Relativity and gravity: from time dilation to gravitational lenses

At a glance

Relativity replaced Newton’s absolute space and time. Special relativity (1905) describes how measurements of time and length depend on motion; general relativity (1915) explains gravity as the curvature of spacetime by mass and energy. Every test so far, from eclipses to orbiting gyroscopes, has agreed with them within its measurement uncertainty.

Values and uncertainties as quoted in the cited papers (1919 values corrected to the solar limb; muon result at 95 % confidence). ″ = arcsecond; mas/yr = milliarcseconds per year. Checked October 2026.

Sources: [1] [2] [3] [4] [5] [6] [7] [8]

Special relativity: time, length and E = mc²

Einstein built special relativity on two postulates: the laws of physics are the same for all observers moving at constant velocity, and all of them measure the same speed of light, about 300,000 km/s. It follows that a clock moving at speed v relative to us ticks slower by the Lorentz factor γ = 1/√(1 − v²/c²) (time dilation); a moving object is shorter along its direction of motion by the same factor (length contraction); and mass is a form of energy, E = mc², which sets the energy released by nuclear fusion in the Sun.

A muon at rest decays after about 2.2 microseconds on average, in which time light travels only about 660 metres. In 1977 a team at CERN circulated muons with γ = 29.33 in a storage ring and measured mean lifetimes of about 64.4 microseconds, confirming the time-dilation factor to 2 parts in 1,000. The same effect lets muons created by cosmic rays high in the atmosphere survive long enough to reach the ground.

Sources: [1] [6]

General relativity: gravity as curved spacetime

General relativity starts from the equivalence principle: inside a small, freely falling laboratory the effects of gravity vanish, so all bodies fall with the same acceleration whatever they are made of. Torsion balances confirm this to about 2 parts in 10¹³, and lunar laser ranging shows that the Earth and Moon fall alike to 1.4 parts in 10¹³. The MICROSCOPE satellite compared titanium and platinum test masses in orbit; its final 2022 analysis gave an Eötvös parameter η = [−1.5 ± 2.3 (stat) ± 1.5 (syst)] × 10⁻¹⁵, consistent with zero.

If all bodies fall alike, gravity can be treated as a property of spacetime itself. In general relativity, mass and energy curve spacetime, and freely moving bodies and light follow the straightest possible paths, called geodesics, through it. In the Solar System the theory predicts small departures from Newton: clocks run slower deeper in a gravitational field, light is deflected and delayed as it passes a mass, orbits precess, and a rotating body drags spacetime around with it. Deviations are measured with parameters such as γ, the space curvature produced by unit mass: 1 in general relativity, 0 in Newtonian gravity.

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The classic tests: Mercury, starlight, clocks and radio echoes

Mercury. Mercury‘s perihelion, the orbit’s closest point to the Sun, slowly turns; the other planets explain most of this motion, but not a small excess. General relativity predicts an extra advance of 42.98 arcseconds per century, matching the observed discrepancy.

The 1919 eclipse. A ray of starlight grazing the Sun should be bent by 1.75 arcseconds, twice the 0.87″ obtained by treating light as Newtonian particles. During the total eclipse of 29 May 1919, British expeditions photographed stars around the darkened Sun from Sobral in Brazil and from Príncipe off West Africa, and compared their positions with night-time images of the same field. Corrected to the solar limb, Sobral’s 4-inch lens gave 1.98 ± 0.12″ and Príncipe 1.61 ± 0.30″; a third Sobral data set, giving 0.93″, was set aside. Announced in London on 6 November 1919, the results helped make Einstein famous; a 2020 re-examination rejects later claims that the data were selected to favour him. Today radio interferometers measure the bending of quasar light: data up to 2010 give γ − 1 = (−0.8 ± 1.2) × 10⁻⁴.

Gravitational redshift. Clocks deeper in a gravitational field run slower, so light climbing out of it arrives at a lower frequency. In 1959 Robert Pound and Glen Rebka proposed measuring this over the 22 m height of a tower at Harvard, using the sharp gamma-ray resonance of iron-57. Their 1960 result was 1.05 ± 0.10 times the predicted shift, and later work by Pound and J. L. Snider reached about 1 per cent. In 1976 a hydrogen-maser clock flown on a rocket, Gravity Probe A, confirmed the effect to 2 parts in 10⁴.

