Gravity

Gravity is the fundamental interaction by which all objects with [mass] or energy attract one another. It governs the fall of objects toward the ground, the orbits of planets around the Sun, the formation of stars and galaxies, and the large-scale structure of the universe. Of the four [fundamental forces] of nature — gravity, [electromagnetism], the [weak nuclear force], and the [strong nuclear force] — gravity is by far the weakest at the scale of subatomic particles, yet it dominates at astronomical distances because it is universally attractive, has infinite range, and cannot be shielded.

Two theoretical frameworks describe gravity. [Isaac Newton]'s law of universal gravitation (1687) treats gravity as a force between masses and provides excellent predictions for most everyday and astronomical situations. [Albert Einstein]'s [general theory of relativity] (1915) supersedes Newton's account by describing gravity as the curvature of [spacetime] caused by mass and energy, and it is required for situations where gravitational fields are strong or speeds are high. A longstanding open problem in physics is how to reconcile general relativity with [quantum mechanics]; no complete and experimentally validated theory of [quantum gravity] yet exists.

Newtonian gravity

Isaac Newton formulated the law of universal gravitation in his Philosophiæ Naturalis Principia Mathematica, first published on July 5, 1687. The law states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. In modern notation:

F = G · mM / r²

where F is the magnitude of the gravitational force, m and M are the two masses, r is the distance between them, and G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N·m²/kg²). The publication of this law has been called the "first great unification" in physics: it unified the previously separate phenomena of falling bodies on Earth with the motions of the Moon, planets, and comets, all shown to follow from a single mathematical principle.^[1:1]

Newton himself did not explain the physical cause of gravity. In the famous General Scholium added to the second edition of Principia (1713), he wrote that he had explained the phenomena of the heavens and seas by the force of gravity but had not yet assigned a cause to it — expressing this in the Latin phrase hypotheses non fingo ("I feign no hypotheses").

The gravitational constant G does not appear explicitly in Newton's original work, as he could only compute forces relative to one another. Its first accurate experimental measurement came in 1798, when Henry Cavendish used a torsion-balance apparatus to measure the tiny gravitational attraction between laboratory-scale masses — more than a century after Newton's publication.^[1:2] Cavendish's value differs by less than 1% from the modern accepted value.

Newtonian gravity remains highly useful. It is accurate enough to plan spacecraft trajectories throughout the solar system, and it reduces to an excellent approximation of general relativity wherever gravitational fields are weak and velocities are small compared to the speed of light.

General relativity

In the late 19th and early 20th centuries, the development of [special relativity] exposed a fundamental problem with Newton's theory: it requires gravity to act instantaneously across any distance, meaning a change in the Sun's position would be felt on Earth at the same moment it occurred.^[2:1] Special relativity, however, prohibits any influence from propagating faster than the speed of light. A new theory of gravity was therefore needed.

Albert Einstein developed [general relativity] between 1907 and 1915, publishing its final form in November 1915. Rather than treating gravity as a force transmitted between bodies, Einstein reconceived it as a geometric property of four-dimensional spacetime: mass and energy curve the fabric of spacetime, and objects moving through that curved spacetime follow the straightest possible paths (called [geodesics]). What we experience as gravitational attraction is the effect of this curvature on motion.

The central guiding idea is the equivalence principle: on a local scale — that is, within a small enough region of space and time — the physical effects of gravity are indistinguishable from those of acceleration.^[2:2] A person in a sealed, freely falling elevator cannot perform any local experiment to determine whether they are in free fall in a gravitational field or floating in deep space far from any mass. Einstein elevated this observation into the foundation of the theory.

General relativity makes several predictions that go beyond Newton's theory, all of which have been confirmed experimentally:

• Precession of Mercury's perihelion. Mercury's orbit precesses by about 43 arcseconds per century more than Newtonian gravity predicts. General relativity accounts for this discrepancy exactly.
• Deflection of starlight. Massive bodies bend the path of light passing near them. This was confirmed during the solar eclipse of May 29, 1919, when stars near the Sun were observed to be shifted in position by the amount Einstein predicted.
• Gravitational redshift. Light escaping a gravitational field loses energy and shifts to longer (redder) wavelengths. This has been measured in laboratory experiments and confirmed with high precision by atomic clocks at different altitudes.
• Gravitational time dilation. Clocks run slower in stronger gravitational fields. This effect is large enough to require correction in [GPS] satellites, which would accumulate navigational errors of several kilometers per day without relativistic adjustments.

