The theory of relativity is a framework in physics developed principally by Albert Einstein, comprising special relativity, published in 1905, and general relativity, whose completed field equations were presented in November 1915. Special relativity describes space, time, and motion when gravitational effects can be neglected. General relativity describes gravitation through the geometry of spacetime. Together, they replace universal Newtonian space and time with a framework in which measurements depend on an observer’s motion and gravitational environment, while physical laws retain an observer-independent form. (einstein.caltech.edu)
Historical foundations
In classical mechanics, time is treated as universal, and velocities combine by ordinary addition. Nineteenth-century electromagnetism, particularly Maxwell’s equations, created difficulties for this framework: its description of electromagnetic waves did not fit the same transformations between moving observers. Einstein’s 1905 paper, “On the Electrodynamics of Moving Bodies,” resolved this incompatibility by reconsidering how clocks are synchronized and how observers define distance and simultaneity. (gutenberg.org)
Einstein subsequently sought a theory of gravity compatible with these ideas. On November 25, 1915, he presented the completed gravitational field equations. That month, he also showed that his theory accounted for the previously unexplained contribution to Mercury’s orbital precession, approximately 43 arcseconds per century. This was an important early test because the discrepancy had already been established astronomically. (einstein.caltech.edu)
Special relativity
Special relativity rests on two postulates: the laws of physics take the same form in every inertial reference frame, and the speed of light in vacuum, denoted (c), is the same for all inertial observers, regardless of the motion of the source. An inertial frame is one in which a body subject to no net force moves at constant velocity. These principles replace the assumption that different observers share one universal time. (sites.pitt.edu)
The Lorentz transformations relate the spatial and temporal coordinates assigned to an event by observers moving uniformly relative to one another. Their consequences include the relativity of simultaneity: two spatially separated events that are simultaneous in one frame need not be simultaneous in another. This is a difference in assigning times to events, not simply a delay in receiving light from them. (gutenberg.org)
Two further consequences are time dilation and length contraction. Relative to an inertial observer, a moving clock accumulates less time between its ticks than an identical stationary clock. A moving object is measured as shorter along its direction of motion than in its own rest frame. For relative speed (v), these effects involve the Lorentz factor:
[ \gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}. ]
A clock’s elapsed proper time (\Delta\tau) corresponds to coordinate time (\Delta t=\gamma\Delta\tau); a rod of rest length (L_0) has moving-frame length (L=L_0/\gamma), with its endpoints measured simultaneously in that frame. These effects are negligible at ordinary speeds but substantial near (c). (gutenberg.org)
Special relativity also establishes mass–energy equivalence. A body with invariant mass (m) possesses rest energy
[ E_0=mc^{2}. ]
The distinction between rest energy and total energy matters: a moving body also has kinetic energy. Processes that change a system’s internal energy can change its mass; energy associated with matter is therefore not a separate quantity unrelated to inertia. (gutenberg.org)
General relativity
The equivalence principle provided the starting point for general relativity. Within a sufficiently small region and over a sufficiently short interval, an observer in free fall can describe nongravitational experiments using special relativity. Conversely, acceleration can reproduce effects resembling gravity. This equivalence is local: variations in a gravitational field, including tidal effects, cannot generally be removed throughout an extended region. (einstein-online.info)
General relativity interprets gravity as spacetime curvature rather than a force acting within a fixed background. The metric tensor specifies spacetime geometry, including measured distances and elapsed times. Using differential geometry, the Einstein field equations relate this geometry to matter’s energy, momentum, pressure, and stresses. Freely falling bodies follow natural spacetime paths called geodesics. In appropriate weak-field, slow-motion conditions, the theory reproduces Newtonian gravity. (ocw.mit.edu)
Its consequences include gravitational time dilation, the deflection of light, and black holes. It also supplies the gravitational framework for cosmology, allowing spacetime itself to evolve rather than treating the universe as matter moving on an unchanging stage. Another prediction is gravitational waves: propagating disturbances in spacetime geometry. (einstein-online.info)
Experimental evidence and applications
Time dilation has been tested through the extended lifetimes of rapidly moving unstable particles. Precision atomic clocks also measure gravitational differences in elapsed time, including differences across millimeter-scale height separations. Such experiments test predictions about time using independently measurable physical processes. (einstein-online.info)
On September 14, 2015, LIGO directly detected gravitational waves from the merger of two black holes. The discovery was announced on February 11, 2016. The observed signal agreed with the predicted sequence of inspiral, merger, and the settling of the resulting black hole. (arxiv.org)
Relativity also has practical consequences for satellite navigation. Global Positioning System satellites carry atomic clocks whose rates differ from clocks on Earth because of both orbital motion and gravitational conditions. GPS timing incorporates relativistic corrections so that satellite signals can support accurate positioning. (nist.gov)
Relationship to quantum theory
Special relativity is incorporated into quantum field theory, which combines relativistic principles with quantum mechanics. General relativity, however, remains a classical description of gravity. Developing a consistent, experimentally established quantum theory of gravity is an unresolved problem, especially for conditions where both strong gravitational effects and quantum behavior are essential. (einstein-online.info)