Relativity

The Unity of Space, Time, and Gravity

Relativity is the pair of theories, both due to Albert Einstein, that replaced Newton’s absolute space and time. Special relativity (1905) unifies space and time into a single spacetime whose geometry is the same for every inertial observer, with the speed of light as an invariant; its consequences include time dilation, length contraction, and $E = mc^2$. General relativity (1915) extends this to gravity, which becomes the curvature of spacetime by mass and energy. Together they underlie GPS timing, black-hole and gravitational-wave astronomy, and modern cosmology.

This hub links the eight pages in this section and shows how they depend on each other.

Pages in This Section

Page Covers
Special Relativity The postulates, relativity of simultaneity, Lorentz transformations, time dilation, length contraction, velocity addition, $E = mc^2$, four-vectors
General Relativity The equivalence principle, metric and geodesics, curvature, the Einstein field equations, the Schwarzschild solution, classical and modern experimental tests
Graduate Topics Hub How the five deep-dive pages below fit together, with prerequisites and a reading order
Tensor Formalism Manifolds, tensors, the covariant derivative, Riemann and Ricci curvature, two derivations of the field equations
Black Holes Schwarzschild, Reissner–Nordström and Kerr geometries, horizons, Penrose diagrams, black-hole thermodynamics, the information paradox
Relativistic Cosmology The FLRW metric, Friedmann equations, distances and horizons, thermal history, $\Lambda$CDM parameters, the Hubble tension, inflation
Gravitational Waves Linearized gravity, polarizations, the quadrupole formula, compact binaries, interferometers, the observational record through LIGO–Virgo–KAGRA’s O4 run
Quantum Gravity Why GR and quantum theory conflict, non-renormalizability, string theory, loop quantum gravity, holography

Prerequisites. The conceptual content of special relativity needs only algebra; Lorentz transformations and four-vectors use basic linear algebra. General relativity at the level of its own page needs calculus and some comfort with index notation. The deep-dive pages assume the tensor formalism. Read Special Relativity first; everything else builds on it.

The Logical Structure

Each step in the chain below is forced by the one before. One experimental fact (the invariance of the speed of light) yields special relativity; one further principle (the equivalence of gravity and acceleration) yields general relativity.

graph TD
    MM["Speed of light c is the same<br/>for every inertial observer"] --> POST["Postulates of<br/>special relativity"]
    POST --> LT["Lorentz transformations"]
    LT --> TD["Time dilation"]
    LT --> LC["Length contraction"]
    LT --> RS["Relativity of simultaneity"]
    LT --> EMC["Mass-energy equivalence<br/>E = mc^2"]
    TD --> ST["Minkowski spacetime"]
    LC --> ST
    RS --> ST
    ST --> EP["Equivalence principle:<br/>gravity is locally<br/>indistinguishable from acceleration"]
    EMC --> EP
    EP --> CURV["Gravity as spacetime curvature"]
    CURV --> EFE["Einstein field equations"]
    EFE --> BH["Black holes"]
    EFE --> COS["Cosmology"]
    EFE --> GW["Gravitational waves"]
    EFE --> QG["Limits: singularities,<br/>quantum gravity"]

Core Ideas

  • The speed of light is invariant. Every inertial observer measures the same $c$; simultaneity, lengths, and durations become observer-dependent.
  • Spacetime, not space and time. The invariant interval $ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$ replaces separately invariant distances and durations. What a clock measures is the proper time along its worldline.
  • Energy and mass are equivalent. $E^2 = (pc)^2 + (mc^2)^2$, which reduces to $E = mc^2$ at rest.
  • Gravity is geometry. Mass and energy curve spacetime according to $G_{\mu\nu} + \Lambda g_{\mu\nu} = (8\pi G/c^4)\,T_{\mu\nu}$, and freely falling bodies follow geodesics of that curved spacetime.
  • Confirmed across scales. From laboratory clocks resolving the gravitational redshift over a millimetre, through GPS and Solar-System tests, to binary pulsars, black-hole images, and gravitational waves from merging black holes, no experiment has found a deviation from general relativity.
  • Not the final word. GR predicts singularities where it fails, conflicts with quantum mechanics, and in cosmology requires a dark sector whose nature is unknown.

See Also