For weak gravitational fields and velocities much less than the speed of light, the predictions of general relativity converge on those of Newton's law, explaining why Newton's theory remains an excellent approximation in most practical contexts.

Gravitational waves

General relativity predicts that accelerating masses radiate energy in the form of gravitational waves — ripples in the curvature of spacetime that propagate outward at the speed of light. Einstein himself doubted these waves could ever be detected directly, because even the most cataclysmic astrophysical events produce distortions in spacetime that are extraordinarily small by the time they reach Earth.

On September 14, 2015, the two detectors of the [Laser Interferometer Gravitational-Wave Observatory] (LIGO), located in Hanford, Washington, and Livingston, Louisiana, simultaneously recorded the signal now designated GW150914. The signal matched the waveform predicted by general relativity for the inspiral and merger of two black holes — one of approximately 36 solar masses and one of approximately 29 solar masses — at a distance of roughly 1.3 billion light-years. During the final fraction of a second of the merger, about 3 solar masses' worth of energy was radiated as gravitational waves, briefly releasing more power than all the stars in the observable universe combined.^[3:1] The detection confirmed a major prediction of general relativity in an extreme physical regime that had never previously been tested.^[3:2]

The discovery was announced on February 11, 2016. The Nobel Prize in Physics 2017 was awarded to Rainer Weiss, Barry C. Barish, and Kip S. Thorne for their decisive contributions to the LIGO detector and the observation of gravitational waves.^[4:1]

As of early 2026, LIGO and its partner detector [Virgo] have together catalogued hundreds of gravitational-wave events, including black hole mergers, neutron star mergers, and mixed neutron star–black hole systems. This has established [gravitational-wave astronomy] as a new observational discipline, providing information about compact objects that is inaccessible through electromagnetic radiation.

Quantum gravity

General relativity is a classical theory: it treats spacetime as a smooth, continuous, dynamical geometry. The other three fundamental forces are described by [quantum field theory] within the [Standard Model] of particle physics, a framework that has achieved extraordinary experimental precision. Combining these two descriptions into a single, consistent theory — [quantum gravity] — has remained an unsolved problem for nearly a century.

The core difficulty is structural. General relativity models gravity as the curvature of a dynamic spacetime, while quantum field theory is formulated on a fixed, non-dynamic spacetime background. When physicists attempt to apply the standard quantization procedures to gravity, the resulting theory is not [renormalizable]: calculations produce divergent (infinite) results that cannot be absorbed by a finite number of adjustable parameters, as they can in the quantum theories of the other forces.^[5:1] This is not merely a technical inconvenience; it signals that the framework breaks down at extreme scales.

Reconciling quantum theory and general relativity has proven deeply difficult, and no proposed approach has yet achieved complete theoretical consistency and experimental vindication.^[6:1] The two leading research programs are:

• [String theory], which proposes that the fundamental constituents of nature are one-dimensional extended objects (strings) rather than point particles. In string theory, the graviton — the hypothetical force-carrying particle for gravity — arises naturally as one of the vibrational modes of a string, and the theory is finite (free of the renormalization problem). However, string theory requires extra spatial dimensions and has so far made no prediction that has been tested experimentally.
• [Loop quantum gravity], which attempts to quantize spacetime geometry directly, without extra dimensions or new particles. It predicts that space itself has a discrete structure at the Planck scale (~10⁻³⁵ m), far smaller than anything currently measurable.

Both programs remain active areas of research. The energy scales at which quantum gravitational effects would become observable — the [Planck scale] — are roughly 15 orders of magnitude beyond the reach of current particle accelerators, making direct experimental tests extremely challenging. How this conflict between the two pillars of modern physics is ultimately resolved remains one of the most fundamental open questions in science.