneously, which violates special relativity (nothing travels faster than $c$c). Moreover, Newton could not explain the advance of Mercury's perihelion (~43 arcseconds/century).

1. The equivalence principle (1907) — Einstein realised that a person in free fall does not feel gravity: acceleration and gravity are locally indistinguishable. He called it "the happiest thought of [his] life". Consequence: gravity is not a force, but an effect of geometry.

2. Curved spacetime — Mass-energy deforms the fabric of spacetime the way a heavy ball deforms a stretched sheet. Objects follow the straightest possible lines through this curved geometry (geodesics). The Earth does not "fall" toward the Sun — it follows the curvature of spacetime created by the Sun's mass.

3. The field equation — $G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$Gμν​=c48πG​Tμν​. On the left: the geometry of spacetime (Einstein tensor). On the right: the matter-energy content (stress-energy tensor). Matter tells space how to curve; space tells matter how to move. The cosmological constant term $\Lambda g_{\mu\nu}$Λgμν​ is not part of the November 1915 equations: Einstein only introduced it in 1917.

4. Gravitational time dilation — A clock in a weak gravitational field runs faster than a clock in a strong one. On Earth: a clock at the top of a 100 m tower gains ~1 ns/day relative to ground level. GPS must correct this offset of 38 µs/day (general relativity: +45 µs, special relativity: −7 µs) or positioning errors of ~10 km/day would build up.

Why it worked

Einstein's genius was to recast gravity as a problem of geometry rather than force. By using Riemann's differential geometry (mathematics developed 50 years earlier with no physical application), he eliminated the problem of instantaneous action: curvature propagates at the speed of light in the form of gravitational waves.

The comparison with Newton is quantitative: the advance of Mercury's perihelion, ~43 arcseconds per century, remained unexplained by Newtonian mechanics; general relativity reproduces it exactly, to within less than 0.1%. Across all the tests carried out since, the observed deviation remains below 10⁻¹⁴.

Predictions and confirmations

Causal chain

General relativity (1915) → Eddington confirmation (1919) → Modern cosmology / Big Bang (Lemaître, 1927) → Theoretical black holes (Schwarzschild, Kerr) → GPS (mandatory relativistic correction) → Detection of gravitational waves (LIGO, 2015) → Image of a black hole (EHT, 2019)

Anecdote

Einstein took 8 years to develop general relativity, learning differential geometry with the help of his mathematician friend Marcel Grossmann. He would describe the equivalence principle as "der glücklichste Gedanke meines Lebens" (the happiest thought of his life). In 1916 he predicted gravitational waves — then came to doubt them, before being corrected by the reviewer of his manuscript. They were detected on 14 September 2015, exactly one hundred years after the theory, from the merger of two black holes 1.3 billion light-years away.

In November 1915, David Hilbert was working in parallel to reach the same equations independently. That race has come down to us as the "Einstein-Hilbert priority dispute", but the physical insight belongs to Einstein — and Hilbert himself acknowledged as much.

Legacy and current data

General relativity is the most precise theory of gravity ever formulated. After 110 years of testing, no deviation has been observed. It is essential to the everyday operation of GPS and to our understanding of the universe.

One of the great open projects of contemporary physics remains the unification of general relativity, which describes the very large scales, with quantum mechanics, which describes the very small. Near the singularity of a black hole both theories are required at once — and the unified theory, "quantum gravity", does not yet exist.

Sources

References verified during the August 2026 fact-checking audit: these are the pages
against which this bulletin's claims were checked.

1. Arch and Scaffold: How Einstein Found His Field Equations — Physics Today
2. The Genesis of General Relativity (analysis of the November 1915 communications)
3. Was Einstein the First to Discover General Relativity? — Princeton University Press