General relativity

Einstein developed general relativity in the decade after formulating special relativity. His goal was to describe gravitation consistently with a relativistic account of space and time. On 25 November 1915, he presented the gravitational field equations that became the mathematical heart of the theory. The principle of equivalence—locally, the effects of gravity and acceleration can be difficult to distinguish—was one of the ideas that guided this development.

In Newtonian mechanics, gravity is modeled as a force between masses. General relativity instead describes the gravitational phenomena associated with matter and energy through the curvature of spacetime. Freely falling bodies follow paths determined by this geometry, rather than being pulled off an otherwise flat path by a conventional force. The familiar image of a heavy ball making a dent in a stretched sheet can help suggest curvature, but it is only an analogy: the theory concerns four-dimensional spacetime, not a two-dimensional surface bending into an external space.

The Einstein field equations describe how gravitational fields and spacetime geometry are related to physical sources. A separate equation of motion—the geodesic equation—describes how bodies move in a gravitational field. Together, these ideas yield predictions beyond the simplest Newtonian description. Among the well-known examples are the additional precession of Mercury's orbit and the deflection of light passing through a gravitational field. Observations of Mercury and starlight near the Sun became important tests of the theory.

General relativity also has practical consequences for systems that depend on precise clocks. GPS satellites experience both gravitational and motion-related time shifts relative to clocks on Earth. The net relativistic effect must be included when satellite timing is used to calculate a receiver's position; otherwise, navigation errors would accumulate rapidly. This everyday application depends on general relativity together with special relativity, rather than on general relativity alone.