Shapiro delay. In 1964 Irwin Shapiro showed that radio signals passing close to the Sun should also be delayed. The most precise test used radio links with the Cassini spacecraft, on its way to Saturn, around the favourable solar conjunction of 2002: γ = 1 + (2.1 ± 2.3) × 10⁻⁵, agreeing with general relativity to about 2 parts in 100,000.

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Frame dragging: a spinning Earth twists spacetime

A gyroscope orbiting the Earth should show two subtle effects: geodetic precession, caused by the curvature of space around the planet, and frame dragging (the Lense–Thirring effect), caused by the Earth’s rotation. NASA’s Gravity Probe B, launched on 20 April 2004, collected data with four cryogenic gyroscopes from August 2004 to August 2005. Its final analysis, published in 2011, confirmed both effects, with precisions of about 0.3 and 20 per cent.

Frame dragging also slowly turns the orbital planes of satellites. Laser tracking of the two LAGEOS satellites gave a 5–10 per cent confirmation; the LARES-2 satellite has now improved on this by a factor of fifty or more (see Current research).

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Relativity in orbit: why GPS needs Einstein

GPS receivers turn the travel times of signals from satellite atomic clocks into distances. Compared with ground clocks, a GPS satellite clock gains about 46 microseconds per day because it sits higher in Earth’s gravitational field and loses about 7 because of its orbital speed of about 3.9 km/s. Neil Ashby’s detailed treatment gives a net rate difference of 4.4647 parts in 10¹⁰, or 38.6 microseconds per day. Light travels about 11.6 km in that time, and without the correction GPS could not work at its stated accuracy.

The correction is built into the hardware: before launch the satellite clocks are set to 10.22999999543 MHz instead of the nominal 10.23 MHz, so that in orbit they keep time with ground clocks; a periodic term from slightly eccentric orbits (up to about 23 ns for an eccentricity of 0.01) is corrected separately. The two effects cancel for a circular orbit with a radius of about 9,545 km, roughly 3,200 km above the surface: clocks lower down, such as those on the International Space Station, run slow overall, and clocks higher up run fast (Figure 2).

Sources: [1] [8]

Calculator: relativity and satellite clocks

The calculator opens on a GPS orbit. Lower the altitude towards the ISS preset and watch the net offset change sign near 3,200 km, then compare the Galileo and geostationary presets.

The calculator assumes a circular orbit around a spherical, non-rotating Earth (see its formula notes), yet for GPS it returns about +45.7 µs per day from gravity, −7.2 µs from speed and +38.5 µs net, within 0.1 µs of Ashby’s result.

Gravitational lensing: rings, arcs and microlensing

Because mass bends light, a galaxy or a galaxy cluster can act as a lens for more distant sources, producing multiple images, arcs or, when source, lens and observer line up, a complete Einstein ring. Einstein worked out the case of one star lensing another in a short 1936 note, adding that there was “no hope of observing this phenomenon directly”. The first lensed quasar, a double image of Q0957+561 at redshift 1.41, was found in 1979, and the first complete Einstein ring in 1998. Today strong lensing weighs galaxies and clusters, dark matter included, and weak lensing, the slight distortion of countless background galaxies, maps dark matter for surveys such as Euclid.

Microlensing is the stellar case Einstein thought unobservable. When a foreground star drifts almost exactly in front of a background star, the two images are far too close to separate (for a typical lens in our Galaxy the Einstein ring is about half a milliarcsecond in radius), but their combined light brightens and fades over weeks. A planet around the lens star adds a brief extra signal, and a free-floating planet of Jupiter’s mass produces an event lasting only a day or two. The method is most sensitive to planets 1–5 au from their stars, around the snow line, complementing the techniques on our exoplanets page. The longest-running survey, OGLE, has watched the Milky Way‘s bulge since 1992 with the 1.3 m Warsaw Telescope at Las Campanas, Chile; MOA uses a 1.8 m telescope in New Zealand; and the Korea Microlensing Telescope Network (KMTNet), with telescopes in Chile, South Africa and Australia carrying 4-square-degree cameras, has run its large-scale survey since 2016.

Sources: [9] [10]

Simulator: gravitational lensing

The simulator starts with a typical microlensing event: a 0.3-solar-mass star 4,000 parsecs away passing in front of a bulge star at 8,000 parsecs. Note the Einstein radius and the duration, then reduce the closest approach to watch the peak brightening climb, or try the galaxy and cluster presets.

For the default event it gives an Einstein radius of about 550 microarcseconds (0.55 milliarcseconds, or 2.2 au in the lens plane), a peak magnification of about 3.4 and a crossing time of about 19 days. Lens and source are treated as points, and its notes explain why the galaxy and cluster results are only indicative.

Strong gravity: pulsars, gravitational waves and black holes

The orbit of the Hulse–Taylor binary pulsar shrinks as the system radiates gravitational waves, at 0.997 ± 0.002 of the predicted rate, and in the double pulsar discovered in 2003 the geodetic precession of one pulsar’s spin matches the theory to about 13 per cent (see neutron stars). Gravitational waves have since been detected directly; our gravitational waves page explains how black-hole and neutron-star mergers test the theory where gravity is strongest.

General relativity also predicts black holes, from which not even light escapes; gas falling into supermassive ones powers active galaxies and quasars.

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Current research (2024–2026)

Frame dragging to a part in a thousand. In July 2026 the LARES-2 team reported in Nature a measurement of Earth’s frame dragging from laser ranging to LARES-2 and LAGEOS, combined with gravity-field data from the GRACE missions. The authors quote a relative uncertainty at the one-part-in-a-thousand level, against about 20 per cent for Gravity Probe B, and call the result a stringent confirmation of general relativity near Earth; the error budget rests on how well Earth’s uneven gravity field is modelled.

Atomic clocks on the space station. ESA’s Atomic Clock Ensemble in Space (ACES) was launched on 21 April 2025 and mounted outside the Columbus module four days later. It combines a caesium clock, PHARAO, with a hydrogen maser and can compare the best ground clocks at about one part in 10¹⁷, testing gravitational time dilation and searching for slow changes in fundamental constants. It is planned to operate for 30 months, beginning with six months of commissioning.

Time on the Moon. In August 2024 a NIST study by Neil Ashby and Bijunath Patla found that clocks on the lunar surface tick faster than clocks on Earth by about 56 microseconds per day, a correction that navigation for future missions to the Moon must include.

Microlensing from space. NASA’s Nancy Grace Roman Space Telescope was launched on 30 August 2026 and in late October was in its final commissioning phase. Its Galactic Bulge Time-Domain Survey will image the bulge every 12.1 minutes during six seasons and aims to find more than a thousand wide-orbit planets by microlensing, plus more than 100,000 transiting planets.

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Open questions and going further

General relativity and quantum mechanics are each superbly tested, yet they cannot both be the final word: relativity predicts singularities inside black holes and at the start of cosmic expansion, where a quantum theory of gravity should take over, and no experiment has yet chosen between candidate theories. The accelerating expansion of the Universe is described by adding a cosmological constant, or dark energy, to Einstein’s equations, but its nature is unknown (see dark matter and dark energy and the Big Bang). Any rival theory must reproduce every result in the table above.

Much of the primary data is public. The International Laser Ranging Service distributes laser-ranging data for satellites such as LAGEOS; the International GNSS Service publishes precise satellite orbits and clock corrections; OGLE’s Early Warning System lists microlensing events as they are found (938 candidates in the 2026 season by late October); the NASA Exoplanet Archive counts 292 microlensing planets among 6,451 confirmed exoplanets; and the Gravitational Wave Open Science Center releases detector data.

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Known vs open questions

Established results

• Moving clocks run slow and clocks higher in a gravitational field run fast, as predicted; GPS corrects for both.
• The Sun bends and delays light as predicted; γ = 1 holds to about 2 parts in 100,000.
• Bodies of different composition fall alike to about one part in 10¹⁵.
• The rotating Earth drags spacetime, now measured to about a part in a thousand.
• Gravitational lensing is a routine tool, from Einstein rings to microlensing planets.

Open questions

• How can general relativity be reconciled with quantum mechanics, and what replaces its singularities?
• What is dark energy, and does it change over time?
• Is dark matter made of particles, or does gravity behave differently on galactic scales?
• Will clocks in space or gravitational-wave observatories reveal any deviation from Einstein’s theory?

Related on this site

• Research dossier: cosmology
• Gravitational waves
• Black holes
• Active galaxies and quasars
• Eclipses
• Dark matter and dark energy
• Orbit lab